").append( jQuery.parseHTML( responseText ) ).find( selector ) :
+
+ // Otherwise use the full result
+ responseText );
+
+ }).complete( callback && function( jqXHR, status ) {
+ self.each( callback, response || [ jqXHR.responseText, status, jqXHR ] );
+ });
+ }
+
+ return this;
+};
+
+
+
+
+jQuery.expr.filters.animated = function( elem ) {
+ return jQuery.grep(jQuery.timers, function( fn ) {
+ return elem === fn.elem;
+ }).length;
+};
+
+
+
+
+
+var docElem = window.document.documentElement;
+
+/**
+ * Gets a window from an element
+ */
+function getWindow( elem ) {
+ return jQuery.isWindow( elem ) ?
+ elem :
+ elem.nodeType === 9 ?
+ elem.defaultView || elem.parentWindow :
+ false;
+}
+
+jQuery.offset = {
+ setOffset: function( elem, options, i ) {
+ var curPosition, curLeft, curCSSTop, curTop, curOffset, curCSSLeft, calculatePosition,
+ position = jQuery.css( elem, "position" ),
+ curElem = jQuery( elem ),
+ props = {};
+
+ // set position first, in-case top/left are set even on static elem
+ if ( position === "static" ) {
+ elem.style.position = "relative";
+ }
+
+ curOffset = curElem.offset();
+ curCSSTop = jQuery.css( elem, "top" );
+ curCSSLeft = jQuery.css( elem, "left" );
+ calculatePosition = ( position === "absolute" || position === "fixed" ) &&
+ jQuery.inArray("auto", [ curCSSTop, curCSSLeft ] ) > -1;
+
+ // need to be able to calculate position if either top or left is auto and position is either absolute or fixed
+ if ( calculatePosition ) {
+ curPosition = curElem.position();
+ curTop = curPosition.top;
+ curLeft = curPosition.left;
+ } else {
+ curTop = parseFloat( curCSSTop ) || 0;
+ curLeft = parseFloat( curCSSLeft ) || 0;
+ }
+
+ if ( jQuery.isFunction( options ) ) {
+ options = options.call( elem, i, curOffset );
+ }
+
+ if ( options.top != null ) {
+ props.top = ( options.top - curOffset.top ) + curTop;
+ }
+ if ( options.left != null ) {
+ props.left = ( options.left - curOffset.left ) + curLeft;
+ }
+
+ if ( "using" in options ) {
+ options.using.call( elem, props );
+ } else {
+ curElem.css( props );
+ }
+ }
+};
+
+jQuery.fn.extend({
+ offset: function( options ) {
+ if ( arguments.length ) {
+ return options === undefined ?
+ this :
+ this.each(function( i ) {
+ jQuery.offset.setOffset( this, options, i );
+ });
+ }
+
+ var docElem, win,
+ box = { top: 0, left: 0 },
+ elem = this[ 0 ],
+ doc = elem && elem.ownerDocument;
+
+ if ( !doc ) {
+ return;
+ }
+
+ docElem = doc.documentElement;
+
+ // Make sure it's not a disconnected DOM node
+ if ( !jQuery.contains( docElem, elem ) ) {
+ return box;
+ }
+
+ // If we don't have gBCR, just use 0,0 rather than error
+ // BlackBerry 5, iOS 3 (original iPhone)
+ if ( typeof elem.getBoundingClientRect !== strundefined ) {
+ box = elem.getBoundingClientRect();
+ }
+ win = getWindow( doc );
+ return {
+ top: box.top + ( win.pageYOffset || docElem.scrollTop ) - ( docElem.clientTop || 0 ),
+ left: box.left + ( win.pageXOffset || docElem.scrollLeft ) - ( docElem.clientLeft || 0 )
+ };
+ },
+
+ position: function() {
+ if ( !this[ 0 ] ) {
+ return;
+ }
+
+ var offsetParent, offset,
+ parentOffset = { top: 0, left: 0 },
+ elem = this[ 0 ];
+
+ // fixed elements are offset from window (parentOffset = {top:0, left: 0}, because it is its only offset parent
+ if ( jQuery.css( elem, "position" ) === "fixed" ) {
+ // we assume that getBoundingClientRect is available when computed position is fixed
+ offset = elem.getBoundingClientRect();
+ } else {
+ // Get *real* offsetParent
+ offsetParent = this.offsetParent();
+
+ // Get correct offsets
+ offset = this.offset();
+ if ( !jQuery.nodeName( offsetParent[ 0 ], "html" ) ) {
+ parentOffset = offsetParent.offset();
+ }
+
+ // Add offsetParent borders
+ parentOffset.top += jQuery.css( offsetParent[ 0 ], "borderTopWidth", true );
+ parentOffset.left += jQuery.css( offsetParent[ 0 ], "borderLeftWidth", true );
+ }
+
+ // Subtract parent offsets and element margins
+ // note: when an element has margin: auto the offsetLeft and marginLeft
+ // are the same in Safari causing offset.left to incorrectly be 0
+ return {
+ top: offset.top - parentOffset.top - jQuery.css( elem, "marginTop", true ),
+ left: offset.left - parentOffset.left - jQuery.css( elem, "marginLeft", true)
+ };
+ },
+
+ offsetParent: function() {
+ return this.map(function() {
+ var offsetParent = this.offsetParent || docElem;
+
+ while ( offsetParent && ( !jQuery.nodeName( offsetParent, "html" ) && jQuery.css( offsetParent, "position" ) === "static" ) ) {
+ offsetParent = offsetParent.offsetParent;
+ }
+ return offsetParent || docElem;
+ });
+ }
+});
+
+// Create scrollLeft and scrollTop methods
+jQuery.each( { scrollLeft: "pageXOffset", scrollTop: "pageYOffset" }, function( method, prop ) {
+ var top = /Y/.test( prop );
+
+ jQuery.fn[ method ] = function( val ) {
+ return access( this, function( elem, method, val ) {
+ var win = getWindow( elem );
+
+ if ( val === undefined ) {
+ return win ? (prop in win) ? win[ prop ] :
+ win.document.documentElement[ method ] :
+ elem[ method ];
+ }
+
+ if ( win ) {
+ win.scrollTo(
+ !top ? val : jQuery( win ).scrollLeft(),
+ top ? val : jQuery( win ).scrollTop()
+ );
+
+ } else {
+ elem[ method ] = val;
+ }
+ }, method, val, arguments.length, null );
+ };
+});
+
+// Add the top/left cssHooks using jQuery.fn.position
+// Webkit bug: https://bugs.webkit.org/show_bug.cgi?id=29084
+// getComputedStyle returns percent when specified for top/left/bottom/right
+// rather than make the css module depend on the offset module, we just check for it here
+jQuery.each( [ "top", "left" ], function( i, prop ) {
+ jQuery.cssHooks[ prop ] = addGetHookIf( support.pixelPosition,
+ function( elem, computed ) {
+ if ( computed ) {
+ computed = curCSS( elem, prop );
+ // if curCSS returns percentage, fallback to offset
+ return rnumnonpx.test( computed ) ?
+ jQuery( elem ).position()[ prop ] + "px" :
+ computed;
+ }
+ }
+ );
+});
+
+
+// Create innerHeight, innerWidth, height, width, outerHeight and outerWidth methods
+jQuery.each( { Height: "height", Width: "width" }, function( name, type ) {
+ jQuery.each( { padding: "inner" + name, content: type, "": "outer" + name }, function( defaultExtra, funcName ) {
+ // margin is only for outerHeight, outerWidth
+ jQuery.fn[ funcName ] = function( margin, value ) {
+ var chainable = arguments.length && ( defaultExtra || typeof margin !== "boolean" ),
+ extra = defaultExtra || ( margin === true || value === true ? "margin" : "border" );
+
+ return access( this, function( elem, type, value ) {
+ var doc;
+
+ if ( jQuery.isWindow( elem ) ) {
+ // As of 5/8/2012 this will yield incorrect results for Mobile Safari, but there
+ // isn't a whole lot we can do. See pull request at this URL for discussion:
+ // https://github.com/jquery/jquery/pull/764
+ return elem.document.documentElement[ "client" + name ];
+ }
+
+ // Get document width or height
+ if ( elem.nodeType === 9 ) {
+ doc = elem.documentElement;
+
+ // Either scroll[Width/Height] or offset[Width/Height] or client[Width/Height], whichever is greatest
+ // unfortunately, this causes bug #3838 in IE6/8 only, but there is currently no good, small way to fix it.
+ return Math.max(
+ elem.body[ "scroll" + name ], doc[ "scroll" + name ],
+ elem.body[ "offset" + name ], doc[ "offset" + name ],
+ doc[ "client" + name ]
+ );
+ }
+
+ return value === undefined ?
+ // Get width or height on the element, requesting but not forcing parseFloat
+ jQuery.css( elem, type, extra ) :
+
+ // Set width or height on the element
+ jQuery.style( elem, type, value, extra );
+ }, type, chainable ? margin : undefined, chainable, null );
+ };
+ });
+});
+
+
+// The number of elements contained in the matched element set
+jQuery.fn.size = function() {
+ return this.length;
+};
+
+jQuery.fn.andSelf = jQuery.fn.addBack;
+
+
+
+
+// Register as a named AMD module, since jQuery can be concatenated with other
+// files that may use define, but not via a proper concatenation script that
+// understands anonymous AMD modules. A named AMD is safest and most robust
+// way to register. Lowercase jquery is used because AMD module names are
+// derived from file names, and jQuery is normally delivered in a lowercase
+// file name. Do this after creating the global so that if an AMD module wants
+// to call noConflict to hide this version of jQuery, it will work.
+
+// Note that for maximum portability, libraries that are not jQuery should
+// declare themselves as anonymous modules, and avoid setting a global if an
+// AMD loader is present. jQuery is a special case. For more information, see
+// https://github.com/jrburke/requirejs/wiki/Updating-existing-libraries#wiki-anon
+
+if ( typeof define === "function" && define.amd ) {
+ define( "jquery", [], function() {
+ return jQuery;
+ });
+}
+
+
+
+
+var
+ // Map over jQuery in case of overwrite
+ _jQuery = window.jQuery,
+
+ // Map over the $ in case of overwrite
+ _$ = window.$;
+
+jQuery.noConflict = function( deep ) {
+ if ( window.$ === jQuery ) {
+ window.$ = _$;
+ }
+
+ if ( deep && window.jQuery === jQuery ) {
+ window.jQuery = _jQuery;
+ }
+
+ return jQuery;
+};
+
+// Expose jQuery and $ identifiers, even in
+// AMD (#7102#comment:10, https://github.com/jquery/jquery/pull/557)
+// and CommonJS for browser emulators (#13566)
+if ( typeof noGlobal === strundefined ) {
+ window.jQuery = window.$ = jQuery;
+}
+
+
+
+
+return jQuery;
+
+}));
diff --git a/_static/jquery.js b/_static/jquery.js
new file mode 100644
index 0000000..ab28a24
--- /dev/null
+++ b/_static/jquery.js
@@ -0,0 +1,4 @@
+/*! jQuery v1.11.1 | (c) 2005, 2014 jQuery Foundation, Inc. | jquery.org/license */
+!function(a,b){"object"==typeof module&&"object"==typeof module.exports?module.exports=a.document?b(a,!0):function(a){if(!a.document)throw new Error("jQuery requires a window with a document");return b(a)}:b(a)}("undefined"!=typeof window?window:this,function(a,b){var c=[],d=c.slice,e=c.concat,f=c.push,g=c.indexOf,h={},i=h.toString,j=h.hasOwnProperty,k={},l="1.11.1",m=function(a,b){return new m.fn.init(a,b)},n=/^[\s\uFEFF\xA0]+|[\s\uFEFF\xA0]+$/g,o=/^-ms-/,p=/-([\da-z])/gi,q=function(a,b){return b.toUpperCase()};m.fn=m.prototype={jquery:l,constructor:m,selector:"",length:0,toArray:function(){return d.call(this)},get:function(a){return null!=a?0>a?this[a+this.length]:this[a]:d.call(this)},pushStack:function(a){var b=m.merge(this.constructor(),a);return b.prevObject=this,b.context=this.context,b},each:function(a,b){return m.each(this,a,b)},map:function(a){return this.pushStack(m.map(this,function(b,c){return a.call(b,c,b)}))},slice:function(){return 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+ this.dots = $('
').appendTo(this.out);
+ this.output = $('').appendTo(this.out);
+
+ $('#search-progress').text(_('Preparing search...'));
+ this.startPulse();
+
+ // index already loaded, the browser was quick!
+ if (this.hasIndex())
+ this.query(query);
+ else
+ this.deferQuery(query);
+ },
+
+ /**
+ * execute search (requires search index to be loaded)
+ */
+ query : function(query) {
+ var i;
+ var stopwords = ["a","and","are","as","at","be","but","by","for","if","in","into","is","it","near","no","not","of","on","or","such","that","the","their","then","there","these","they","this","to","was","will","with"];
+
+ // stem the searchterms and add them to the correct list
+ var stemmer = new Stemmer();
+ var searchterms = [];
+ var excluded = [];
+ var hlterms = [];
+ var tmp = query.split(/\s+/);
+ var objectterms = [];
+ for (i = 0; i < tmp.length; i++) {
+ if (tmp[i] !== "") {
+ objectterms.push(tmp[i].toLowerCase());
+ }
+
+ if ($u.indexOf(stopwords, tmp[i].toLowerCase()) != -1 || tmp[i].match(/^\d+$/) ||
+ tmp[i] === "") {
+ // skip this "word"
+ continue;
+ }
+ // stem the word
+ var word = stemmer.stemWord(tmp[i].toLowerCase());
+ var toAppend;
+ // select the correct list
+ if (word[0] == '-') {
+ toAppend = excluded;
+ word = word.substr(1);
+ }
+ else {
+ toAppend = searchterms;
+ hlterms.push(tmp[i].toLowerCase());
+ }
+ // only add if not already in the list
+ if (!$u.contains(toAppend, word))
+ toAppend.push(word);
+ }
+ var highlightstring = '?highlight=' + $.urlencode(hlterms.join(" "));
+
+ // console.debug('SEARCH: searching for:');
+ // console.info('required: ', searchterms);
+ // console.info('excluded: ', excluded);
+
+ // prepare search
+ var terms = this._index.terms;
+ var titleterms = this._index.titleterms;
+
+ // array of [filename, title, anchor, descr, score]
+ var results = [];
+ $('#search-progress').empty();
+
+ // lookup as object
+ for (i = 0; i < objectterms.length; i++) {
+ var others = [].concat(objectterms.slice(0, i),
+ objectterms.slice(i+1, objectterms.length));
+ results = results.concat(this.performObjectSearch(objectterms[i], others));
+ }
+
+ // lookup as search terms in fulltext
+ results = results.concat(this.performTermsSearch(searchterms, excluded, terms, titleterms));
+
+ // let the scorer override scores with a custom scoring function
+ if (Scorer.score) {
+ for (i = 0; i < results.length; i++)
+ results[i][4] = Scorer.score(results[i]);
+ }
+
+ // now sort the results by score (in opposite order of appearance, since the
+ // display function below uses pop() to retrieve items) and then
+ // alphabetically
+ results.sort(function(a, b) {
+ var left = a[4];
+ var right = b[4];
+ if (left > right) {
+ return 1;
+ } else if (left < right) {
+ return -1;
+ } else {
+ // same score: sort alphabetically
+ left = a[1].toLowerCase();
+ right = b[1].toLowerCase();
+ return (left > right) ? -1 : ((left < right) ? 1 : 0);
+ }
+ });
+
+ // for debugging
+ //Search.lastresults = results.slice(); // a copy
+ //console.info('search results:', Search.lastresults);
+
+ // print the results
+ var resultCount = results.length;
+ function displayNextItem() {
+ // results left, load the summary and display it
+ if (results.length) {
+ var item = results.pop();
+ var listItem = $(' (' + item[3] + ') '));
+ Search.output.append(listItem);
+ listItem.slideDown(5, function() {
+ displayNextItem();
+ });
+ } else if (DOCUMENTATION_OPTIONS.HAS_SOURCE) {
+ $.ajax({url: DOCUMENTATION_OPTIONS.URL_ROOT + '_sources/' + item[0] + '.txt',
+ dataType: "text",
+ complete: function(jqxhr, textstatus) {
+ var data = jqxhr.responseText;
+ if (data !== '' && data !== undefined) {
+ listItem.append(Search.makeSearchSummary(data, searchterms, hlterms));
+ }
+ Search.output.append(listItem);
+ listItem.slideDown(5, function() {
+ displayNextItem();
+ });
+ }});
+ } else {
+ // no source available, just display title
+ Search.output.append(listItem);
+ listItem.slideDown(5, function() {
+ displayNextItem();
+ });
+ }
+ }
+ // search finished, update title and status message
+ else {
+ Search.stopPulse();
+ Search.title.text(_('Search Results'));
+ if (!resultCount)
+ Search.status.text(_('Your search did not match any documents. Please make sure that all words are spelled correctly and that you\'ve selected enough categories.'));
+ else
+ Search.status.text(_('Search finished, found %s page(s) matching the search query.').replace('%s', resultCount));
+ Search.status.fadeIn(500);
+ }
+ }
+ displayNextItem();
+ },
+
+ /**
+ * search for object names
+ */
+ performObjectSearch : function(object, otherterms) {
+ var filenames = this._index.filenames;
+ var objects = this._index.objects;
+ var objnames = this._index.objnames;
+ var titles = this._index.titles;
+
+ var i;
+ var results = [];
+
+ for (var prefix in objects) {
+ for (var name in objects[prefix]) {
+ var fullname = (prefix ? prefix + '.' : '') + name;
+ if (fullname.toLowerCase().indexOf(object) > -1) {
+ var score = 0;
+ var parts = fullname.split('.');
+ // check for different match types: exact matches of full name or
+ // "last name" (i.e. last dotted part)
+ if (fullname == object || parts[parts.length - 1] == object) {
+ score += Scorer.objNameMatch;
+ // matches in last name
+ } else if (parts[parts.length - 1].indexOf(object) > -1) {
+ score += Scorer.objPartialMatch;
+ }
+ var match = objects[prefix][name];
+ var objname = objnames[match[1]][2];
+ var title = titles[match[0]];
+ // If more than one term searched for, we require other words to be
+ // found in the name/title/description
+ if (otherterms.length > 0) {
+ var haystack = (prefix + ' ' + name + ' ' +
+ objname + ' ' + title).toLowerCase();
+ var allfound = true;
+ for (i = 0; i < otherterms.length; i++) {
+ if (haystack.indexOf(otherterms[i]) == -1) {
+ allfound = false;
+ break;
+ }
+ }
+ if (!allfound) {
+ continue;
+ }
+ }
+ var descr = objname + _(', in ') + title;
+
+ var anchor = match[3];
+ if (anchor === '')
+ anchor = fullname;
+ else if (anchor == '-')
+ anchor = objnames[match[1]][1] + '-' + fullname;
+ // add custom score for some objects according to scorer
+ if (Scorer.objPrio.hasOwnProperty(match[2])) {
+ score += Scorer.objPrio[match[2]];
+ } else {
+ score += Scorer.objPrioDefault;
+ }
+ results.push([filenames[match[0]], fullname, '#'+anchor, descr, score]);
+ }
+ }
+ }
+
+ return results;
+ },
+
+ /**
+ * search for full-text terms in the index
+ */
+ performTermsSearch : function(searchterms, excluded, terms, titleterms) {
+ var filenames = this._index.filenames;
+ var titles = this._index.titles;
+
+ var i, j, file;
+ var fileMap = {};
+ var scoreMap = {};
+ var results = [];
+
+ // perform the search on the required terms
+ for (i = 0; i < searchterms.length; i++) {
+ var word = searchterms[i];
+ var files = [];
+ var _o = [
+ {files: terms[word], score: Scorer.term},
+ {files: titleterms[word], score: Scorer.title}
+ ];
+
+ // no match but word was a required one
+ if ($u.every(_o, function(o){return o.files === undefined;})) {
+ break;
+ }
+ // found search word in contents
+ $u.each(_o, function(o) {
+ var _files = o.files;
+ if (_files === undefined)
+ return
+
+ if (_files.length === undefined)
+ _files = [_files];
+ files = files.concat(_files);
+
+ // set score for the word in each file to Scorer.term
+ for (j = 0; j < _files.length; j++) {
+ file = _files[j];
+ if (!(file in scoreMap))
+ scoreMap[file] = {}
+ scoreMap[file][word] = o.score;
+ }
+ });
+
+ // create the mapping
+ for (j = 0; j < files.length; j++) {
+ file = files[j];
+ if (file in fileMap)
+ fileMap[file].push(word);
+ else
+ fileMap[file] = [word];
+ }
+ }
+
+ // now check if the files don't contain excluded terms
+ for (file in fileMap) {
+ var valid = true;
+
+ // check if all requirements are matched
+ if (fileMap[file].length != searchterms.length)
+ continue;
+
+ // ensure that none of the excluded terms is in the search result
+ for (i = 0; i < excluded.length; i++) {
+ if (terms[excluded[i]] == file ||
+ titleterms[excluded[i]] == file ||
+ $u.contains(terms[excluded[i]] || [], file) ||
+ $u.contains(titleterms[excluded[i]] || [], file)) {
+ valid = false;
+ break;
+ }
+ }
+
+ // if we have still a valid result we can add it to the result list
+ if (valid) {
+ // select one (max) score for the file.
+ // for better ranking, we should calculate ranking by using words statistics like basic tf-idf...
+ var score = $u.max($u.map(fileMap[file], function(w){return scoreMap[file][w]}));
+ results.push([filenames[file], titles[file], '', null, score]);
+ }
+ }
+ return results;
+ },
+
+ /**
+ * helper function to return a node containing the
+ * search summary for a given text. keywords is a list
+ * of stemmed words, hlwords is the list of normal, unstemmed
+ * words. the first one is used to find the occurrence, the
+ * latter for highlighting it.
+ */
+ makeSearchSummary : function(text, keywords, hlwords) {
+ var textLower = text.toLowerCase();
+ var start = 0;
+ $.each(keywords, function() {
+ var i = textLower.indexOf(this.toLowerCase());
+ if (i > -1)
+ start = i;
+ });
+ start = Math.max(start - 120, 0);
+ var excerpt = ((start > 0) ? '...' : '') +
+ $.trim(text.substr(start, 240)) +
+ ((start + 240 - text.length) ? '...' : '');
+ var rv = $('
').text(excerpt);
+ $.each(hlwords, function() {
+ rv = rv.highlightText(this, 'highlighted');
+ });
+ return rv;
+ }
+};
+
+$(document).ready(function() {
+ Search.init();
+});
\ No newline at end of file
diff --git a/_static/underscore-1.3.1.js b/_static/underscore-1.3.1.js
new file mode 100644
index 0000000..208d4cd
--- /dev/null
+++ b/_static/underscore-1.3.1.js
@@ -0,0 +1,999 @@
+// Underscore.js 1.3.1
+// (c) 2009-2012 Jeremy Ashkenas, DocumentCloud Inc.
+// Underscore is freely distributable under the MIT license.
+// Portions of Underscore are inspired or borrowed from Prototype,
+// Oliver Steele's Functional, and John Resig's Micro-Templating.
+// For all details and documentation:
+// http://documentcloud.github.com/underscore
+
+(function() {
+
+ // Baseline setup
+ // --------------
+
+ // Establish the root object, `window` in the browser, or `global` on the server.
+ var root = this;
+
+ // Save the previous value of the `_` variable.
+ var previousUnderscore = root._;
+
+ // Establish the object that gets returned to break out of a loop iteration.
+ var breaker = {};
+
+ // Save bytes in the minified (but not gzipped) version:
+ var ArrayProto = Array.prototype, ObjProto = Object.prototype, FuncProto = Function.prototype;
+
+ // Create quick reference variables for speed access to core prototypes.
+ var slice = ArrayProto.slice,
+ unshift = ArrayProto.unshift,
+ toString = ObjProto.toString,
+ hasOwnProperty = ObjProto.hasOwnProperty;
+
+ // All **ECMAScript 5** native function implementations that we hope to use
+ // are declared here.
+ var
+ nativeForEach = ArrayProto.forEach,
+ nativeMap = ArrayProto.map,
+ nativeReduce = ArrayProto.reduce,
+ nativeReduceRight = ArrayProto.reduceRight,
+ nativeFilter = ArrayProto.filter,
+ nativeEvery = ArrayProto.every,
+ nativeSome = ArrayProto.some,
+ nativeIndexOf = ArrayProto.indexOf,
+ nativeLastIndexOf = ArrayProto.lastIndexOf,
+ nativeIsArray = Array.isArray,
+ nativeKeys = Object.keys,
+ nativeBind = FuncProto.bind;
+
+ // Create a safe reference to the Underscore object for use below.
+ var _ = function(obj) { return new wrapper(obj); };
+
+ // Export the Underscore object for **Node.js**, with
+ // backwards-compatibility for the old `require()` API. If we're in
+ // the browser, add `_` as a global object via a string identifier,
+ // for Closure Compiler "advanced" mode.
+ if (typeof exports !== 'undefined') {
+ if (typeof module !== 'undefined' && module.exports) {
+ exports = module.exports = _;
+ }
+ exports._ = _;
+ } else {
+ root['_'] = _;
+ }
+
+ // Current version.
+ _.VERSION = '1.3.1';
+
+ // Collection Functions
+ // --------------------
+
+ // The cornerstone, an `each` implementation, aka `forEach`.
+ // Handles objects with the built-in `forEach`, arrays, and raw objects.
+ // Delegates to **ECMAScript 5**'s native `forEach` if available.
+ var each = _.each = _.forEach = function(obj, iterator, context) {
+ if (obj == null) return;
+ if (nativeForEach && obj.forEach === nativeForEach) {
+ obj.forEach(iterator, context);
+ } else if (obj.length === +obj.length) {
+ for (var i = 0, l = obj.length; i < l; i++) {
+ if (i in obj && iterator.call(context, obj[i], i, obj) === breaker) return;
+ }
+ } else {
+ for (var key in obj) {
+ if (_.has(obj, key)) {
+ if (iterator.call(context, obj[key], key, obj) === breaker) return;
+ }
+ }
+ }
+ };
+
+ // Return the results of applying the iterator to each element.
+ // Delegates to **ECMAScript 5**'s native `map` if available.
+ _.map = _.collect = function(obj, iterator, context) {
+ var results = [];
+ if (obj == null) return results;
+ if (nativeMap && obj.map === nativeMap) return obj.map(iterator, context);
+ each(obj, function(value, index, list) {
+ results[results.length] = iterator.call(context, value, index, list);
+ });
+ if (obj.length === +obj.length) results.length = obj.length;
+ return results;
+ };
+
+ // **Reduce** builds up a single result from a list of values, aka `inject`,
+ // or `foldl`. Delegates to **ECMAScript 5**'s native `reduce` if available.
+ _.reduce = _.foldl = _.inject = function(obj, iterator, memo, context) {
+ var initial = arguments.length > 2;
+ if (obj == null) obj = [];
+ if (nativeReduce && obj.reduce === nativeReduce) {
+ if (context) iterator = _.bind(iterator, context);
+ return initial ? obj.reduce(iterator, memo) : obj.reduce(iterator);
+ }
+ each(obj, function(value, index, list) {
+ if (!initial) {
+ memo = value;
+ initial = true;
+ } else {
+ memo = iterator.call(context, memo, value, index, list);
+ }
+ });
+ if (!initial) throw new TypeError('Reduce of empty array with no initial value');
+ return memo;
+ };
+
+ // The right-associative version of reduce, also known as `foldr`.
+ // Delegates to **ECMAScript 5**'s native `reduceRight` if available.
+ _.reduceRight = _.foldr = function(obj, iterator, memo, context) {
+ var initial = arguments.length > 2;
+ if (obj == null) obj = [];
+ if (nativeReduceRight && obj.reduceRight === nativeReduceRight) {
+ if (context) iterator = _.bind(iterator, context);
+ return initial ? obj.reduceRight(iterator, memo) : obj.reduceRight(iterator);
+ }
+ var reversed = _.toArray(obj).reverse();
+ if (context && !initial) iterator = _.bind(iterator, context);
+ return initial ? _.reduce(reversed, iterator, memo, context) : _.reduce(reversed, iterator);
+ };
+
+ // Return the first value which passes a truth test. Aliased as `detect`.
+ _.find = _.detect = function(obj, iterator, context) {
+ var result;
+ any(obj, function(value, index, list) {
+ if (iterator.call(context, value, index, list)) {
+ result = value;
+ return true;
+ }
+ });
+ return result;
+ };
+
+ // Return all the elements that pass a truth test.
+ // Delegates to **ECMAScript 5**'s native `filter` if available.
+ // Aliased as `select`.
+ _.filter = _.select = function(obj, iterator, context) {
+ var results = [];
+ if (obj == null) return results;
+ if (nativeFilter && obj.filter === nativeFilter) return obj.filter(iterator, context);
+ each(obj, function(value, index, list) {
+ if (iterator.call(context, value, index, list)) results[results.length] = value;
+ });
+ return results;
+ };
+
+ // Return all the elements for which a truth test fails.
+ _.reject = function(obj, iterator, context) {
+ var results = [];
+ if (obj == null) return results;
+ each(obj, function(value, index, list) {
+ if (!iterator.call(context, value, index, list)) results[results.length] = value;
+ });
+ return results;
+ };
+
+ // Determine whether all of the elements match a truth test.
+ // Delegates to **ECMAScript 5**'s native `every` if available.
+ // Aliased as `all`.
+ _.every = _.all = function(obj, iterator, context) {
+ var result = true;
+ if (obj == null) return result;
+ if (nativeEvery && obj.every === nativeEvery) return obj.every(iterator, context);
+ each(obj, function(value, index, list) {
+ if (!(result = result && iterator.call(context, value, index, list))) return breaker;
+ });
+ return result;
+ };
+
+ // Determine if at least one element in the object matches a truth test.
+ // Delegates to **ECMAScript 5**'s native `some` if available.
+ // Aliased as `any`.
+ var any = _.some = _.any = function(obj, iterator, context) {
+ iterator || (iterator = _.identity);
+ var result = false;
+ if (obj == null) return result;
+ if (nativeSome && obj.some === nativeSome) return obj.some(iterator, context);
+ each(obj, function(value, index, list) {
+ if (result || (result = iterator.call(context, value, index, list))) return breaker;
+ });
+ return !!result;
+ };
+
+ // Determine if a given value is included in the array or object using `===`.
+ // Aliased as `contains`.
+ _.include = _.contains = function(obj, target) {
+ var found = false;
+ if (obj == null) return found;
+ if (nativeIndexOf && obj.indexOf === nativeIndexOf) return obj.indexOf(target) != -1;
+ found = any(obj, function(value) {
+ return value === target;
+ });
+ return found;
+ };
+
+ // Invoke a method (with arguments) on every item in a collection.
+ _.invoke = function(obj, method) {
+ var args = slice.call(arguments, 2);
+ return _.map(obj, function(value) {
+ return (_.isFunction(method) ? method || value : value[method]).apply(value, args);
+ });
+ };
+
+ // Convenience version of a common use case of `map`: fetching a property.
+ _.pluck = function(obj, key) {
+ return _.map(obj, function(value){ return value[key]; });
+ };
+
+ // Return the maximum element or (element-based computation).
+ _.max = function(obj, iterator, context) {
+ if (!iterator && _.isArray(obj)) return Math.max.apply(Math, obj);
+ if (!iterator && _.isEmpty(obj)) return -Infinity;
+ var result = {computed : -Infinity};
+ each(obj, function(value, index, list) {
+ var computed = iterator ? iterator.call(context, value, index, list) : value;
+ computed >= result.computed && (result = {value : value, computed : computed});
+ });
+ return result.value;
+ };
+
+ // Return the minimum element (or element-based computation).
+ _.min = function(obj, iterator, context) {
+ if (!iterator && _.isArray(obj)) return Math.min.apply(Math, obj);
+ if (!iterator && _.isEmpty(obj)) return Infinity;
+ var result = {computed : Infinity};
+ each(obj, function(value, index, list) {
+ var computed = iterator ? iterator.call(context, value, index, list) : value;
+ computed < result.computed && (result = {value : value, computed : computed});
+ });
+ return result.value;
+ };
+
+ // Shuffle an array.
+ _.shuffle = function(obj) {
+ var shuffled = [], rand;
+ each(obj, function(value, index, list) {
+ if (index == 0) {
+ shuffled[0] = value;
+ } else {
+ rand = Math.floor(Math.random() * (index + 1));
+ shuffled[index] = shuffled[rand];
+ shuffled[rand] = value;
+ }
+ });
+ return shuffled;
+ };
+
+ // Sort the object's values by a criterion produced by an iterator.
+ _.sortBy = function(obj, iterator, context) {
+ return _.pluck(_.map(obj, function(value, index, list) {
+ return {
+ value : value,
+ criteria : iterator.call(context, value, index, list)
+ };
+ }).sort(function(left, right) {
+ var a = left.criteria, b = right.criteria;
+ return a < b ? -1 : a > b ? 1 : 0;
+ }), 'value');
+ };
+
+ // Groups the object's values by a criterion. Pass either a string attribute
+ // to group by, or a function that returns the criterion.
+ _.groupBy = function(obj, val) {
+ var result = {};
+ var iterator = _.isFunction(val) ? val : function(obj) { return obj[val]; };
+ each(obj, function(value, index) {
+ var key = iterator(value, index);
+ (result[key] || (result[key] = [])).push(value);
+ });
+ return result;
+ };
+
+ // Use a comparator function to figure out at what index an object should
+ // be inserted so as to maintain order. Uses binary search.
+ _.sortedIndex = function(array, obj, iterator) {
+ iterator || (iterator = _.identity);
+ var low = 0, high = array.length;
+ while (low < high) {
+ var mid = (low + high) >> 1;
+ iterator(array[mid]) < iterator(obj) ? low = mid + 1 : high = mid;
+ }
+ return low;
+ };
+
+ // Safely convert anything iterable into a real, live array.
+ _.toArray = function(iterable) {
+ if (!iterable) return [];
+ if (iterable.toArray) return iterable.toArray();
+ if (_.isArray(iterable)) return slice.call(iterable);
+ if (_.isArguments(iterable)) return slice.call(iterable);
+ return _.values(iterable);
+ };
+
+ // Return the number of elements in an object.
+ _.size = function(obj) {
+ return _.toArray(obj).length;
+ };
+
+ // Array Functions
+ // ---------------
+
+ // Get the first element of an array. Passing **n** will return the first N
+ // values in the array. Aliased as `head`. The **guard** check allows it to work
+ // with `_.map`.
+ _.first = _.head = function(array, n, guard) {
+ return (n != null) && !guard ? slice.call(array, 0, n) : array[0];
+ };
+
+ // Returns everything but the last entry of the array. Especcialy useful on
+ // the arguments object. Passing **n** will return all the values in
+ // the array, excluding the last N. The **guard** check allows it to work with
+ // `_.map`.
+ _.initial = function(array, n, guard) {
+ return slice.call(array, 0, array.length - ((n == null) || guard ? 1 : n));
+ };
+
+ // Get the last element of an array. Passing **n** will return the last N
+ // values in the array. The **guard** check allows it to work with `_.map`.
+ _.last = function(array, n, guard) {
+ if ((n != null) && !guard) {
+ return slice.call(array, Math.max(array.length - n, 0));
+ } else {
+ return array[array.length - 1];
+ }
+ };
+
+ // Returns everything but the first entry of the array. Aliased as `tail`.
+ // Especially useful on the arguments object. Passing an **index** will return
+ // the rest of the values in the array from that index onward. The **guard**
+ // check allows it to work with `_.map`.
+ _.rest = _.tail = function(array, index, guard) {
+ return slice.call(array, (index == null) || guard ? 1 : index);
+ };
+
+ // Trim out all falsy values from an array.
+ _.compact = function(array) {
+ return _.filter(array, function(value){ return !!value; });
+ };
+
+ // Return a completely flattened version of an array.
+ _.flatten = function(array, shallow) {
+ return _.reduce(array, function(memo, value) {
+ if (_.isArray(value)) return memo.concat(shallow ? value : _.flatten(value));
+ memo[memo.length] = value;
+ return memo;
+ }, []);
+ };
+
+ // Return a version of the array that does not contain the specified value(s).
+ _.without = function(array) {
+ return _.difference(array, slice.call(arguments, 1));
+ };
+
+ // Produce a duplicate-free version of the array. If the array has already
+ // been sorted, you have the option of using a faster algorithm.
+ // Aliased as `unique`.
+ _.uniq = _.unique = function(array, isSorted, iterator) {
+ var initial = iterator ? _.map(array, iterator) : array;
+ var result = [];
+ _.reduce(initial, function(memo, el, i) {
+ if (0 == i || (isSorted === true ? _.last(memo) != el : !_.include(memo, el))) {
+ memo[memo.length] = el;
+ result[result.length] = array[i];
+ }
+ return memo;
+ }, []);
+ return result;
+ };
+
+ // Produce an array that contains the union: each distinct element from all of
+ // the passed-in arrays.
+ _.union = function() {
+ return _.uniq(_.flatten(arguments, true));
+ };
+
+ // Produce an array that contains every item shared between all the
+ // passed-in arrays. (Aliased as "intersect" for back-compat.)
+ _.intersection = _.intersect = function(array) {
+ var rest = slice.call(arguments, 1);
+ return _.filter(_.uniq(array), function(item) {
+ return _.every(rest, function(other) {
+ return _.indexOf(other, item) >= 0;
+ });
+ });
+ };
+
+ // Take the difference between one array and a number of other arrays.
+ // Only the elements present in just the first array will remain.
+ _.difference = function(array) {
+ var rest = _.flatten(slice.call(arguments, 1));
+ return _.filter(array, function(value){ return !_.include(rest, value); });
+ };
+
+ // Zip together multiple lists into a single array -- elements that share
+ // an index go together.
+ _.zip = function() {
+ var args = slice.call(arguments);
+ var length = _.max(_.pluck(args, 'length'));
+ var results = new Array(length);
+ for (var i = 0; i < length; i++) results[i] = _.pluck(args, "" + i);
+ return results;
+ };
+
+ // If the browser doesn't supply us with indexOf (I'm looking at you, **MSIE**),
+ // we need this function. Return the position of the first occurrence of an
+ // item in an array, or -1 if the item is not included in the array.
+ // Delegates to **ECMAScript 5**'s native `indexOf` if available.
+ // If the array is large and already in sort order, pass `true`
+ // for **isSorted** to use binary search.
+ _.indexOf = function(array, item, isSorted) {
+ if (array == null) return -1;
+ var i, l;
+ if (isSorted) {
+ i = _.sortedIndex(array, item);
+ return array[i] === item ? i : -1;
+ }
+ if (nativeIndexOf && array.indexOf === nativeIndexOf) return array.indexOf(item);
+ for (i = 0, l = array.length; i < l; i++) if (i in array && array[i] === item) return i;
+ return -1;
+ };
+
+ // Delegates to **ECMAScript 5**'s native `lastIndexOf` if available.
+ _.lastIndexOf = function(array, item) {
+ if (array == null) return -1;
+ if (nativeLastIndexOf && array.lastIndexOf === nativeLastIndexOf) return array.lastIndexOf(item);
+ var i = array.length;
+ while (i--) if (i in array && array[i] === item) return i;
+ return -1;
+ };
+
+ // Generate an integer Array containing an arithmetic progression. A port of
+ // the native Python `range()` function. See
+ // [the Python documentation](http://docs.python.org/library/functions.html#range).
+ _.range = function(start, stop, step) {
+ if (arguments.length <= 1) {
+ stop = start || 0;
+ start = 0;
+ }
+ step = arguments[2] || 1;
+
+ var len = Math.max(Math.ceil((stop - start) / step), 0);
+ var idx = 0;
+ var range = new Array(len);
+
+ while(idx < len) {
+ range[idx++] = start;
+ start += step;
+ }
+
+ return range;
+ };
+
+ // Function (ahem) Functions
+ // ------------------
+
+ // Reusable constructor function for prototype setting.
+ var ctor = function(){};
+
+ // Create a function bound to a given object (assigning `this`, and arguments,
+ // optionally). Binding with arguments is also known as `curry`.
+ // Delegates to **ECMAScript 5**'s native `Function.bind` if available.
+ // We check for `func.bind` first, to fail fast when `func` is undefined.
+ _.bind = function bind(func, context) {
+ var bound, args;
+ if (func.bind === nativeBind && nativeBind) return nativeBind.apply(func, slice.call(arguments, 1));
+ if (!_.isFunction(func)) throw new TypeError;
+ args = slice.call(arguments, 2);
+ return bound = function() {
+ if (!(this instanceof bound)) return func.apply(context, args.concat(slice.call(arguments)));
+ ctor.prototype = func.prototype;
+ var self = new ctor;
+ var result = func.apply(self, args.concat(slice.call(arguments)));
+ if (Object(result) === result) return result;
+ return self;
+ };
+ };
+
+ // Bind all of an object's methods to that object. Useful for ensuring that
+ // all callbacks defined on an object belong to it.
+ _.bindAll = function(obj) {
+ var funcs = slice.call(arguments, 1);
+ if (funcs.length == 0) funcs = _.functions(obj);
+ each(funcs, function(f) { obj[f] = _.bind(obj[f], obj); });
+ return obj;
+ };
+
+ // Memoize an expensive function by storing its results.
+ _.memoize = function(func, hasher) {
+ var memo = {};
+ hasher || (hasher = _.identity);
+ return function() {
+ var key = hasher.apply(this, arguments);
+ return _.has(memo, key) ? memo[key] : (memo[key] = func.apply(this, arguments));
+ };
+ };
+
+ // Delays a function for the given number of milliseconds, and then calls
+ // it with the arguments supplied.
+ _.delay = function(func, wait) {
+ var args = slice.call(arguments, 2);
+ return setTimeout(function(){ return func.apply(func, args); }, wait);
+ };
+
+ // Defers a function, scheduling it to run after the current call stack has
+ // cleared.
+ _.defer = function(func) {
+ return _.delay.apply(_, [func, 1].concat(slice.call(arguments, 1)));
+ };
+
+ // Returns a function, that, when invoked, will only be triggered at most once
+ // during a given window of time.
+ _.throttle = function(func, wait) {
+ var context, args, timeout, throttling, more;
+ var whenDone = _.debounce(function(){ more = throttling = false; }, wait);
+ return function() {
+ context = this; args = arguments;
+ var later = function() {
+ timeout = null;
+ if (more) func.apply(context, args);
+ whenDone();
+ };
+ if (!timeout) timeout = setTimeout(later, wait);
+ if (throttling) {
+ more = true;
+ } else {
+ func.apply(context, args);
+ }
+ whenDone();
+ throttling = true;
+ };
+ };
+
+ // Returns a function, that, as long as it continues to be invoked, will not
+ // be triggered. The function will be called after it stops being called for
+ // N milliseconds.
+ _.debounce = function(func, wait) {
+ var timeout;
+ return function() {
+ var context = this, args = arguments;
+ var later = function() {
+ timeout = null;
+ func.apply(context, args);
+ };
+ clearTimeout(timeout);
+ timeout = setTimeout(later, wait);
+ };
+ };
+
+ // Returns a function that will be executed at most one time, no matter how
+ // often you call it. Useful for lazy initialization.
+ _.once = function(func) {
+ var ran = false, memo;
+ return function() {
+ if (ran) return memo;
+ ran = true;
+ return memo = func.apply(this, arguments);
+ };
+ };
+
+ // Returns the first function passed as an argument to the second,
+ // allowing you to adjust arguments, run code before and after, and
+ // conditionally execute the original function.
+ _.wrap = function(func, wrapper) {
+ return function() {
+ var args = [func].concat(slice.call(arguments, 0));
+ return wrapper.apply(this, args);
+ };
+ };
+
+ // Returns a function that is the composition of a list of functions, each
+ // consuming the return value of the function that follows.
+ _.compose = function() {
+ var funcs = arguments;
+ return function() {
+ var args = arguments;
+ for (var i = funcs.length - 1; i >= 0; i--) {
+ args = [funcs[i].apply(this, args)];
+ }
+ return args[0];
+ };
+ };
+
+ // Returns a function that will only be executed after being called N times.
+ _.after = function(times, func) {
+ if (times <= 0) return func();
+ return function() {
+ if (--times < 1) { return func.apply(this, arguments); }
+ };
+ };
+
+ // Object Functions
+ // ----------------
+
+ // Retrieve the names of an object's properties.
+ // Delegates to **ECMAScript 5**'s native `Object.keys`
+ _.keys = nativeKeys || function(obj) {
+ if (obj !== Object(obj)) throw new TypeError('Invalid object');
+ var keys = [];
+ for (var key in obj) if (_.has(obj, key)) keys[keys.length] = key;
+ return keys;
+ };
+
+ // Retrieve the values of an object's properties.
+ _.values = function(obj) {
+ return _.map(obj, _.identity);
+ };
+
+ // Return a sorted list of the function names available on the object.
+ // Aliased as `methods`
+ _.functions = _.methods = function(obj) {
+ var names = [];
+ for (var key in obj) {
+ if (_.isFunction(obj[key])) names.push(key);
+ }
+ return names.sort();
+ };
+
+ // Extend a given object with all the properties in passed-in object(s).
+ _.extend = function(obj) {
+ each(slice.call(arguments, 1), function(source) {
+ for (var prop in source) {
+ obj[prop] = source[prop];
+ }
+ });
+ return obj;
+ };
+
+ // Fill in a given object with default properties.
+ _.defaults = function(obj) {
+ each(slice.call(arguments, 1), function(source) {
+ for (var prop in source) {
+ if (obj[prop] == null) obj[prop] = source[prop];
+ }
+ });
+ return obj;
+ };
+
+ // Create a (shallow-cloned) duplicate of an object.
+ _.clone = function(obj) {
+ if (!_.isObject(obj)) return obj;
+ return _.isArray(obj) ? obj.slice() : _.extend({}, obj);
+ };
+
+ // Invokes interceptor with the obj, and then returns obj.
+ // The primary purpose of this method is to "tap into" a method chain, in
+ // order to perform operations on intermediate results within the chain.
+ _.tap = function(obj, interceptor) {
+ interceptor(obj);
+ return obj;
+ };
+
+ // Internal recursive comparison function.
+ function eq(a, b, stack) {
+ // Identical objects are equal. `0 === -0`, but they aren't identical.
+ // See the Harmony `egal` proposal: http://wiki.ecmascript.org/doku.php?id=harmony:egal.
+ if (a === b) return a !== 0 || 1 / a == 1 / b;
+ // A strict comparison is necessary because `null == undefined`.
+ if (a == null || b == null) return a === b;
+ // Unwrap any wrapped objects.
+ if (a._chain) a = a._wrapped;
+ if (b._chain) b = b._wrapped;
+ // Invoke a custom `isEqual` method if one is provided.
+ if (a.isEqual && _.isFunction(a.isEqual)) return a.isEqual(b);
+ if (b.isEqual && _.isFunction(b.isEqual)) return b.isEqual(a);
+ // Compare `[[Class]]` names.
+ var className = toString.call(a);
+ if (className != toString.call(b)) return false;
+ switch (className) {
+ // Strings, numbers, dates, and booleans are compared by value.
+ case '[object String]':
+ // Primitives and their corresponding object wrappers are equivalent; thus, `"5"` is
+ // equivalent to `new String("5")`.
+ return a == String(b);
+ case '[object Number]':
+ // `NaN`s are equivalent, but non-reflexive. An `egal` comparison is performed for
+ // other numeric values.
+ return a != +a ? b != +b : (a == 0 ? 1 / a == 1 / b : a == +b);
+ case '[object Date]':
+ case '[object Boolean]':
+ // Coerce dates and booleans to numeric primitive values. Dates are compared by their
+ // millisecond representations. Note that invalid dates with millisecond representations
+ // of `NaN` are not equivalent.
+ return +a == +b;
+ // RegExps are compared by their source patterns and flags.
+ case '[object RegExp]':
+ return a.source == b.source &&
+ a.global == b.global &&
+ a.multiline == b.multiline &&
+ a.ignoreCase == b.ignoreCase;
+ }
+ if (typeof a != 'object' || typeof b != 'object') return false;
+ // Assume equality for cyclic structures. The algorithm for detecting cyclic
+ // structures is adapted from ES 5.1 section 15.12.3, abstract operation `JO`.
+ var length = stack.length;
+ while (length--) {
+ // Linear search. Performance is inversely proportional to the number of
+ // unique nested structures.
+ if (stack[length] == a) return true;
+ }
+ // Add the first object to the stack of traversed objects.
+ stack.push(a);
+ var size = 0, result = true;
+ // Recursively compare objects and arrays.
+ if (className == '[object Array]') {
+ // Compare array lengths to determine if a deep comparison is necessary.
+ size = a.length;
+ result = size == b.length;
+ if (result) {
+ // Deep compare the contents, ignoring non-numeric properties.
+ while (size--) {
+ // Ensure commutative equality for sparse arrays.
+ if (!(result = size in a == size in b && eq(a[size], b[size], stack))) break;
+ }
+ }
+ } else {
+ // Objects with different constructors are not equivalent.
+ if ('constructor' in a != 'constructor' in b || a.constructor != b.constructor) return false;
+ // Deep compare objects.
+ for (var key in a) {
+ if (_.has(a, key)) {
+ // Count the expected number of properties.
+ size++;
+ // Deep compare each member.
+ if (!(result = _.has(b, key) && eq(a[key], b[key], stack))) break;
+ }
+ }
+ // Ensure that both objects contain the same number of properties.
+ if (result) {
+ for (key in b) {
+ if (_.has(b, key) && !(size--)) break;
+ }
+ result = !size;
+ }
+ }
+ // Remove the first object from the stack of traversed objects.
+ stack.pop();
+ return result;
+ }
+
+ // Perform a deep comparison to check if two objects are equal.
+ _.isEqual = function(a, b) {
+ return eq(a, b, []);
+ };
+
+ // Is a given array, string, or object empty?
+ // An "empty" object has no enumerable own-properties.
+ _.isEmpty = function(obj) {
+ if (_.isArray(obj) || _.isString(obj)) return obj.length === 0;
+ for (var key in obj) if (_.has(obj, key)) return false;
+ return true;
+ };
+
+ // Is a given value a DOM element?
+ _.isElement = function(obj) {
+ return !!(obj && obj.nodeType == 1);
+ };
+
+ // Is a given value an array?
+ // Delegates to ECMA5's native Array.isArray
+ _.isArray = nativeIsArray || function(obj) {
+ return toString.call(obj) == '[object Array]';
+ };
+
+ // Is a given variable an object?
+ _.isObject = function(obj) {
+ return obj === Object(obj);
+ };
+
+ // Is a given variable an arguments object?
+ _.isArguments = function(obj) {
+ return toString.call(obj) == '[object Arguments]';
+ };
+ if (!_.isArguments(arguments)) {
+ _.isArguments = function(obj) {
+ return !!(obj && _.has(obj, 'callee'));
+ };
+ }
+
+ // Is a given value a function?
+ _.isFunction = function(obj) {
+ return toString.call(obj) == '[object Function]';
+ };
+
+ // Is a given value a string?
+ _.isString = function(obj) {
+ return toString.call(obj) == '[object String]';
+ };
+
+ // Is a given value a number?
+ _.isNumber = function(obj) {
+ return toString.call(obj) == '[object Number]';
+ };
+
+ // Is the given value `NaN`?
+ _.isNaN = function(obj) {
+ // `NaN` is the only value for which `===` is not reflexive.
+ return obj !== obj;
+ };
+
+ // Is a given value a boolean?
+ _.isBoolean = function(obj) {
+ return obj === true || obj === false || toString.call(obj) == '[object Boolean]';
+ };
+
+ // Is a given value a date?
+ _.isDate = function(obj) {
+ return toString.call(obj) == '[object Date]';
+ };
+
+ // Is the given value a regular expression?
+ _.isRegExp = function(obj) {
+ return toString.call(obj) == '[object RegExp]';
+ };
+
+ // Is a given value equal to null?
+ _.isNull = function(obj) {
+ return obj === null;
+ };
+
+ // Is a given variable undefined?
+ _.isUndefined = function(obj) {
+ return obj === void 0;
+ };
+
+ // Has own property?
+ _.has = function(obj, key) {
+ return hasOwnProperty.call(obj, key);
+ };
+
+ // Utility Functions
+ // -----------------
+
+ // Run Underscore.js in *noConflict* mode, returning the `_` variable to its
+ // previous owner. Returns a reference to the Underscore object.
+ _.noConflict = function() {
+ root._ = previousUnderscore;
+ return this;
+ };
+
+ // Keep the identity function around for default iterators.
+ _.identity = function(value) {
+ return value;
+ };
+
+ // Run a function **n** times.
+ _.times = function (n, iterator, context) {
+ for (var i = 0; i < n; i++) iterator.call(context, i);
+ };
+
+ // Escape a string for HTML interpolation.
+ _.escape = function(string) {
+ return (''+string).replace(/&/g, '&').replace(//g, '>').replace(/"/g, '"').replace(/'/g, ''').replace(/\//g,'/');
+ };
+
+ // Add your own custom functions to the Underscore object, ensuring that
+ // they're correctly added to the OOP wrapper as well.
+ _.mixin = function(obj) {
+ each(_.functions(obj), function(name){
+ addToWrapper(name, _[name] = obj[name]);
+ });
+ };
+
+ // Generate a unique integer id (unique within the entire client session).
+ // Useful for temporary DOM ids.
+ var idCounter = 0;
+ _.uniqueId = function(prefix) {
+ var id = idCounter++;
+ return prefix ? prefix + id : id;
+ };
+
+ // By default, Underscore uses ERB-style template delimiters, change the
+ // following template settings to use alternative delimiters.
+ _.templateSettings = {
+ evaluate : /<%([\s\S]+?)%>/g,
+ interpolate : /<%=([\s\S]+?)%>/g,
+ escape : /<%-([\s\S]+?)%>/g
+ };
+
+ // When customizing `templateSettings`, if you don't want to define an
+ // interpolation, evaluation or escaping regex, we need one that is
+ // guaranteed not to match.
+ var noMatch = /.^/;
+
+ // Within an interpolation, evaluation, or escaping, remove HTML escaping
+ // that had been previously added.
+ var unescape = function(code) {
+ return code.replace(/\\\\/g, '\\').replace(/\\'/g, "'");
+ };
+
+ // JavaScript micro-templating, similar to John Resig's implementation.
+ // Underscore templating handles arbitrary delimiters, preserves whitespace,
+ // and correctly escapes quotes within interpolated code.
+ _.template = function(str, data) {
+ var c = _.templateSettings;
+ var tmpl = 'var __p=[],print=function(){__p.push.apply(__p,arguments);};' +
+ 'with(obj||{}){__p.push(\'' +
+ str.replace(/\\/g, '\\\\')
+ .replace(/'/g, "\\'")
+ .replace(c.escape || noMatch, function(match, code) {
+ return "',_.escape(" + unescape(code) + "),'";
+ })
+ .replace(c.interpolate || noMatch, function(match, code) {
+ return "'," + unescape(code) + ",'";
+ })
+ .replace(c.evaluate || noMatch, function(match, code) {
+ return "');" + unescape(code).replace(/[\r\n\t]/g, ' ') + ";__p.push('";
+ })
+ .replace(/\r/g, '\\r')
+ .replace(/\n/g, '\\n')
+ .replace(/\t/g, '\\t')
+ + "');}return __p.join('');";
+ var func = new Function('obj', '_', tmpl);
+ if (data) return func(data, _);
+ return function(data) {
+ return func.call(this, data, _);
+ };
+ };
+
+ // Add a "chain" function, which will delegate to the wrapper.
+ _.chain = function(obj) {
+ return _(obj).chain();
+ };
+
+ // The OOP Wrapper
+ // ---------------
+
+ // If Underscore is called as a function, it returns a wrapped object that
+ // can be used OO-style. This wrapper holds altered versions of all the
+ // underscore functions. Wrapped objects may be chained.
+ var wrapper = function(obj) { this._wrapped = obj; };
+
+ // Expose `wrapper.prototype` as `_.prototype`
+ _.prototype = wrapper.prototype;
+
+ // Helper function to continue chaining intermediate results.
+ var result = function(obj, chain) {
+ return chain ? _(obj).chain() : obj;
+ };
+
+ // A method to easily add functions to the OOP wrapper.
+ var addToWrapper = function(name, func) {
+ wrapper.prototype[name] = function() {
+ var args = slice.call(arguments);
+ unshift.call(args, this._wrapped);
+ return result(func.apply(_, args), this._chain);
+ };
+ };
+
+ // Add all of the Underscore functions to the wrapper object.
+ _.mixin(_);
+
+ // Add all mutator Array functions to the wrapper.
+ each(['pop', 'push', 'reverse', 'shift', 'sort', 'splice', 'unshift'], function(name) {
+ var method = ArrayProto[name];
+ wrapper.prototype[name] = function() {
+ var wrapped = this._wrapped;
+ method.apply(wrapped, arguments);
+ var length = wrapped.length;
+ if ((name == 'shift' || name == 'splice') && length === 0) delete wrapped[0];
+ return result(wrapped, this._chain);
+ };
+ });
+
+ // Add all accessor Array functions to the wrapper.
+ each(['concat', 'join', 'slice'], function(name) {
+ var method = ArrayProto[name];
+ wrapper.prototype[name] = function() {
+ return result(method.apply(this._wrapped, arguments), this._chain);
+ };
+ });
+
+ // Start chaining a wrapped Underscore object.
+ wrapper.prototype.chain = function() {
+ this._chain = true;
+ return this;
+ };
+
+ // Extracts the result from a wrapped and chained object.
+ wrapper.prototype.value = function() {
+ return this._wrapped;
+ };
+
+}).call(this);
diff --git a/_static/underscore.js b/_static/underscore.js
new file mode 100644
index 0000000..5b55f32
--- /dev/null
+++ b/_static/underscore.js
@@ -0,0 +1,31 @@
+// Underscore.js 1.3.1
+// (c) 2009-2012 Jeremy Ashkenas, DocumentCloud Inc.
+// Underscore is freely distributable under the MIT license.
+// Portions of Underscore are inspired or borrowed from Prototype,
+// Oliver Steele's Functional, and John Resig's Micro-Templating.
+// For all details and documentation:
+// http://documentcloud.github.com/underscore
+(function(){function q(a,c,d){if(a===c)return a!==0||1/a==1/c;if(a==null||c==null)return a===c;if(a._chain)a=a._wrapped;if(c._chain)c=c._wrapped;if(a.isEqual&&b.isFunction(a.isEqual))return a.isEqual(c);if(c.isEqual&&b.isFunction(c.isEqual))return c.isEqual(a);var e=l.call(a);if(e!=l.call(c))return false;switch(e){case "[object String]":return a==String(c);case "[object Number]":return a!=+a?c!=+c:a==0?1/a==1/c:a==+c;case "[object Date]":case "[object Boolean]":return+a==+c;case "[object RegExp]":return a.source==
+c.source&&a.global==c.global&&a.multiline==c.multiline&&a.ignoreCase==c.ignoreCase}if(typeof a!="object"||typeof c!="object")return false;for(var f=d.length;f--;)if(d[f]==a)return true;d.push(a);var f=0,g=true;if(e=="[object Array]"){if(f=a.length,g=f==c.length)for(;f--;)if(!(g=f in a==f in c&&q(a[f],c[f],d)))break}else{if("constructor"in a!="constructor"in c||a.constructor!=c.constructor)return false;for(var h in a)if(b.has(a,h)&&(f++,!(g=b.has(c,h)&&q(a[h],c[h],d))))break;if(g){for(h in c)if(b.has(c,
+h)&&!f--)break;g=!f}}d.pop();return g}var r=this,G=r._,n={},k=Array.prototype,o=Object.prototype,i=k.slice,H=k.unshift,l=o.toString,I=o.hasOwnProperty,w=k.forEach,x=k.map,y=k.reduce,z=k.reduceRight,A=k.filter,B=k.every,C=k.some,p=k.indexOf,D=k.lastIndexOf,o=Array.isArray,J=Object.keys,s=Function.prototype.bind,b=function(a){return new m(a)};if(typeof exports!=="undefined"){if(typeof module!=="undefined"&&module.exports)exports=module.exports=b;exports._=b}else r._=b;b.VERSION="1.3.1";var j=b.each=
+b.forEach=function(a,c,d){if(a!=null)if(w&&a.forEach===w)a.forEach(c,d);else if(a.length===+a.length)for(var e=0,f=a.length;e2;a==
+null&&(a=[]);if(y&&a.reduce===y)return e&&(c=b.bind(c,e)),f?a.reduce(c,d):a.reduce(c);j(a,function(a,b,i){f?d=c.call(e,d,a,b,i):(d=a,f=true)});if(!f)throw new TypeError("Reduce of empty array with no initial value");return d};b.reduceRight=b.foldr=function(a,c,d,e){var f=arguments.length>2;a==null&&(a=[]);if(z&&a.reduceRight===z)return e&&(c=b.bind(c,e)),f?a.reduceRight(c,d):a.reduceRight(c);var g=b.toArray(a).reverse();e&&!f&&(c=b.bind(c,e));return f?b.reduce(g,c,d,e):b.reduce(g,c)};b.find=b.detect=
+function(a,c,b){var e;E(a,function(a,g,h){if(c.call(b,a,g,h))return e=a,true});return e};b.filter=b.select=function(a,c,b){var e=[];if(a==null)return e;if(A&&a.filter===A)return a.filter(c,b);j(a,function(a,g,h){c.call(b,a,g,h)&&(e[e.length]=a)});return e};b.reject=function(a,c,b){var e=[];if(a==null)return e;j(a,function(a,g,h){c.call(b,a,g,h)||(e[e.length]=a)});return e};b.every=b.all=function(a,c,b){var e=true;if(a==null)return e;if(B&&a.every===B)return a.every(c,b);j(a,function(a,g,h){if(!(e=
+e&&c.call(b,a,g,h)))return n});return e};var E=b.some=b.any=function(a,c,d){c||(c=b.identity);var e=false;if(a==null)return e;if(C&&a.some===C)return a.some(c,d);j(a,function(a,b,h){if(e||(e=c.call(d,a,b,h)))return n});return!!e};b.include=b.contains=function(a,c){var b=false;if(a==null)return b;return p&&a.indexOf===p?a.indexOf(c)!=-1:b=E(a,function(a){return a===c})};b.invoke=function(a,c){var d=i.call(arguments,2);return b.map(a,function(a){return(b.isFunction(c)?c||a:a[c]).apply(a,d)})};b.pluck=
+function(a,c){return b.map(a,function(a){return a[c]})};b.max=function(a,c,d){if(!c&&b.isArray(a))return Math.max.apply(Math,a);if(!c&&b.isEmpty(a))return-Infinity;var e={computed:-Infinity};j(a,function(a,b,h){b=c?c.call(d,a,b,h):a;b>=e.computed&&(e={value:a,computed:b})});return e.value};b.min=function(a,c,d){if(!c&&b.isArray(a))return Math.min.apply(Math,a);if(!c&&b.isEmpty(a))return Infinity;var e={computed:Infinity};j(a,function(a,b,h){b=c?c.call(d,a,b,h):a;bd?1:0}),"value")};b.groupBy=function(a,c){var d={},e=b.isFunction(c)?c:function(a){return a[c]};j(a,function(a,b){var c=e(a,b);(d[c]||(d[c]=[])).push(a)});return d};b.sortedIndex=function(a,
+c,d){d||(d=b.identity);for(var e=0,f=a.length;e>1;d(a[g])=0})})};b.difference=function(a){var c=b.flatten(i.call(arguments,1));return b.filter(a,function(a){return!b.include(c,a)})};b.zip=function(){for(var a=i.call(arguments),c=b.max(b.pluck(a,"length")),d=Array(c),e=0;e=0;d--)b=[a[d].apply(this,b)];return b[0]}};
+b.after=function(a,b){return a<=0?b():function(){if(--a<1)return b.apply(this,arguments)}};b.keys=J||function(a){if(a!==Object(a))throw new TypeError("Invalid object");var c=[],d;for(d in a)b.has(a,d)&&(c[c.length]=d);return c};b.values=function(a){return b.map(a,b.identity)};b.functions=b.methods=function(a){var c=[],d;for(d in a)b.isFunction(a[d])&&c.push(d);return c.sort()};b.extend=function(a){j(i.call(arguments,1),function(b){for(var d in b)a[d]=b[d]});return a};b.defaults=function(a){j(i.call(arguments,
+1),function(b){for(var d in b)a[d]==null&&(a[d]=b[d])});return a};b.clone=function(a){return!b.isObject(a)?a:b.isArray(a)?a.slice():b.extend({},a)};b.tap=function(a,b){b(a);return a};b.isEqual=function(a,b){return q(a,b,[])};b.isEmpty=function(a){if(b.isArray(a)||b.isString(a))return a.length===0;for(var c in a)if(b.has(a,c))return false;return true};b.isElement=function(a){return!!(a&&a.nodeType==1)};b.isArray=o||function(a){return l.call(a)=="[object Array]"};b.isObject=function(a){return a===Object(a)};
+b.isArguments=function(a){return l.call(a)=="[object Arguments]"};if(!b.isArguments(arguments))b.isArguments=function(a){return!(!a||!b.has(a,"callee"))};b.isFunction=function(a){return l.call(a)=="[object Function]"};b.isString=function(a){return l.call(a)=="[object String]"};b.isNumber=function(a){return l.call(a)=="[object Number]"};b.isNaN=function(a){return a!==a};b.isBoolean=function(a){return a===true||a===false||l.call(a)=="[object Boolean]"};b.isDate=function(a){return l.call(a)=="[object Date]"};
+b.isRegExp=function(a){return l.call(a)=="[object RegExp]"};b.isNull=function(a){return a===null};b.isUndefined=function(a){return a===void 0};b.has=function(a,b){return I.call(a,b)};b.noConflict=function(){r._=G;return this};b.identity=function(a){return a};b.times=function(a,b,d){for(var e=0;eNo comments yet. ');
+ ul.data('empty', true);
+ } else {
+ // If there are comments, sort them and put them in the list.
+ var comments = sortComments(data.comments);
+ speed = data.comments.length * 100;
+ appendComments(comments, ul);
+ ul.data('empty', false);
+ }
+ $('#cn' + id).slideUp(speed + 200);
+ ul.slideDown(speed);
+ },
+ error: function(request, textStatus, error) {
+ showError('Oops, there was a problem retrieving the comments.');
+ },
+ dataType: 'json'
+ });
+ }
+
+ /**
+ * Add a comment via ajax and insert the comment into the comment tree.
+ */
+ function addComment(form) {
+ var node_id = form.find('input[name="node"]').val();
+ var parent_id = form.find('input[name="parent"]').val();
+ var text = form.find('textarea[name="comment"]').val();
+ var proposal = form.find('textarea[name="proposal"]').val();
+
+ if (text == '') {
+ showError('Please enter a comment.');
+ return;
+ }
+
+ // Disable the form that is being submitted.
+ form.find('textarea,input').attr('disabled', 'disabled');
+
+ // Send the comment to the server.
+ $.ajax({
+ type: "POST",
+ url: opts.addCommentURL,
+ dataType: 'json',
+ data: {
+ node: node_id,
+ parent: parent_id,
+ text: text,
+ proposal: proposal
+ },
+ success: function(data, textStatus, error) {
+ // Reset the form.
+ if (node_id) {
+ hideProposeChange(node_id);
+ }
+ form.find('textarea')
+ .val('')
+ .add(form.find('input'))
+ .removeAttr('disabled');
+ var ul = $('#cl' + (node_id || parent_id));
+ if (ul.data('empty')) {
+ $(ul).empty();
+ ul.data('empty', false);
+ }
+ insertComment(data.comment);
+ var ao = $('#ao' + node_id);
+ ao.find('img').attr({'src': opts.commentBrightImage});
+ if (node_id) {
+ // if this was a "root" comment, remove the commenting box
+ // (the user can get it back by reopening the comment popup)
+ $('#ca' + node_id).slideUp();
+ }
+ },
+ error: function(request, textStatus, error) {
+ form.find('textarea,input').removeAttr('disabled');
+ showError('Oops, there was a problem adding the comment.');
+ }
+ });
+ }
+
+ /**
+ * Recursively append comments to the main comment list and children
+ * lists, creating the comment tree.
+ */
+ function appendComments(comments, ul) {
+ $.each(comments, function() {
+ var div = createCommentDiv(this);
+ ul.append($(document.createElement('li')).html(div));
+ appendComments(this.children, div.find('ul.comment-children'));
+ // To avoid stagnating data, don't store the comments children in data.
+ this.children = null;
+ div.data('comment', this);
+ });
+ }
+
+ /**
+ * After adding a new comment, it must be inserted in the correct
+ * location in the comment tree.
+ */
+ function insertComment(comment) {
+ var div = createCommentDiv(comment);
+
+ // To avoid stagnating data, don't store the comments children in data.
+ comment.children = null;
+ div.data('comment', comment);
+
+ var ul = $('#cl' + (comment.node || comment.parent));
+ var siblings = getChildren(ul);
+
+ var li = $(document.createElement('li'));
+ li.hide();
+
+ // Determine where in the parents children list to insert this comment.
+ for(i=0; i < siblings.length; i++) {
+ if (comp(comment, siblings[i]) <= 0) {
+ $('#cd' + siblings[i].id)
+ .parent()
+ .before(li.html(div));
+ li.slideDown('fast');
+ return;
+ }
+ }
+
+ // If we get here, this comment rates lower than all the others,
+ // or it is the only comment in the list.
+ ul.append(li.html(div));
+ li.slideDown('fast');
+ }
+
+ function acceptComment(id) {
+ $.ajax({
+ type: 'POST',
+ url: opts.acceptCommentURL,
+ data: {id: id},
+ success: function(data, textStatus, request) {
+ $('#cm' + id).fadeOut('fast');
+ $('#cd' + id).removeClass('moderate');
+ },
+ error: function(request, textStatus, error) {
+ showError('Oops, there was a problem accepting the comment.');
+ }
+ });
+ }
+
+ function deleteComment(id) {
+ $.ajax({
+ type: 'POST',
+ url: opts.deleteCommentURL,
+ data: {id: id},
+ success: function(data, textStatus, request) {
+ var div = $('#cd' + id);
+ if (data == 'delete') {
+ // Moderator mode: remove the comment and all children immediately
+ div.slideUp('fast', function() {
+ div.remove();
+ });
+ return;
+ }
+ // User mode: only mark the comment as deleted
+ div
+ .find('span.user-id:first')
+ .text('[deleted]').end()
+ .find('div.comment-text:first')
+ .text('[deleted]').end()
+ .find('#cm' + id + ', #dc' + id + ', #ac' + id + ', #rc' + id +
+ ', #sp' + id + ', #hp' + id + ', #cr' + id + ', #rl' + id)
+ .remove();
+ var comment = div.data('comment');
+ comment.username = '[deleted]';
+ comment.text = '[deleted]';
+ div.data('comment', comment);
+ },
+ error: function(request, textStatus, error) {
+ showError('Oops, there was a problem deleting the comment.');
+ }
+ });
+ }
+
+ function showProposal(id) {
+ $('#sp' + id).hide();
+ $('#hp' + id).show();
+ $('#pr' + id).slideDown('fast');
+ }
+
+ function hideProposal(id) {
+ $('#hp' + id).hide();
+ $('#sp' + id).show();
+ $('#pr' + id).slideUp('fast');
+ }
+
+ function showProposeChange(id) {
+ $('#pc' + id).hide();
+ $('#hc' + id).show();
+ var textarea = $('#pt' + id);
+ textarea.val(textarea.data('source'));
+ $.fn.autogrow.resize(textarea[0]);
+ textarea.slideDown('fast');
+ }
+
+ function hideProposeChange(id) {
+ $('#hc' + id).hide();
+ $('#pc' + id).show();
+ var textarea = $('#pt' + id);
+ textarea.val('').removeAttr('disabled');
+ textarea.slideUp('fast');
+ }
+
+ function toggleCommentMarkupBox(id) {
+ $('#mb' + id).toggle();
+ }
+
+ /** Handle when the user clicks on a sort by link. */
+ function handleReSort(link) {
+ var classes = link.attr('class').split(/\s+/);
+ for (var i=0; iThank you! Your comment will show up '
+ + 'once it is has been approved by a moderator.');
+ }
+ // Prettify the comment rating.
+ comment.pretty_rating = comment.rating + ' point' +
+ (comment.rating == 1 ? '' : 's');
+ // Make a class (for displaying not yet moderated comments differently)
+ comment.css_class = comment.displayed ? '' : ' moderate';
+ // Create a div for this comment.
+ var context = $.extend({}, opts, comment);
+ var div = $(renderTemplate(commentTemplate, context));
+
+ // If the user has voted on this comment, highlight the correct arrow.
+ if (comment.vote) {
+ var direction = (comment.vote == 1) ? 'u' : 'd';
+ div.find('#' + direction + 'v' + comment.id).hide();
+ div.find('#' + direction + 'u' + comment.id).show();
+ }
+
+ if (opts.moderator || comment.text != '[deleted]') {
+ div.find('a.reply').show();
+ if (comment.proposal_diff)
+ div.find('#sp' + comment.id).show();
+ if (opts.moderator && !comment.displayed)
+ div.find('#cm' + comment.id).show();
+ if (opts.moderator || (opts.username == comment.username))
+ div.find('#dc' + comment.id).show();
+ }
+ return div;
+ }
+
+ /**
+ * A simple template renderer. Placeholders such as <%id%> are replaced
+ * by context['id'] with items being escaped. Placeholders such as <#id#>
+ * are not escaped.
+ */
+ function renderTemplate(template, context) {
+ var esc = $(document.createElement('div'));
+
+ function handle(ph, escape) {
+ var cur = context;
+ $.each(ph.split('.'), function() {
+ cur = cur[this];
+ });
+ return escape ? esc.text(cur || "").html() : cur;
+ }
+
+ return template.replace(/<([%#])([\w\.]*)\1>/g, function() {
+ return handle(arguments[2], arguments[1] == '%' ? true : false);
+ });
+ }
+
+ /** Flash an error message briefly. */
+ function showError(message) {
+ $(document.createElement('div')).attr({'class': 'popup-error'})
+ .append($(document.createElement('div'))
+ .attr({'class': 'error-message'}).text(message))
+ .appendTo('body')
+ .fadeIn("slow")
+ .delay(2000)
+ .fadeOut("slow");
+ }
+
+ /** Add a link the user uses to open the comments popup. */
+ $.fn.comment = function() {
+ return this.each(function() {
+ var id = $(this).attr('id').substring(1);
+ var count = COMMENT_METADATA[id];
+ var title = count + ' comment' + (count == 1 ? '' : 's');
+ var image = count > 0 ? opts.commentBrightImage : opts.commentImage;
+ var addcls = count == 0 ? ' nocomment' : '';
+ $(this)
+ .append(
+ $(document.createElement('a')).attr({
+ href: '#',
+ 'class': 'sphinx-comment-open' + addcls,
+ id: 'ao' + id
+ })
+ .append($(document.createElement('img')).attr({
+ src: image,
+ alt: 'comment',
+ title: title
+ }))
+ .click(function(event) {
+ event.preventDefault();
+ show($(this).attr('id').substring(2));
+ })
+ )
+ .append(
+ $(document.createElement('a')).attr({
+ href: '#',
+ 'class': 'sphinx-comment-close hidden',
+ id: 'ah' + id
+ })
+ .append($(document.createElement('img')).attr({
+ src: opts.closeCommentImage,
+ alt: 'close',
+ title: 'close'
+ }))
+ .click(function(event) {
+ event.preventDefault();
+ hide($(this).attr('id').substring(2));
+ })
+ );
+ });
+ };
+
+ var opts = {
+ processVoteURL: '/_process_vote',
+ addCommentURL: '/_add_comment',
+ getCommentsURL: '/_get_comments',
+ acceptCommentURL: '/_accept_comment',
+ deleteCommentURL: '/_delete_comment',
+ commentImage: '/static/_static/comment.png',
+ closeCommentImage: '/static/_static/comment-close.png',
+ loadingImage: '/static/_static/ajax-loader.gif',
+ commentBrightImage: '/static/_static/comment-bright.png',
+ upArrow: '/static/_static/up.png',
+ downArrow: '/static/_static/down.png',
+ upArrowPressed: '/static/_static/up-pressed.png',
+ downArrowPressed: '/static/_static/down-pressed.png',
+ voting: false,
+ moderator: false
+ };
+
+ if (typeof COMMENT_OPTIONS != "undefined") {
+ opts = jQuery.extend(opts, COMMENT_OPTIONS);
+ }
+
+ var popupTemplate = '\
+ ';
+
+ var commentTemplate = '\
+ \
+ ';
+
+ var replyTemplate = '\
+ \
+ \
+ \
+
\
+ ';
+
+ $(document).ready(function() {
+ init();
+ });
+})(jQuery);
+
+$(document).ready(function() {
+ // add comment anchors for all paragraphs that are commentable
+ $('.sphinx-has-comment').comment();
+
+ // highlight search words in search results
+ $("div.context").each(function() {
+ var params = $.getQueryParameters();
+ var terms = (params.q) ? params.q[0].split(/\s+/) : [];
+ var result = $(this);
+ $.each(terms, function() {
+ result.highlightText(this.toLowerCase(), 'highlighted');
+ });
+ });
+
+ // directly open comment window if requested
+ var anchor = document.location.hash;
+ if (anchor.substring(0, 9) == '#comment-') {
+ $('#ao' + anchor.substring(9)).click();
+ document.location.hash = '#s' + anchor.substring(9);
+ }
+});
diff --git a/_summaries/bladex.blade.Blade._abs_to_norm.html b/_summaries/bladex.blade.Blade._abs_to_norm.html
new file mode 100644
index 0000000..aab0832
--- /dev/null
+++ b/_summaries/bladex.blade.Blade._abs_to_norm.html
@@ -0,0 +1,254 @@
+
+
+
+
+
+
+ bladex.blade.Blade._abs_to_norm — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade._abs_to_norm
+
+
+Blade._abs_to_norm( D_prop ) [source]
+Private method to normalize the blade parameters.
+
+
+Parameters: D_prop (float
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade._check_errors — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade._check_errors
+
+
+static Blade._check_errors( upper_face , lower_face ) [source]
+Private method to check if either the blade upper face or lower face
+is passed in the generate_iges method. Otherwise it raises an exception
+
+
+Parameters:
+upper_face (string lower_face (string
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade._check_params — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade._check_params
+
+
+Blade._check_params( ) [source]
+Private method to check if all the blade arguments are numpy.ndarrays
+with the same shape.
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade._check_string — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade._check_string
+
+
+static Blade._check_string( filename ) [source]
+Private method to check if the parameter type is string
+
+
+Parameters: filename (string
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade._compute_pitch_angle — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade._compute_pitch_angle
+
+
+Blade._compute_pitch_angle( ) [source]
+Private method that computes the pitch angle from the linear pitch for
+all blade sections.
+
+
+Returns: pitch angle in radians
+Return type: numpy.ndarray
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade._generate_lower_face — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade._generate_lower_face
+
+
+Blade._generate_lower_face( maxDeg ) [source]
+Private method to generate the blade lower face.
+
+
+Parameters: maxDeg (int
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade._generate_tip — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade._generate_tip
+
+
+Blade._generate_tip( maxDeg ) [source]
+Private method to generate the surface that closing the blade tip.
+
+
+Parameters: maxDeg (int
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade._generate_upper_face — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade._generate_upper_face
+
+
+Blade._generate_upper_face( maxDeg ) [source]
+Private method to generate the blade upper face.
+
+
+Parameters: maxDeg (int
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade._import_occ_libs — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade._import_occ_libs
+
+
+static Blade._import_occ_libs( ) [source]
+Private static method to import specific modules from the OCC package.
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade._induced_rake_from_skew — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade._induced_rake_from_skew
+
+
+Blade._induced_rake_from_skew( ) [source]
+Private method that computes the induced rake from skew for all the
+blade sections, according to mytransformation_operations .
+
+
+Returns: induced rake from skew
+Return type: numpy.ndarray
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade._norm_to_abs — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade._norm_to_abs
+
+
+Blade._norm_to_abs( D_prop ) [source]
+Private method that converts the normalized blade parameters into the
+actual values.
+
+
+Parameters: D_prop (float
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade._planar_to_cylindrical — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade._planar_to_cylindrical
+
+
+Blade._planar_to_cylindrical( ) [source]
+Private method that transforms the 2D planar airfoils into 3D
+cylindrical sections.
+The cylindrical transformation is defined by the following formulas:
+
+
+After transformation, the method also fills the numpy.ndarray
+“blade_coordinates_up” and “blade_coordinates_down” with the new
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade._write_blade_errors — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade._write_blade_errors
+
+
+Blade._write_blade_errors( upper_face , lower_face , errors ) [source]
+Private method to write the errors between the generated foil points in
+3D space from the parametric transformations, and their projections on
+the generated blade faces from the OCC algorithm.
+
+
+Parameters:
+upper_face (string lower_face (string errors (string
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade.apply_transformations — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
bladex.blade.Blade.export_ppg — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade.export_ppg
+
+
+Blade.export_ppg( filename='data_out.ppg' , D_prop=0.25 , D_hub=0.075 , n_blades=5 , params_normalized=False ) [source]
+Export the generated blade parameters and sectional profiles into
+.ppg format.
+
+
+Parameters:
+filename (string D_prop (float D_hub (float n_blades (float params_normalized (bool
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade.generate_iges — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade.generate_iges
+
+
+Blade.generate_iges( upper_face=None , lower_face=None , tip=None , maxDeg=1 , display=False , errors=None ) [source]
+Generate and export the .iges CAD for the blade upper face, lower face,
+and tip. This method requires PythonOCC to be installed.
+
+
+Parameters:
+upper_face (string lower_face (string tip (string maxDeg (int display (bool errors (string
+
+
+We note that the blade object must have its radial sections be arranged
+in order from the blade root to the blade tip, so that generate_iges
+method can build the CAD surface that passes through the corresponding
+airfoils. Also to be able to identify and close the blade tip.
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade.generate_stl — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade.generate_stl
+
+
+Blade.generate_stl( min_length=None , max_length=None , outfile_stl=None ) [source]
+Generate and export the .STL surface mesh for the blade as a whole,
+including the upper face, lower face and tip. The method utilizes
+modules from OCC SMESH which is standalone mesh framework based on
+SALOME mesher project. Please refer to https://github.com/tpaviot
+and http://docs.salome-platform.org/7/gui/SMESH/index.html for
+further details.
+This method requires PythonOCC and SMESH to be installed.
+
+
+Parameters:
+min_length (double ) – smallest distance between two nodes. Default
+value is Nonemax_length (double ) – largest distance between two nodes. Default
+value is Noneoutfile_stl (string
+
+
+We note that since the current implementation performs triangulation
+based on a topological compound that combines the blade 3 generated
+shapes without “fusion”, it may happen that the generated triangulation
+of the upper and lower blade faces do not share the same exact nodes
+on the joint edge/wire resulting from the faces intersection. The
+current implementation can be enough for visualization purpose. However
+if the generated mesh is intended for computational analysis then a
+manual mesh healing is recommended by the user (e.g. see
+“Repair > Sewing” in SALOME GUI) for a proper mesh closure.
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade.plot — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade.plot
+
+
+Blade.plot( elev=None , azim=None , ax=None , outfile=None ) [source]
+Plot the generated blade sections.
+
+
+Parameters:
+elev (int azim (int ax (matplotlib.axes outfile (string
+
+
+EXAMPLE:
+Assume we already have the arrays radii, chord, pitch, rake, skew for
+10 blade sections.
+>>> sections_1 = np . asarray ([ blade . NacaProfile ( digits = '0012' )
+ for i in range(10)])
+>>> blade_1 = blade . Blade ( sections = sections ,
+ radii=radii,
+ chord_lengths=chord,
+ pitch=pitch,
+ rake=rake,
+ skew_angles=skew)
+>>> blade_1 . apply_transformations ()
+
+
>>> sections_2 = np . asarray ([ blade . NacaProfile ( digits = '0012' )
+ for i in range(10)])
+>>> blade_2 = blade . Blade ( sections = sections ,
+ radii=radii,
+ chord_lengths=chord,
+ pitch=pitch,
+ rake=rake,
+ skew_angles=skew)
+>>> blade_2 . apply_transformations ()
+>>> blade_2 . rotate ( rot_angle_deg = 72 )
+
+
>>> fig = plt . figure ()
+>>> ax = fig . gca ( projection = Axes3D . name )
+>>> blade_1 . plot ( ax = ax )
+>>> blade_2 . plot ( ax = ax )
+
+
On the other hand, if we need to plot for a single blade object,
+we can just ignore such parameter, and the method will internally
+create a new instance for the figure axes, i.e.
+>>> sections = np . asarray ([ blade . NacaProfile ( digits = '0012' )
+ for i in range(10)])
+>>> blade = blade . Blade ( sections = sections ,
+ radii=radii,
+ chord_lengths=chord,
+ pitch=pitch,
+ rake=rake,
+ skew_angles=skew)
+>>> blade . apply_transformations ()
+>>> blade . plot ()
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade.rotate — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.blade.Blade.rotate
+
+
+Blade.rotate( deg_angle=None , rad_angle=None ) [source]
+3D counter clockwise rotation about the X-axis of the Cartesian
+coordinate system, which is the axis of rotation of the propeller hub.
+The rotation matrix,
+
+
+
+
Given the coordinates of point
+
+
+
Then, the rotated coordinates will be:
+
+
+
+
+Parameters:
+deg_angle (float rad_angle (float
+Raises: ValueError – if both rad_angle and deg_angle are inserted,
+or if neither is inserted
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.deform.Deformation._check_control_points — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
bladex.deform.Deformation._check_deformed — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
bladex.deform.Deformation._check_param — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
bladex.deform.Deformation._check_spline — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
bladex.deform.Deformation._optimum_control_points — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
bladex.deform.Deformation.compute_all — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
bladex.deform.Deformation.compute_control_points — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
bladex.deform.Deformation.compute_deformed_parameters — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
bladex.deform.Deformation.export_param_file — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
bladex.deform.Deformation.generate_spline — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
bladex.deform.Deformation.plot — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
bladex.deform.Deformation.update_control_points — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
bladex.ndinterpolator.RBF.beckert_wendland_c2_basis — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.ndinterpolator.RBF.beckert_wendland_c2_basis
+
+
+static RBF.beckert_wendland_c2_basis( X , r ) [source]
+It implements the following formula:
+
+
+
+
+Parameters:
+X (numpy.ndarray r (float
+Returns: result: the result of the formula above.
+Return type: float
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.ndinterpolator.RBF.gaussian_spline — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.ndinterpolator.RBF.gaussian_spline
+
+
+static RBF.gaussian_spline( X , r ) [source]
+It implements the following formula:
+
+
+
+
+Parameters:
+X (numpy.ndarray r (float
+Returns: result: the result of the formula above.
+Return type: float
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.ndinterpolator.RBF.inv_multi_quadratic_biharmonic_spline — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.ndinterpolator.RBF.inv_multi_quadratic_biharmonic_spline
+
+
+static RBF.inv_multi_quadratic_biharmonic_spline( X , r ) [source]
+It implements the following formula:
+
+
+
+
+Parameters:
+X (numpy.ndarray r (float
+Returns: result: the result of the formula above.
+Return type: float
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.ndinterpolator.RBF.multi_quadratic_biharmonic_spline — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.ndinterpolator.RBF.multi_quadratic_biharmonic_spline
+
+
+static RBF.multi_quadratic_biharmonic_spline( X , r ) [source]
+It implements the following formula:
+
+
+
+
+Parameters:
+X (numpy.ndarray r (float
+Returns: result: the result of the formula above.
+Return type: float
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.ndinterpolator.RBF.thin_plate_spline — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.ndinterpolator.RBF.thin_plate_spline
+
+
+static RBF.thin_plate_spline( X , r ) [source]
+It implements the following formula:
+
+
+
+
+Parameters:
+X (numpy.ndarray r (float
+Returns: result: the result of the formula above.
+Return type: float
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.ndinterpolator.RBF.weights_matrix — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.ndinterpolator.RBF.weights_matrix
+
+
+RBF.weights_matrix( X1 , X2 ) [source]
+This method returns the following matrix:
+
+
+
+
+Parameters:
+
+Returns: matrix: the matrix D.
+Return type: numpy.ndarray
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.ndinterpolator.reconstruct_f — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.ndinterpolator.reconstruct_f
+
+
+reconstruct_f( original_input , original_output , rbf_input , rbf_output , basis , radius ) [source]
+Reconstruct a function by using the radial basis function approximations.
+
+
+Parameters:
+original_input (array_like ) – the original values of function inputs.original_output (array_like ) – the original values of function output.rbf_input (array_like ) – the input data for RBF approximation.rbf_output (array_like ) – the array elements to be updated with the RBF
+interpolated outputs after the approximation.basis (string radius (float
+Example: >>> import numpy as np
+>>> from bladex.ndinterpolator import reconstruct_f
+>>> x = np . arange ( 10 )
+>>> y = np . square ( x )
+>>> radius = 10
+>>> n_interp = 50
+>>> x_rbf = np . linspace ( x [ 0 ], x [ - 1 ], num = n_interp )
+>>> y_rbf = np . zeros ( n_interp )
+>>> reconstruct_f ( original_input = x , original_output = y , rbf_input = x_rbf ,
+ rbf_output=y_rbf, radius=radius, basis='beckert_wendland_c2_basis')
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.ndinterpolator.scipy_bspline — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.ndinterpolator.scipy_bspline
+
+
+scipy_bspline( cv , npoints , degree ) [source]
+Construct B-Spline curve via the control points.
+
+
+Parameters:
+cv (array_like ) – control points vector (spline coefficients).npoints (int degree (int
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.params.ParamFile.__str__ — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.params.ParamFile.__str__
+
+
+ParamFile.__str__( ) [source]
+This method prints all the parameters on the screen. Its purpose is
+for debugging.
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.params.ParamFile._check_params — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.params.ParamFile._check_params
+
+
+ParamFile._check_params( ) [source]
+Private method that is called while writing a parameter file.
+1. The method checks if the user specifies a radii array, otherwise it
+raises exception.
+2. In case no values assigned to any of the remaining parameter arrays
+then an array of zeros is assigned, in which its length is equal
+to the radii array.
+3. Any array that is not numpy is converted to be one. Finally, in case
+the user specifies the parameter array values but not with same length,
+then an exception is raised.
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.params.ParamFile.read_parameters — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.params.ParamFile.read_parameters
+
+
+ParamFile.read_parameters( filename='parameters.prm' ) [source]
+Reads in the parameters file and fill the self structure.
+
+
+Parameters: filename (str
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.params.ParamFile.write_parameters — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.params.ParamFile.write_parameters
+
+
+ParamFile.write_parameters( filename='parameters.prm' ) [source]
+This method writes a parameters file (.prm) called filename and fills
+it with all the parameters class members. Default value is
+parameters.prm.
+
+
+Parameters:
+filename (str param_pptc (bool
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase._update_edges — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase._update_edges
+
+
+ProfileBase._update_edges( ) [source]
+Private method that identifies and updates the airfoil’s leading and
+trailing edges.
+Given the airfoil coordinates from the leading to the trailing edge,
+if the trailing edge has a non-zero thickness, then the average value
+between the upper and lower trailing edges is taken as the true
+trailing edge, hence both the leading and the trailing edges are always
+unique.
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase.chord_length — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase.chord_length
+
+
+ProfileBase.chord_length
+Measure the l2-norm (Euclidean distance) between the leading edge
+and the trailing edge.
+
+
+Returns: chord length
+Return type: float
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase.compute_camber_line — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase.compute_camber_line
+
+
+ProfileBase.compute_camber_line( n_interpolated_points=None ) [source]
+Compute the 2D coordinates of the camber line. Also updates the
+camber_line class member.
+The camber line is defined by the curve passing through all the mid
+points between the upper surface and the lower surface of the airfoil.
+
+
+Parameters: n_interpolated_points (int
+
+We note that a uniform interpolation becomes necessary for the cases
+when the X-coordinates of the upper and lower surfaces do not
+correspond to the same vertical sections, since this would imply
+inaccurate measurements for obtaining the camber line.
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase.compute_chord_line — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase.compute_chord_line
+
+
+ProfileBase.compute_chord_line( n_interpolated_points=None ) [source]
+Compute the 2D coordinates of the chord line. Also updates
+the chord_line class member.
+The chord line is the straight line that joins between the leading edge
+and the trailing edge. It is simply computed from the equation of
+a line passing through two points, the LE and TE.
+
+
+Parameters: n_interpolated_points (int
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase.deform_camber_line — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase.interpolate_coordinates — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase.interpolate_coordinates
+
+
+ProfileBase.interpolate_coordinates( num=500 , radius=1.0 ) [source]
+Interpolate the airfoil coordinates from the given data set of
+discrete points.
+The interpolation applies the Radial Basis Function (RBF) method,
+to construct approximations of the two functions that correspond to the
+airfoil upper half and lower half coordinates. The RBF implementation
+is present in RBF ndinterpolator
+References:
+Buhmann, Martin D. (2003), Radial Basis Functions: Theory
+and Implementations.
+http://www.cs.bham.ac.uk/~jxb/NN/l12.pdf
+https://www.cc.gatech.edu/~isbell/tutorials/rbf-intro.pdf
+
+
+Parameters:
+num (int radius (float
+Returns: interpolation points for the airfoil upper half X-component,
+interpolation points for the airfoil lower half X-component,
+interpolation points for the airfoil upper half Y-component,
+interpolation points for the airfoil lower half Y-component
+Return type: numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray
+Raises:
+TypeError – if num is not of type intValueError – if num is not positive, or if radius is not
+positive
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase.max_camber — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase.max_camber
+
+
+ProfileBase.max_camber( n_interpolated_points=500 ) [source]
+Return the magnitude of the airfoil’s maximum camber.
+Camber is defined as the distance between the chord line and the mean
+camber line, and is measured along the line perpendicular to the chord
+line.
+
+
+Parameters:
+interpolate (bool n_interpolated_points (int
+Returns: maximum camber
+Return type: float
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase.max_thickness — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase.max_thickness
+
+
+ProfileBase.max_thickness( n_interpolated_points=None ) [source]
+Return the airfoil’s maximum thickness.
+Thickness is defined as the distnace between the upper and lower
+surfaces of the airfoil, and can be measured in two different ways:
+
+
+American convention: measures along the line perpendicular to the mean camber line.
+British convention: measures along the line perpendicular to the chord line.
+
+
+In this implementation, the british convention is used to evaluate
+the maximum thickness.
+References:
+
+Phillips, Warren F. (2010). Mechanics of Flight (2nd ed.). Wiley & Sons. p. 27. ISBN 978-0-470-53975-0.
+
Bertin, John J.; Cummings, Russel M. (2009). Pearson Prentice Hall, ed. Aerodynamics for Engineers (5th ed.). p. 199. ISBN 978-0-13-227268-1.
+
+
+
+Parameters:
+interpolate (bool n_interpolated_points (int
+Returns: maximum thickness
+Return type: float
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase.plot — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase.plot
+
+
+ProfileBase.plot( profile=True , chord_line=False , camber_line=False , ref_point=False , outfile=None ) [source]
+Plot the airfoil coordinates.
+
+
+Parameters:
+profile (bool chord_line (bool camber_line (bool ref_point (bool outfile (str
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase.reference_point — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase.reference_point
+
+
+ProfileBase.reference_point
+Return the coordinates of the chord’s mid point.
+
+
+Returns: reference point in 2D
+Return type: numpy.ndarray
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase.reflect — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase.reflect
+
+
+ProfileBase.reflect( ) [source]
+Reflect the airfoil coordinates about the origin, i.e. a mirror
+transformation is performed about both the X-axis and the Y-axis.
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase.rotate — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase.rotate
+
+
+ProfileBase.rotate( rad_angle=None , deg_angle=None ) [source]
+2D counter clockwise rotation about the origin of the Cartesian
+coordinate system.
+The rotation matrix,
+
+
+
+
Given the coordinates of point
+
+
+
Then, the rotated coordinates will be:
+
+
+
If a standard right-handed Cartesian coordinate system is used, with
+the X-axis to the right and the Y-axis up, the rotation
+
+
+
+Parameters:
+rad_angle (float deg_angle (float
+Raises: ValueError – if both rad_angle and deg_angle are inserted,
+or if neither is inserted
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase.scale — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase.scale
+
+
+ProfileBase.scale( factor ) [source]
+Scale the airfoil coordinates according to a scaling factor.
+In order to apply the scaling without affecting the position of the
+reference point, the method translates the airfoil by its refernce
+point to be centered in the origin, then the scaling is applied, and
+finally the airfoil is translated back by its reference point to the
+initial position.
+
+
+Parameters: factor (float
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase.translate — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profilebase.ProfileBase.translate
+
+
+ProfileBase.translate( translation ) [source]
+Translate the airfoil coordinates according to a 2D translation vector.
+
+
+Parameters: translation (array_like ) – the translation vector in 2D
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profiles.CustomProfile._check_coordinates — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profiles.CustomProfile._check_coordinates
+
+
+CustomProfile._check_coordinates( ) [source]
+Private method that checks whether the airfoil coordinates defined
+are provided correctly.
+We note that each array of coordinates must be consistent with the
+other arrays. The upper and lower surfaces should start from exactly
+the same point, the leading edge, and proceed on the way till the
+trailing edge. The trailing edge might have a non-zero thickness as
+in the case of some NACA-airfoils. In case of an open trailing edge,
+the average coordinate between upper and lower part is taken as the
+unique value.
+
+
+Raises:
+ValueError – if either xup, xdown, yup, ydown is NoneValueError – if the 1D arrays xup, yup or xdown, ydown do not
+have the same lengthValueError – if array yup not greater than or equal array ydown
+element-wiseValueError – if xdown[0] != xup[0] or ydown[0] != yup[0]
+or xdown[-1] != xup[-1]
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profiles.NacaProfile._check_args — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profiles.NacaProfile._check_args
+
+
+NacaProfile._check_args( ) [source]
+Private method to check that the number of the airfoil discrete points
+is a positive integer.
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profiles.NacaProfile._generate_coordinates — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
bladex.profiles.NacaProfile._generate_coordinates
+
+
+NacaProfile._generate_coordinates( ) [source]
+Private method that generates the coordinates of the NACA 4 or 5 digits
+airfoil profile. The method assumes a zero-thickness trailing edge, and
+no half-cosine spacing.
+
+
+
+
+
+
+
+
+
+
+
+
+
Blade — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Blade
+
Module for the blade bottom-up parametrized construction.
+
+
+
+
+Blade._abs_to_norm Private method to normalize the blade parameters.
+Blade._check_errors Private method to check if either the blade upper face or lower face is passed in the generate_iges method.
+Blade._check_params Private method to check if all the blade arguments are numpy.ndarrays with the same shape.
+Blade._check_string Private method to check if the parameter type is string
+Blade._compute_pitch_angle Private method that computes the pitch angle from the linear pitch for all blade sections.
+Blade._generate_lower_face Private method to generate the blade lower face.
+Blade._generate_tip Private method to generate the surface that closing the blade tip.
+Blade._generate_upper_face Private method to generate the blade upper face.
+Blade._import_occ_libs Private static method to import specific modules from the OCC package.
+Blade._induced_rake_from_skew Private method that computes the induced rake from skew for all the blade sections, according to mytransformation_operations .
+Blade._norm_to_abs Private method that converts the normalized blade parameters into the actual values.
+Blade._planar_to_cylindrical Private method that transforms the 2D planar airfoils into 3D cylindrical sections.
+Blade._write_blade_errors Private method to write the errors between the generated foil points in 3D space from the parametric transformations, and their projections on the generated blade faces from the OCC algorithm.
+Blade.apply_transformations Generate a bottom-up constructed propeller blade based on the airfoil transformations, see mytransformation_operations .
+Blade.generate_iges Generate and export the .iges CAD for the blade upper face, lower face, and tip.
+Blade.generate_stl Generate and export the .STL surface mesh for the blade as a whole, including the upper face, lower face and tip.
+Blade.export_ppg Export the generated blade parameters and sectional profiles into .ppg format.
+Blade.plot Plot the generated blade sections.
+Blade.rotate 3D counter clockwise rotation about the X-axis of the Cartesian
+
+
+
+
+class Blade( sections , radii , chord_lengths , pitch , rake , skew_angles ) [source]
+Bases: object
+Bottom-up parametrized blade construction.
+Given the following parameters of a propeller blade:
+
+
+then, a bottom-up construction procedure is performed by applying series of
+transformation operations on the airfoils according to the provided
+parameters, to end up with a 3D CAD model of the blade, which can be
+exported into IGES format. Also surface or volume meshes can be obtained.
+Useful definitions on the propeller geometry:
+
+
+Blade cylindrical section: the cross section of a blade cut by a
+cylinder whose centerline is the propeller axis of rotation.
+We may also refer as “radial section”.
+Pitch
+
+
+
+
+Rake: the fore or aft slant of the blade with respect to a line
+perpendicular to the propeller axis of rotation.
+Skew: the transverse sweeping of a blade such that viewing the blades
+from fore or aft would show an asymmetrical shape.
+
+
+References:
+
+Transformation operations according to the provided parameters:
+
+
+
+Parameters:
+sections (array_like ) – 1D array, each element is an object of the
+BaseProfile class at specific radial section.radii (array_like ) – 1D array, contains the radii values of the
+sectional profiles.chord_lengths (array_like ) – 1D array, contains the value of the
+airfoil’s chord length for each radial section of the blade.pitch (array_like ) – 1D array, contains the local pitch values
+(in unit length) for each radial section of the blade.rake (array_like ) – 1D array, contains the local rake values for each
+radial section of the blade.skew_angles (array_like ) – 1D array, contains the skew angles
+(in degrees) for each radial section of the blade.
+
+
+Note that, each of the previous array_like parameters must be consistent
+with the other parameters in terms of the radial ordering of the blade
+sections. In particular, an array_like elements must follow the radial
+distribution of the blade sections starting from the blade root and ends up
+with the blade tip since the blade surface generator depends on that order.
+Finally, beware that the profiles class objects in the array ‘sections’
+undergo several transformations that affect their coordinates. Therefore
+the array must be specific to each blade class instance. For example, if
+we generate 12 sectional profiles using NACA airfoils and we need to use
+them in two different blade classes, then we should instantiate two class
+objects for the profiles, as well as the blade. The following example
+explains the fault and the correct implementations (assuming we already
+have the arrays radii, chord, pitch, rake, skew):
+INCORRECT IMPLEMENTATION:
+>>> sections = [ bladex . profiles . NacaProfile ( digits = '0012' , n_points = 240 ,
+ cosine_spacing=True) for i in range(12)]
+>>> blade_1 = Blade (
+ sections=sections,
+ radii=radii,
+ chord_lengths=chord,
+ pitch=pitch,
+ rake=rake,
+ skew_angles=skew)
+>>> blade_1 . apply_transformations ()
+>>> blade_2 = Blade (
+ sections=sections,
+ radii=radii,
+ chord_lengths=chord,
+ pitch=pitch,
+ rake=rake,
+ skew_angles=skew)
+>>> blade_2 . apply_transformations ()
+
+
The previous implementation would lead into erroneous blade coordinates due
+to the transformed data in the array sections
+CORRECT IMPLEMENTATION:
+>>> sections_1 = [ bladex . profiles . NacaProfile ( digits = '0012' , n_points = 240 ,
+ cosine_spacing=True) for i in range(12)]
+>>> sections_2 = [ bladex . profiles . NacaProfile ( digits = '0012' , n_points = 240 ,
+ cosine_spacing=True) for i in range(12)]
+>>> blade_1 = Blade (
+ sections=sections_1,
+ radii=radii,
+ chord_lengths=chord,
+ pitch=pitch,
+ rake=rake,
+ skew_angles=skew)
+>>> blade_1 . apply_transformations ()
+>>> blade_2 = Blade (
+ sections=sections_2,
+ radii=radii,
+ chord_lengths=chord,
+ pitch=pitch,
+ rake=rake,
+ skew_angles=skew)
+>>> blade_2 . apply_transformations ()
+
+
+
+_abs_to_norm( D_prop ) [source]
+Private method to normalize the blade parameters.
+
+
+Parameters: D_prop (float
+
+
+
+
+
+static _check_errors( upper_face , lower_face ) [source]
+Private method to check if either the blade upper face or lower face
+is passed in the generate_iges method. Otherwise it raises an exception
+
+
+Parameters:
+upper_face (string lower_face (string
+
+
+
+
+
+
+_check_params( ) [source]
+Private method to check if all the blade arguments are numpy.ndarrays
+with the same shape.
+
+
+
+
+static _check_string( filename ) [source]
+Private method to check if the parameter type is string
+
+
+Parameters: filename (string
+
+
+
+
+
+_compute_pitch_angle( ) [source]
+Private method that computes the pitch angle from the linear pitch for
+all blade sections.
+
+
+Returns: pitch angle in radians
+Return type: numpy.ndarray
+
+
+
+
+
+_generate_lower_face( maxDeg ) [source]
+Private method to generate the blade lower face.
+
+
+Parameters: maxDeg (int
+
+
+
+
+
+_generate_tip( maxDeg ) [source]
+Private method to generate the surface that closing the blade tip.
+
+
+Parameters: maxDeg (int
+
+
+
+
+
+_generate_upper_face( maxDeg ) [source]
+Private method to generate the blade upper face.
+
+
+Parameters: maxDeg (int
+
+
+
+
+
+static _import_occ_libs( ) [source]
+Private static method to import specific modules from the OCC package.
+
+
+
+
+_induced_rake_from_skew( ) [source]
+Private method that computes the induced rake from skew for all the
+blade sections, according to mytransformation_operations .
+
+
+Returns: induced rake from skew
+Return type: numpy.ndarray
+
+
+
+
+
+_norm_to_abs( D_prop ) [source]
+Private method that converts the normalized blade parameters into the
+actual values.
+
+
+Parameters: D_prop (float
+
+
+
+
+
+_planar_to_cylindrical( ) [source]
+Private method that transforms the 2D planar airfoils into 3D
+cylindrical sections.
+The cylindrical transformation is defined by the following formulas:
+
+
+After transformation, the method also fills the numpy.ndarray
+“blade_coordinates_up” and “blade_coordinates_down” with the new
+
+
+
+
+
+_write_blade_errors( upper_face , lower_face , errors ) [source]
+Private method to write the errors between the generated foil points in
+3D space from the parametric transformations, and their projections on
+the generated blade faces from the OCC algorithm.
+
+
+Parameters:
+upper_face (string lower_face (string errors (string
+
+
+
+
+
+
+apply_transformations( reflect=True ) [source]
+Generate a bottom-up constructed propeller blade based on the airfoil
+transformations, see mytransformation_operations .
+The order of the transformation operations is as follows:
+
+
+Translate airfoils by reference points into origin.
+Scale X, Y coordinates by a factor of the chord length. Also
+reflect the airfoils if necessary.
+Rotate the airfoils counter-clockwise according to the local
+pitch angles. Beware of the orientation system.
+Translate airfoils along X-axis by a magnitude of the local
+rake. Perform another translation for the skew-induced rake.
+Translate airfoils along Y-axis by a magnitude of the skewness.
+Transform the 2D airfoils into cylindrical sections, by laying
+each foil on a cylinder of radius equals to the section radius,
+and the cylinder axis is the propeller axis of rotation.
+
+
+
+
+Parameters: reflect (bool
+
+We note that the implemented transformation operations with the current
+Cartesian coordinate system shown in mytransformation_operations
+assumes a right-handed propeller. In case of a desired left-handed
+propeller the user can either change the code for the negative
+Z-coordinates in the cylindrical transformation (i.e.
+_planar_to_cylindrical private method), or manipulating the
+orientation of the generated CAD with respect to the hub.
+
+
+
+
+export_ppg( filename='data_out.ppg' , D_prop=0.25 , D_hub=0.075 , n_blades=5 , params_normalized=False ) [source]
+Export the generated blade parameters and sectional profiles into
+.ppg format.
+
+
+Parameters:
+filename (string D_prop (float D_hub (float n_blades (float params_normalized (bool
+
+
+
+
+
+
+generate_iges( upper_face=None , lower_face=None , tip=None , maxDeg=1 , display=False , errors=None ) [source]
+Generate and export the .iges CAD for the blade upper face, lower face,
+and tip. This method requires PythonOCC to be installed.
+
+
+Parameters:
+upper_face (string lower_face (string tip (string maxDeg (int display (bool errors (string
+
+
+We note that the blade object must have its radial sections be arranged
+in order from the blade root to the blade tip, so that generate_iges
+method can build the CAD surface that passes through the corresponding
+airfoils. Also to be able to identify and close the blade tip.
+
+
+
+
+generate_stl( min_length=None , max_length=None , outfile_stl=None ) [source]
+Generate and export the .STL surface mesh for the blade as a whole,
+including the upper face, lower face and tip. The method utilizes
+modules from OCC SMESH which is standalone mesh framework based on
+SALOME mesher project. Please refer to https://github.com/tpaviot
+and http://docs.salome-platform.org/7/gui/SMESH/index.html for
+further details.
+This method requires PythonOCC and SMESH to be installed.
+
+
+Parameters:
+min_length (double ) – smallest distance between two nodes. Default
+value is Nonemax_length (double ) – largest distance between two nodes. Default
+value is Noneoutfile_stl (string
+
+
+We note that since the current implementation performs triangulation
+based on a topological compound that combines the blade 3 generated
+shapes without “fusion”, it may happen that the generated triangulation
+of the upper and lower blade faces do not share the same exact nodes
+on the joint edge/wire resulting from the faces intersection. The
+current implementation can be enough for visualization purpose. However
+if the generated mesh is intended for computational analysis then a
+manual mesh healing is recommended by the user (e.g. see
+“Repair > Sewing” in SALOME GUI) for a proper mesh closure.
+
+
+
+
+plot( elev=None , azim=None , ax=None , outfile=None ) [source]
+Plot the generated blade sections.
+
+
+Parameters:
+elev (int azim (int ax (matplotlib.axes outfile (string
+
+
+EXAMPLE:
+Assume we already have the arrays radii, chord, pitch, rake, skew for
+10 blade sections.
+>>> sections_1 = np . asarray ([ blade . NacaProfile ( digits = '0012' )
+ for i in range(10)])
+>>> blade_1 = blade . Blade ( sections = sections ,
+ radii=radii,
+ chord_lengths=chord,
+ pitch=pitch,
+ rake=rake,
+ skew_angles=skew)
+>>> blade_1 . apply_transformations ()
+
+
>>> sections_2 = np . asarray ([ blade . NacaProfile ( digits = '0012' )
+ for i in range(10)])
+>>> blade_2 = blade . Blade ( sections = sections ,
+ radii=radii,
+ chord_lengths=chord,
+ pitch=pitch,
+ rake=rake,
+ skew_angles=skew)
+>>> blade_2 . apply_transformations ()
+>>> blade_2 . rotate ( rot_angle_deg = 72 )
+
+
>>> fig = plt . figure ()
+>>> ax = fig . gca ( projection = Axes3D . name )
+>>> blade_1 . plot ( ax = ax )
+>>> blade_2 . plot ( ax = ax )
+
+
On the other hand, if we need to plot for a single blade object,
+we can just ignore such parameter, and the method will internally
+create a new instance for the figure axes, i.e.
+>>> sections = np . asarray ([ blade . NacaProfile ( digits = '0012' )
+ for i in range(10)])
+>>> blade = blade . Blade ( sections = sections ,
+ radii=radii,
+ chord_lengths=chord,
+ pitch=pitch,
+ rake=rake,
+ skew_angles=skew)
+>>> blade . apply_transformations ()
+>>> blade . plot ()
+
+
+
+
+
+rotate( deg_angle=None , rad_angle=None ) [source]
+3D counter clockwise rotation about the X-axis of the Cartesian
+coordinate system, which is the axis of rotation of the propeller hub.
+The rotation matrix,
+
+
+
+
Given the coordinates of point
+
+
+
Then, the rotated coordinates will be:
+
+
+
+
+Parameters:
+deg_angle (float rad_angle (float
+Raises: ValueError – if both rad_angle and deg_angle are inserted,
+or if neither is inserted
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
.iges
- :param string lower_face: if string is passed then the method generates
- the blade lower surface using the BRepOffsetAPI_ThruSections
- algorithm, then exports the generated CAD into .iges file holding
- the name .iges
- :param string errors: if string is passed then the method writes out
- the distances between each discrete point used to construct the
- blade and the nearest point on the CAD that is perpendicular to
- that point
- """
- from OCC.Core.gp import gp_Pnt
- from OCC.Core.BRepBuilderAPI import BRepBuilderAPI_MakeVertex
- from OCC.Core.BRepExtrema import BRepExtrema_DistShapeShape
-
- output_string = '\n'
- with open(errors + '.txt', 'w') as f:
- if upper_face:
- output_string += '########## UPPER FACE ##########\n\n'
- output_string += 'N_section\t\tN_point\t\t\tX_crds\t\t\t\t'
- output_string += 'Y_crds\t\t\t\t\tZ_crds\t\t\t\t\tDISTANCE'
- output_string += '\n\n'
- for i in range(self.n_sections):
- alength = len(self.blade_coordinates_up[i][0])
- for j in range(alength):
- vertex = BRepBuilderAPI_MakeVertex(
- gp_Pnt(
- 1000 * self.blade_coordinates_up[i][0][j],
- 1000 * self.blade_coordinates_up[i][1][j], 1000
- * self.blade_coordinates_up[i][2][j])).Vertex()
- projection = BRepExtrema_DistShapeShape(
- self.generated_upper_face, vertex)
- projection.Perform()
- output_string += str(
- i) + '\t\t\t' + str(j) + '\t\t\t' + str(
- 1000 *
- self.blade_coordinates_up[i][0][j]) + '\t\t\t'
- output_string += str(
- 1000 * self.blade_coordinates_up[i][1]
- [j]) + '\t\t\t' + str(
- 1000 * self.blade_coordinates_up[i][2]
- [j]) + '\t\t\t' + str(projection.Value())
- output_string += '\n'
-
- if lower_face:
- output_string += '########## LOWER FACE ##########\n\n'
- output_string += 'N_section\t\tN_point\t\t\tX_crds\t\t\t\t'
- output_string += 'Y_crds\t\t\t\t\tZ_crds\t\t\t\t\tDISTANCE'
- output_string += '\n\n'
- for i in range(self.n_sections):
- alength = len(self.blade_coordinates_down[i][0])
- for j in range(alength):
- vertex = BRepBuilderAPI_MakeVertex(
- gp_Pnt(
- 1000 * self.blade_coordinates_down[i][0][j],
- 1000 * self.blade_coordinates_down[i][1][j],
- 1000 *
- self.blade_coordinates_down[i][2][j])).Vertex()
- projection = BRepExtrema_DistShapeShape(
- self.generated_lower_face, vertex)
- projection.Perform()
- output_string += str(
- i) + '\t\t\t' + str(j) + '\t\t\t' + str(
- 1000 *
- self.blade_coordinates_down[i][0][j]) + '\t\t\t'
- output_string += str(
- 1000 * self.blade_coordinates_down[i][1]
- [j]) + '\t\t\t' + str(
- 1000 * self.blade_coordinates_down[i][2]
- [j]) + '\t\t\t' + str(projection.Value())
- output_string += '\n'
- f.write(output_string)
-
- def generate_solid(self):
- """
- Generate a solid blade assembling the upper face, lower face, tip and
- root using the BRepBuilderAPI_MakeSolid algorithm.
-
- :param int max_deg: Define the maximal U degree of generated surface.
- Default value is 1
- :raises RuntimeError: if the assembling of the solid blade is not
- completed successfully
- """
- from OCC.Display.SimpleGui import init_display
- from OCC.Core.TopoDS import TopoDS_Shell
- import OCC.Core.TopoDS
- from OCC.Core.BRepBuilderAPI import BRepBuilderAPI_Sewing, \
- BRepBuilderAPI_MakeSolid
-
- faces = [
- self.upper_face, self.lower_face, self.tip_face, self.root_face
- ]
-
- sewer = BRepBuilderAPI_Sewing(1e-7)
- for face in faces:
- sewer.Add(face)
- sewer.Perform()
-
- result_shell = sewer.SewedShape()
- solid_maker = BRepBuilderAPI_MakeSolid()
- solid_maker.Add(OCC.Core.TopoDS.topods.Shell(result_shell))
-
- if not solid_maker.IsDone():
- raise RuntimeError('Unsuccessful assembling of solid blade')
- result_solid = solid_maker.Solid()
-
- return result_solid
-
- def export_stl(self, filename, linear_deflection=0.1):
- """
- Generate and export the .STL file for the entire blade.
- This method requires PythonOCC (7.4.0) to be installed.
- """
- from OCC.Core.BRepBuilderAPI import BRepBuilderAPI_Sewing
- from OCC.Core.BRepMesh import BRepMesh_IncrementalMesh
- from OCC.Extend.DataExchange import write_stl_file
- from OCC.Core.StlAPI import StlAPI_Writer
-
- sewer = BRepBuilderAPI_Sewing(1e-2)
- sewer.Add(self.upper_face)
- sewer.Add(self.lower_face)
- sewer.Add(self.root_face)
- sewer.Add(self.tip_face)
- sewer.Perform()
- sewed_shape = sewer.SewedShape()
-
- triangulation = BRepMesh_IncrementalMesh(sewed_shape, linear_deflection, True)
- triangulation.Perform()
-
- writer = StlAPI_Writer()
- writer.SetASCIIMode(False)
- writer.Write(sewed_shape, filename)
-
- def _generate_leading_edge_curves(self):
- """
- Private method to generate curves that follow the leading edge of the blade
- (top and bottom surfaces).
- """
- self._import_occ_libs()
-
- # Extract points at leftmost 5% for upper and lower surfaces
- upper_points = []
- lower_points = []
-
- for i in range(self.n_sections):
- min_x = np.min(self.sections[i].xdown_coordinates)
- max_x = np.max(self.sections[i].xdown_coordinates)
- delta_x = max_x - min_x
-
- target_x = min_x + 0.95 * delta_x
-
- idx = np.abs(self.sections[i].xdown_coordinates - target_x).argmin()
-
- # Create points for upper and lower curves
- upper_points.append(gp_Pnt(
- 1000 * self.blade_coordinates_up[i][0][idx],
- 1000 * self.blade_coordinates_up[i][1][idx],
- 1000 * self.blade_coordinates_up[i][2][idx]
- ))
-
- lower_points.append(gp_Pnt(
- 1000 * self.blade_coordinates_down[i][0][idx],
- 1000 * self.blade_coordinates_down[i][1][idx],
- 1000 * self.blade_coordinates_down[i][2][idx]
- ))
-
- # Create arrays of points for interpolation
- upper_array = TColgp_HArray1OfPnt(1, len(upper_points))
- lower_array = TColgp_HArray1OfPnt(1, len(lower_points))
-
- for i, (up, low) in enumerate(zip(upper_points, lower_points)):
- upper_array.SetValue(i + 1, up)
- lower_array.SetValue(i + 1, low)
-
- # Create interpolated curves
- upper_curve = GeomAPI_Interpolate(upper_array, False, 1e-9)
- lower_curve = GeomAPI_Interpolate(lower_array, False, 1e-9)
-
- upper_curve.Perform()
- lower_curve.Perform()
-
- # Convert to edges
- self.upper_le_edge = BRepBuilderAPI_MakeEdge(upper_curve.Curve()).Edge()
- self.lower_le_edge = BRepBuilderAPI_MakeEdge(lower_curve.Curve()).Edge()
-
- def export_iges(self, filename, include_le_curves=False):
- """
- Generate and export the .IGES file for the entire blade.
- This method requires PythonOCC (7.4.0) to be installed.
- """
- from OCC.Core.IGESControl import IGESControl_Writer
-
- if include_le_curves:
- self._generate_leading_edge_curves()
-
- iges_writer = IGESControl_Writer()
- iges_writer.AddShape(self.upper_face)
- iges_writer.AddShape(self.lower_face)
- iges_writer.AddShape(self.root_face)
- iges_writer.AddShape(self.tip_face)
-
- if include_le_curves:
- iges_writer.AddShape(self.upper_le_edge)
- iges_writer.AddShape(self.lower_le_edge)
-
- iges_writer.Write(filename)
-
- @staticmethod
- def _check_string(filename):
- """
- Private method to check if the parameter type is string
-
- :param string filename: filename of the generated .iges surface
- """
- if not isinstance(filename, str):
- raise TypeError('IGES filename must be a valid string.')
-
- @staticmethod
- def _check_errors(upper_face, lower_face):
- """
- Private method to check if either the blade upper face or lower face
- is passed in the generate_iges method. Otherwise it raises an exception
-
- :param string upper_face: blade upper face.
- :param string lower_face: blade lower face.
- """
- if not (upper_face or lower_face):
- raise ValueError(
- 'Either upper_face or lower_face must not be None.')
-
- def _abs_to_norm(self, D_prop):
- """
- Private method to normalize the blade parameters.
-
- :param float D_prop: propeller diameter
- """
- self.radii = self.radii * 2. / D_prop
- self.chord_lengths = self.chord_lengths / D_prop
- self.pitch = self.pitch / D_prop
- self.rake = self.rake / D_prop
-
- def _norm_to_abs(self, D_prop):
- """
- Private method that converts the normalized blade parameters into the
- actual values.
-
- :param float D_prop: propeller diameter
- """
- self.radii = self.radii * D_prop / 2.
- self.chord_lengths = self.chord_lengths * D_prop
- self.pitch = self.pitch * D_prop
- self.rake = self.rake * D_prop
-
- def export_ppg(self,
- filename='data_out.ppg',
- D_prop=0.25,
- D_hub=0.075,
- n_blades=5,
- params_normalized=False):
- """
- Export the generated blade parameters and sectional profiles into
- .ppg format.
-
- :param string filename: name of the exported file. Default is
- 'data/data_out.ppg'
- :param float D_prop: propeller diameter
- :param float D_hub: hub diameter
- :param float n_blades: number of blades
- :param bool params_normalized: since the standard .ppg format contains
- the blade parameters in the normalized form, therefore the user
- needs to inform whether the provided parameters (from the class
- Blade) are normalized or not. By default the argument is set to
- False, which assumes the user provides the blade parameters in
- their actual values, i.e. not normalized, hence a normalization
- operation needs to be applied so as to follow the .ppg standard
- format.
- """
- thickness = np.zeros(self.n_sections)
- camber = np.zeros(self.n_sections)
- for i, section in enumerate(self.sections):
- # Evaluate maximum profile thickness and camber for each section.
- # We assume at the current step, that sectional profiles already
- # have the coordinates (x_up,x_down) normalized by chord length (C)
- # and subsequently (y_up,y_down) are also scaled. This implies that
- # the computed thickness and camber are given in their normalized
- # form, i.e. thickness=t/C and camber=f/C.
- thickness[i] = section.max_thickness()
- camber[i] = section.max_camber()
-
- if params_normalized is False:
- # Put the parameters (radii, chord, pitch, rake) in the normalized
- # form.
- self._abs_to_norm(D_prop=D_prop)
-
- output_string = ""
- output_string += 'propeller id = SVA\n'
- output_string += 'propeller diameter = ' + str(D_prop) + '\n'
- output_string += 'hub diameter = ' + str(D_hub) + '\n'
- output_string += 'number of blades = ' + str(n_blades) + '\n'
- output_string += "'Elica PPTC workshop'\n"
- output_string += 'number of radial sections = ' + str(
- self.n_sections) + '\n'
- output_string += 'number of radial sections = ' + str(
- self.n_sections) + '\n'
- output_string += 'number of sectional profiles = ' + str(
- self.n_sections) + '\n'
- output_string += 'description of sectional profiles = BNF\n'
- output_string += ' r/R c/D skew[deg]'\
- ' rake/D P/D t/C'\
- ' f/C\n'
- for i in range(self.n_sections):
- output_string += ' ' + str("%.8e" % self.radii[i]) + ' ' + str(
- "%.8e" % self.chord_lengths[i]) + ' ' + str(
- "%.8e" % self.skew_angles[i]) + ' ' + str(
- "%.8e" % self.rake[i])
- output_string += ' ' + str("%.8e" % self.pitch[i]) + ' ' + str(
- "%.8e" % thickness[i]) + ' ' + str("%.8e" % camber[i]) + '\n'
-
- for i in range(self.n_sections):
- output_string += str("%.8e" % self.radii[i]) + ' ' + str(
- len(self.sections[i].xup_coordinates)) + '\n'
-
- for value in self.sections[i].xup_coordinates:
- output_string += ' ' + str("%.8e" % value)
- output_string += ' \n'
- for value in self.sections[i].yup_coordinates:
- output_string += ' ' + str("%.8e" % value)
- output_string += ' \n'
- for value in self.sections[i].ydown_coordinates:
- output_string += ' ' + str("%.8e" % value)
- output_string += ' \n'
-
- hub_offsets = np.asarray(
- [[-3.0, 0.305], [-0.57, 0.305], [-0.49, 0.305], [-0.41, 0.305],
- [-0.33, 0.305], [-0.25, 0.305], [-0.17, 0.305], [0.23, 0.305],
- [0.31, 0.285], [0.39, 0.2656], [0.47, 0.2432], [0.55, 0.2124],
- [0.63, 0.1684], [0.71, 0.108], [0.79, 0.0]])
-
- output_string += 'number of Hub offsets = ' + str(
- len(hub_offsets)) + '\n'
-
- for i, offset in enumerate(hub_offsets):
- if i == len(hub_offsets) - 1:
- output_string += str("%.8e" % offset[0]) + ' ' + str(
- "%.8e" % hub_offsets[i][1])
-
- continue
- output_string += str("%.8e" % offset[0]) + ' ' + str(
- "%.8e" % offset[1]) + '\n'
-
- with open(filename, 'w') as f:
- f.write(output_string)
-
- if params_normalized is False:
- # Revert back normalized parameters into actual values.
- self._norm_to_abs(D_prop=D_prop)
-
- def __str__(self):
- """
- This method prints all the parameters on the screen. Its purpose is
- for debugging.
- """
- string = ''
- string += 'Blade number of sections = {}'.format(self.n_sections)
- string += '\nBlade radii sections = {}'.format(self.radii)
- string += '\nChord lengths of the sectional profiles'\
- ' = {}'.format(self.chord_lengths)
- string += '\nRadial distribution of the pitch (in unit lengths)'\
- ' = {}'.format(self.pitch)
- string += '\nRadial distribution of the rake (in unit length)'\
- ' = {}'.format(self.rake)
- string += '\nRadial distribution of the skew angles'\
- ' (in degrees) = {}'.format(self.skew_angles)
- string += '\nPitch angles (in radians) for the'\
- ' sections = {}'.format(self.pitch_angles)
- string += '\nInduced rake from skew (in unit length)'\
- ' for the sections = {}'.format(self.induced_rake)
- return string
-
- def display(self):
- """
- Display the propeller with shaft.
- """
- from OCC.Display.SimpleGui import init_display
- display, start_display = init_display()[:2]
- display.DisplayShape(self.upper_face, update=True)
- display.DisplayShape(self.lower_face, update=True)
- display.DisplayShape(self.root_face, update=True)
- display.DisplayShape(self.tip_face, update=True)
- start_display()
\ No newline at end of file
diff --git a/bladex/deform.py b/bladex/deform.py
deleted file mode 100644
index 1fdda05..0000000
--- a/bladex/deform.py
+++ /dev/null
@@ -1,533 +0,0 @@
-"""
-Module to deform blade's parameters, based on a given parameter file.
-"""
-
-import numpy as np
-import matplotlib.pyplot as plt
-from .ndinterpolator import reconstruct_f, scipy_bspline
-from .params import ParamFile
-
-
-class Deformation(object):
- """
- Deform parameter curves {chord, pitch, rake, skew, camber} according to
- specific information passed through a parameter file.
-
- The module contains several methods that are able to:
-
- 1. compute coordinates of the optimal control points, provided their
- number from the parameter file.
-
- 2. update control points Y coordinates, provided the magnitude of the
- Y deformation from the parameter file.
-
- 3. generate B-spline curve using the computed control points (before or
- after their deformation), provided npoints from the parameter file
- for spline estimation.
-
- 4. plot parametric curves, with several options. Finally export a new
- parameter file containing the new deformed parameters.
-
- :param str paramfile: parameter file name
- :cvar str paramfile: parameter file name
- :cvar class param: class object instantiated by the module params, and
- contains all the attributes assigned by reading the parameter file.
- Possible attributes are:
-
- - `param.radii`
- - `param.parameters`
- - `param.nbasis`
- - `param.degree`
- - `param.deformations`
-
- First attribute is array defines the radial sections, while the
- remaining attributes are dictionaries with possible keys: `chord`,
- `pitch`, `rake`, `skew`, `camber`.
-
- :cvar dict deformed_parameters: dictionary that contains the deformed
- parameters at the same radial sections, provided some tolerance due to
- the spline interpolation. Possible dictionary keys are the parameters
- `chord`, `pitch`, `rake`, `skew`, `camber`. Default value is array of
- zeros with length equal to the radial sections.
- :cvar dict control_points: dictionary that contains the 2D coordinates of
- the control points associated with the B-spline parametric curve. The
- dictionary possible keys are the parameters `chord`, `pitch`, `rake`,
- `skew`, `camber`. Default value is None
- :cvar dict spline: dictionary that contains the B-spline interpolation for
- the parametric curves. The dictionary possible keys are the parameters
- `chord`, `pitch`, `rake`, `skew`, `camber`. Each value is a 2D numpy
- array containing the radii interpolations against the interpolations
- for one of the parameters mentioned in the dictionary keys. Default
- value is None.
- """
-
- def __init__(self, paramfile):
- self.paramfile = paramfile
- self.param = ParamFile()
- self.param.read_parameters(filename=paramfile)
- self.deformed_parameters = {
- 'chord': np.zeros(self.param.radii.size),
- 'pitch': np.zeros(self.param.radii.size),
- 'rake': np.zeros(self.param.radii.size),
- 'skew': np.zeros(self.param.radii.size),
- 'camber': np.zeros(self.param.radii.size)
- }
- self.control_points = {
- 'chord': None,
- 'pitch': None,
- 'rake': None,
- 'skew': None,
- 'camber': None
- }
- self.spline = {
- 'chord': None,
- 'pitch': None,
- 'rake': None,
- 'skew': None,
- 'camber': None
- }
-
- @staticmethod
- def _optimum_control_points(X, Y, degree, nbasis, rbf_points):
- """
- Private static method that computes the optimum coordinates of the
- B-spline control points.
-
- :param array_like X: Array of original points of the parametric curve
- X-axis, usually array of the radii sections
- :param array_like Y: radial distribution of parameter `chord` or
- `pitch` or `rake` or `skew` or `camber`, corresponding to the
- radial sections in X
- :param int degree: degree of the B-spline construction for the
- parametric curve
- :param int nbasis: number of control points associated with the
- parametric curve
- :param int rbf_points: if specified greater than zero, then the X and Y
- arrays are interpolated using the Wendland C2 radial basis function
- to produce X and Y arrays with length = rbf_points. The larger
- number of rbf_points implies better estimation of the optimum
- control coordinates. To turn it off (i.e. compute control points
- based on original X, Y arrays) then insert 0. (Negative values or
- None results in same effect as zero)
- :return: control points 2D coordinates
- :rtype: numpy.ndarray
- """
- if not isinstance(rbf_points, int):
- # in case inserted as None, then converts to zero,
- # otherwise returns the inserted value. Useful when dealing with
- # the parameter as a flag
- rbf_points = int(rbf_points or 0)
-
- if rbf_points > 0:
- xx = np.linspace(X[0], X[-1], num=rbf_points)
- yy = np.zeros(rbf_points)
- reconstruct_f(
- original_input=X,
- original_output=Y,
- rbf_input=xx,
- rbf_output=yy,
- basis='beckert_wendland_c2_basis',
- radius=2.0)
- X = xx
- Y = yy
-
- A = np.zeros((len(X), nbasis))
- At = np.zeros((len(X), nbasis - 2))
-
- for i in range(nbasis):
- cv_new = np.zeros((nbasis, 3))
- cv_new[i, 0] = 1.
- # i-th basis function in the reference space
- A[:, i] = scipy_bspline(cv_new, A.shape[0], degree)[:, 0]
-
- # A tilde for the constraints on the first and last point
- At = A[:, 1:-1]
- # x and y of the ctrl points with constrained least square.
- # we subtract the contribution of the first and last basis function
- cvt_x = np.linalg.lstsq(
- At, X - A[:, 0] * X[0] - A[:, -1] * X[-1], rcond=-1)[0]
- cvt_y = np.linalg.lstsq(
- At, Y - A[:, 0] * Y[0] - A[:, -1] * Y[-1], rcond=-1)[0]
-
- # fill with the constraints the first and last point
- opt_ctrl = np.zeros((nbasis, 2))
- opt_ctrl[0, 0] = X[0]
- opt_ctrl[-1, 0] = X[-1]
- opt_ctrl[0, 1] = Y[0]
- opt_ctrl[-1, 1] = Y[-1]
- opt_ctrl[1:-1, 0] = cvt_x
- opt_ctrl[1:-1, 1] = cvt_y
-
- return opt_ctrl
-
- @staticmethod
- def _check_param(param):
- """
- Private static method that checks the passed parameter.
-
- :param str param: passed parameter to check. Valid values
- are: `chord`, `pitch`, `rake`, `skew`, `camber`
- :raises ValueError: if the param value is not one of the previous
- """
- params = ['chord', 'pitch', 'rake', 'skew', 'camber']
- if not param in params:
- raise ValueError(
- 'Valid param values are: "chord", "pitch", "rake", "skew",'\
- ' "camber".')
-
- def _check_control_points(self, param):
- """
- Private method to check if control points are computed.
-
- :param str param: passed parameter to check. Valid values
- are: `chord`, `pitch`, `rake`, `skew`, `camber`
- :raises ValueError: if the control points have None value, i.e. not
- computed
- """
- if self.control_points[param] is None:
- raise ValueError(
- 'control_points has None value. You must compute them first.')
-
- def _check_spline(self, param):
- """
- Private method to check if spline interpolation is computed.
-
- :param str param: passed parameter to check. Valid values
- are: `chord`, `pitch`, `rake`, `skew`, `camber`
- :raises ValueError: if the spline of that parameter curve has None
- value, i.e. not computed
- """
- if self.spline[param] is None:
- raise ValueError(
- param + ' spline is None. You must first generate spline.')
-
- def _check_deformed(self, param):
- """
- Private method to check if the deformed parameters are computed.
-
- :param str param: passed parameter to check. Valid values
- are: `chord`, `pitch`, `rake`, `skew`, `camber`
- :raises ValueError: if the deformed parameters have array of zeros,
- i.e. not computed
- """
- if self.deformed_parameters[param].all() == 0:
- raise ValueError(param + ' deformed points are not computed.')
-
- def compute_control_points(self, param, rbf_points=1000):
- """
- Compute the control points 2D coordinates for one of the parametric
- curves.
-
- :param str param: parameter corresponding to the parametric curve.
- possible values are `chord`, `pitch`, `rake`, `skew`, `camber`
- :param int rbf_points: if greater than zero then the Wendland C2 radial
- basis function is used to interpolate the original arrays for the
- parametric curve, so that the control points are computed according
- to the interpolated arrays. Needless to mention that longer arrays
- would produce better estimation of the control points optimum
- coordinates. In order to turn off the rbf interpolation: specify
- either 0 or -1 (Also a None value can be used too). Default value
- is 1000
- """
- self._check_param(param=param)
- self.control_points[param] = self._optimum_control_points(
- X=self.param.radii,
- Y=self.param.parameters[param],
- degree=self.param.degree[param],
- nbasis=self.param.nbasis[param],
- rbf_points=rbf_points)
-
- def update_control_points(self, param):
- """
- Update the control point Y coordinate with the deformation values
- specified in the parameter file.
-
- :param str param: parameter corresponding to the parametric curve.
- possible values are `chord`, `pitch`, `rake`, `skew`, `camber`
- """
- self._check_param(param=param)
- self._check_control_points(param=param)
-
- if not self.control_points[param].shape[0] == len(
- self.param.deformations[param]):
- raise ValueError(
- 'array of deformations must equal to number of control points')
-
- for i in range(self.control_points[param].shape[0]):
- self.control_points[param][i, 1] += self.param.deformations[param][
- i]
-
- def generate_spline(self, param):
- """
- Generate the B-spline interpolations, using the information: `degree`,
- `npoints` from the parameter file, as well as the computed 2D
- coordinates of the control points.
-
- :param str param: parameter corresponding to the parametric curve.
- possible values are `chord`, `pitch`, `rake`, `skew`, `camber`
- """
- self._check_param(param=param)
- self._check_control_points(param=param)
-
- self.spline[param] = scipy_bspline(
- cv=self.control_points[param],
- npoints=self.param.npoints[param],
- degree=self.param.degree[param])
-
- def compute_deformed_parameters(self, param, tol=1e-3):
- """
- This method uses the spline npoints interpolation of the parametric
- curve to extract the parameters corresponding to the radial
- distribution of the original undeformed array. Therefore the resulting
- deformed parameters should be arrays of same length like that of the
- original parameters.
-
- :param str param: parameter corresponding to the parametric curve.
- possible values are `chord`, `pitch`, `rake`, `skew`, `camber`
- :param float tol: tolerance required to find the B-spline estimation
- within the neighborhood of each of the radii sections. It is
- important to specify the value carefully as it depends on the order
- of the original array values, as well as the number of points for
- the spline interpolations. Default value is 1e-3
- """
- self._check_param(param=param)
- self._check_spline(param=param)
-
- for i, val in enumerate(self.param.radii):
- index = np.where(np.fabs(self.spline[param][:, 0] - val) < tol)[0]
- if len(index) == 0:
- raise ValueError(
- 'Could not compute deformed parameter "' + param +
- '" at radius "' + str(val) +
- '". Either increase the tolerance for that parameter, or'\
- ' increase the spline npoints in the parameter file.'
- )
- if index.shape[0] > 1:
- # In case more neighbors are found, then take first value only.
- index = index[0]
- self.deformed_parameters[param][i] = self.spline[param][index, 1].item()
-
- def compute_all(self,
- rbf_points=1000,
- tol_chord=1e-3,
- tol_pitch=1e-3,
- tol_rake=1e-3,
- tol_skew=1e-3,
- tol_camber=1e-3):
- """
- Computes everything:
- - control points 2D coordinates
- - deformed control points
- - spline npoints interpolations
- - deformed parameters of the original arrays
-
- The previous procedure is applied for all the parameters: `chord`,
- `pitch`, `rake`, `skew`, `camber`
-
- :param int rbf_points: if greater than zero then the Wendland C2 radial
- basis function is used to interpolate the original arrays for the
- parametric curve, so that the control points are computed according
- to the interpolated arrays. Needless to mention that longer arrays
- would produce better estimation of the control points optimum
- coordinates. In order to turn off the rbf interpolation then
- specify either 0 or -1 (Also a None value can be used too). Default
- value is 1000
- :param float tol_chord: tolerance used to extract the chord radial
- distribution for the deformed B-spline interpolation. Default value
- is 1e-3
- :param float tol_pitch: tolerance used to extract the pitch radial
- distribution for the deformed B-spline interpolation. Default value
- is 1e-3
- :param float tol_rake: tolerance used to extract the rake radial
- distribution for the deformed B-spline interpolation. Default value
- is 1e-3
- :param float tol_skew: tolerance used to extract the skew radial
- distribution for the deformed B-spline interpolation. Default value
- is 1e-3
- :param float tol_camber: tolerance used to extract the camber radial
- distribution for the deformed B-spline interpolation. Default value
- is 1e-3
-
- """
- tols = {
- 'chord': tol_chord,
- 'pitch': tol_pitch,
- 'rake': tol_rake,
- 'skew': tol_skew,
- 'camber': tol_camber
- }
- params = ['chord', 'pitch', 'rake', 'skew', 'camber']
- for param in params:
- self.compute_control_points(param=param, rbf_points=rbf_points)
- self.update_control_points(param=param)
- self.generate_spline(param=param)
- self.compute_deformed_parameters(param=param, tol=tols[param])
-
- def _plot_parametric_curve(self,
- param,
- original=True,
- ctrl_points=True,
- spline=True,
- rbf=False,
- rbf_points=500,
- deformed=False,
- outfile=None):
- """
- Private method to plot the parametric curve. Several options
- can be specified.
-
- :param str param: parameter corresponding to the parametric curve
- needs to be plotted. possible values are `chord`, `pitch`, `rake`,
- `skew`, `camber`
- :param bool original: if True, then plot the original points of the
- parameter at the radii sections.
- :param bool ctrl_points: if True, then plot the control points of
- that parametric curve.
- :param bool spline: If True, then plot the B-spline interpolation of
- the parametric curve.
- :param bool rbf: if True, then plot the radial basis functions
- interpolation of the parametric curve.
- :param int rbf_points: number of points used for the rbf interpolation,
- if the flag `rbf` is set True. Beware that this argument does not
- have the same function of that when computing the control points,
- although both uses the radial basis function interpolation with
- the Wendland basis.
- :param bool deformed: if True, then plot the deformed points of the
- parameter radial distribution, estimated using the B-spline
- interpolations within a given tolerance.
- :param str outfile: if string is passed, then the plot is saved
- with that name. If the value is None, then the plot is shown on
- the screen.
- """
- self._check_param(param=param)
-
- plt.figure()
-
- if original:
- plt.plot(
- self.param.radii,
- self.param.parameters[param],
- 'o',
- label='original points')
-
- if ctrl_points:
- self._check_control_points(param=param)
- plt.plot(
- self.control_points[param][:, 0],
- self.control_points[param][:, 1],
- '*-',
- label='control points')
-
- if spline:
- self._check_spline(param=param)
- plt.plot(
- self.spline[param][:, 0],
- self.spline[param][:, 1],
- label='spline')
-
- if rbf:
- xx = np.linspace(
- self.param.radii[0], self.param.radii[-1], num=rbf_points)
- yy = np.zeros(rbf_points)
- reconstruct_f(
- original_input=self.param.radii,
- original_output=self.param.parameters[param],
- rbf_input=xx,
- rbf_output=yy,
- basis='beckert_wendland_c2_basis',
- radius=2.0)
- plt.plot(xx, yy, label='rbf')
-
- if deformed:
- self._check_deformed(param=param)
- plt.plot(
- self.param.radii,
- self.deformed_parameters[param],
- '+',
- label='deformed points')
-
- plt.grid(linestyle='dotted')
- plt.title(param + ' curve')
- plt.legend()
-
- if outfile:
- if not isinstance(outfile, str):
- raise ValueError('Output file name must be string.')
- plt.savefig(outfile)
- else:
- plt.show()
-
- def plot(self,
- param,
- original=True,
- ctrl_points=True,
- spline=True,
- rbf=False,
- rbf_points=500,
- deformed=False,
- outfile=None):
- """
- Plot the parametric curve. Several options
- can be specified.
-
- :param array_like param: array_like of strings corresponding to the
- parametric curve that needs to be plotted. possible values are
- `chord`, `pitch`, `rake`, `skew`, `camber`
- :param bool original: if True, then plot the original points of the
- parameter at the radii sections. Default value is True
- :param bool ctrl_points: if True, then plot the control points of
- that parametric curve. Default value is True
- :param bool spline: If True, then plot the B-spline interpolation of
- the parametric curve. Default value is True
- :param bool rbf: if True, then plot the radial basis functions
- interpolation of the parametric curve. Default value is True
- :param int rbf_points: number of points used for the rbf interpolation,
- if the flag `rbf` is set True. Beware that this argument does not
- have the same function of that when computing the control points,
- although both uses the radial basis function interpolation with
- the Wendland basis. Default value is 500
- :param bool deformed: if True, then plot the deformed points of the
- parameter radial distribution, estimated using the B-spline
- interpolations within a given tolerance. Default value is False
- :param str outfile: if string is passed, then the plot is saved
- with that name. If the value is None, then the plot is shown on
- the screen. Default value is None
- """
- if not isinstance(param, (list, tuple, np.ndarray)):
- param = [param]
-
- for par in param:
- self._plot_parametric_curve(
- param=par,
- original=original,
- ctrl_points=ctrl_points,
- spline=spline,
- rbf=rbf,
- rbf_points=rbf_points,
- deformed=deformed,
- outfile=outfile)
-
- def export_param_file(self, outfile='parameters_mod.prm'):
- """
- Export a new parameter file with the new deformed parameters, while
- all other values are kept the same as in the original parameter file
- with the undeformed parameters. In the new parameter file (i.e. with
- deformed parameters) the deformations arrays become array of zeros.
-
- :param str outfile: file name to be written out
- """
-
- prm = ParamFile()
- prm.radii = self.param.radii
- params = ['chord', 'pitch', 'rake', 'skew', 'camber']
- for param in params:
- if np.all(self.param.deformations[param] == 0):
- prm.parameters[param] = self.param.parameters[param]
- else:
- prm.parameters[param] = self.deformed_parameters[param]
- prm.nbasis[param] = self.param.nbasis[param]
- prm.degree[param] = self.param.nbasis[param]
- prm.npoints[param] = self.param.npoints[param]
- prm.deformations[param] = np.zeros(self.param.nbasis[param])
-
- prm.write_parameters(filename=outfile)
diff --git a/bladex/genericsolid.py b/bladex/genericsolid.py
deleted file mode 100644
index 65d6034..0000000
--- a/bladex/genericsolid.py
+++ /dev/null
@@ -1,11 +0,0 @@
-"""
-Module for the blade bottom-up parametrized construction.
-"""
-import numpy as np
-import matplotlib.pyplot as plt
-from mpl_toolkits.mplot3d import Axes3D
-
-class GenericSolid:
-
- def __init__(self, *args, **kwds):
- pass
\ No newline at end of file
diff --git a/bladex/intepolatedface.py b/bladex/intepolatedface.py
deleted file mode 100644
index df40a06..0000000
--- a/bladex/intepolatedface.py
+++ /dev/null
@@ -1,55 +0,0 @@
-"""
-Module for the blade bottom-up parametrized construction.
-"""
-import numpy as np
-import matplotlib.pyplot as plt
-from mpl_toolkits.mplot3d import Axes3D
-from OCC.Core.BRepOffsetAPI import BRepOffsetAPI_ThruSections
-from OCC.Core.gp import gp_Pnt
-from OCC.Core.TColgp import TColgp_HArray1OfPnt
-from OCC.Core.GeomAPI import GeomAPI_Interpolate
-from OCC.Core.BRepBuilderAPI import BRepBuilderAPI_MakeVertex,\
- BRepBuilderAPI_MakeEdge, BRepBuilderAPI_MakeWire,\
- BRepBuilderAPI_Sewing, BRepBuilderAPI_MakeSolid
-
-class InterpolatedFace:
-
- def __init__(self, pts, max_deg=1, tolerance=1e-6):
-
- print(pts.shape)
- if pts.ndim not in [2, 3]:
- raise ValueError("pts must be a 2D or 3D array.")
-
- if pts.ndim == 2:
- pts = pts[None, :, :]
-
- if pts.shape[1] != 3:
- raise ValueError("Each point must have 3 coordinates for X, Y, Z.")
-
- self.max_deg = max_deg
- self.tolerance = tolerance
-
- generator = BRepOffsetAPI_ThruSections(False, False, tolerance)
- generator.SetMaxDegree(max_deg)
-
- for id_section, section in enumerate(pts):
- vertices = TColgp_HArray1OfPnt(1, section.shape[1])
- for id_pt, pt in enumerate(section.T, start=1):
- vertices.SetValue(id_pt, gp_Pnt(*pt))
-
- # Initializes an algorithm for constructing a constrained
- # BSpline curve passing through the points of the blade last
- # section
- bspline = GeomAPI_Interpolate(vertices, False, tolerance)
- bspline.Perform()
-
- edge = BRepBuilderAPI_MakeEdge(bspline.Curve()).Edge()
-
- if id_section == 0:
- root_edge = edge
-
- # Add BSpline wire to the generator constructor
- generator.AddWire(BRepBuilderAPI_MakeWire(edge).Wire())
-
- generator.Build()
- self.face = generator.GeneratedFace(root_edge)
\ No newline at end of file
diff --git a/bladex/ndinterpolator.py b/bladex/ndinterpolator.py
deleted file mode 100644
index 3a97d9d..0000000
--- a/bladex/ndinterpolator.py
+++ /dev/null
@@ -1,272 +0,0 @@
-import numpy as np
-from scipy.spatial.distance import cdist
-from scipy.interpolate import splev
-
-
-class RBF(object):
- """
- .. _ndinterpolator-label:
-
- RBF ndinterpolator
- ======================
-
- Module focused on the implementation of the Radial Basis Functions
- interpolation technique. This technique is still based on the use of
- a set of parameters, the so-called control points, as for FFD, but RBF
- is interpolatory. Another important key point of RBF strategy relies in
- the way we can locate the control points: in fact, instead of FFD where
- control points need to be placed inside a regular lattice, with RBF we
- havo no more limitations. So we have the possibility to perform localized
- control points refiniments.
-
- :Theoretical Insight:
- As reference please consult M.D. Buhmann, Radial Basis Functions,
- volume 12 of Cambridge monographs on applied and computational
- mathematics. Cambridge University Press, UK, 2003. This implementation
- follows D. Forti and G. Rozza, Efficient geometrical parametrization
- techniques of interfaces for reduced order modelling: application to
- fluid-structure interaction coupling problems, International Journal
- of Computational Fluid Dynamics.
-
- RBF shape parametrization technique is based on the definition of a map
- :math:`\\mathcal{M}(\\boldsymbol{x}) : \\mathbb{R}^n \\rightarrow
- \\mathbb{R}^n`, that allows the possibility of transferring data across
- non-matching grids and facing the dynamic mesh handling. The map
- introduced is defines as follows
-
- .. math::
- \\mathcal{M}(\\boldsymbol{x}) = p(\\boldsymbol{x}) +
- \\sum_{i=1}^{\\mathcal{N}_C} \\gamma_i
- \\varphi(\\| \\boldsymbol{x} - \\boldsymbol{x_{C_i}} \\|)
-
- where :math:`p(\\boldsymbol{x})` is a low_degree polynomial term,
- :math:`\\gamma_i` is the weight, corresponding to the a-priori selected
- :math:`\\mathcal{N}_C` control points, associated to the :math:`i`-th
- basis function, and :math:`\\varphi(\\| \\boldsymbol{x} -
- \\boldsymbol{x_{C_i}} \\|)` a radial function based on the Euclidean
- distance between the control points position :math:`\\boldsymbol{x_{C_i}}`
- and :math:`\\boldsymbol{x}`. A radial basis function, generally, is a
- real-valued function whose value depends only on the distance from the
- origin, so that :math:`\\varphi(\\boldsymbol{x}) = \\tilde{\\varphi}(
- \\|\\boldsymbol{x} \\|)`.
-
- The matrix version of the formula above is:
-
- .. math::
- \\mathcal{M}(\\boldsymbol{x}) = \\boldsymbol{c} +
- \\boldsymbol{Q}\\boldsymbol{x} +
- \\boldsymbol{W^T}\\boldsymbol{d}(\\boldsymbol{x})
-
- The idea is that after the computation of the weights and the
- polynomial terms from the coordinates of the control points before and
- after the deformation, we can deform all the points of the mesh
- accordingly. Among the most common used radial basis functions for
- modelling 2D and 3D shapes, we consider Gaussian splines, Multi-
- uadratic biharmonic splines, Inverted multi-quadratic biharmonic
- splines, Thin-plate splines, Beckert and Wendland :math:`C^2` basis all
- defined and implemented below.
-
- :param string basis: RBF basis function
- :param float radius: cut-off radius
-
- """
-
- def __init__(self, basis, radius):
- self.bases = {
- 'gaussian_spline':
- self.gaussian_spline,
- 'multi_quadratic_biharmonic_spline':
- self.multi_quadratic_biharmonic_spline,
- 'inv_multi_quadratic_biharmonic_spline':
- self.inv_multi_quadratic_biharmonic_spline,
- 'thin_plate_spline':
- self.thin_plate_spline,
- 'beckert_wendland_c2_basis':
- self.beckert_wendland_c2_basis
- }
-
- if basis in self.bases:
- self.basis = self.bases[basis]
- else:
- raise NameError(
- """The name of the basis function is not correct. Check
- the documentation for all the available functions.""")
-
- self.radius = radius
-
- # The following static methods are the implementations
- # of the most common radial basis functions
- @staticmethod
- def gaussian_spline(X, r):
- """
- It implements the following formula:
-
- .. math::
- \\varphi(\\| \\boldsymbol{x} \\|) =
- e^{-\\frac{\\| \\boldsymbol{x} \\|^2}{r^2}}
-
- :param numpy.ndarray X: l2-norm between given inputs of a function
- and the locations to perform rbf approximation to that function.
- :param float r: smoothing length, also called the cut-off radius.
-
- :return: result: the result of the formula above.
- :rtype: float
- """
- return np.exp(-(X * X) / (r * r))
-
- @staticmethod
- def multi_quadratic_biharmonic_spline(X, r):
- """
- It implements the following formula:
-
- .. math::
- \\varphi(\\| \\boldsymbol{x} \\|) =
- \\sqrt{\\| \\boldsymbol{x} \\|^2 + r^2}
-
- :param numpy.ndarray X: l2-norm between given inputs of a function
- and the locations to perform rbf approximation to that function.
- :param float r: smoothing length, also called the cut-off radius.
-
- :return: result: the result of the formula above.
- :rtype: float
- """
- return np.sqrt((X * X) + (r * r))
-
- @staticmethod
- def inv_multi_quadratic_biharmonic_spline(X, r):
- """
- It implements the following formula:
-
- .. math::
- \\varphi(\\| \\boldsymbol{x} \\|) =
- (\\| \\boldsymbol{x} \\|^2 + r^2 )^{-\\frac{1}{2}}
-
- :param numpy.ndarray X: l2-norm between given inputs of a function
- and the locations to perform rbf approximation to that function.
- :param float r: smoothing length, also called the cut-off radius.
-
- :return: result: the result of the formula above.
- :rtype: float
- """
- return 1.0 / (np.sqrt((X * X) + (r * r)))
-
- @staticmethod
- def thin_plate_spline(X, r):
- """
- It implements the following formula:
-
- .. math::
- \\varphi(\\| \\boldsymbol{x} \\|) =
- \\left\\| \\frac{\\boldsymbol{x} }{r} \\right\\|^2
- \\ln \\left\\| \\frac{\\boldsymbol{x} }{r} \\right\\|
-
- :param numpy.ndarray X: l2-norm between given inputs of a function
- and the locations to perform rbf approximation to that function.
- :param float r: smoothing length, also called the cut-off radius.
-
- :return: result: the result of the formula above.
- :rtype: float
- """
- arg = X / r
- result = arg * arg
- result = np.where(arg > 0, result * np.log(arg), result)
- return result
-
- @staticmethod
- def beckert_wendland_c2_basis(X, r):
- """
- It implements the following formula:
-
- .. math::
- \\varphi(\\| \\boldsymbol{x} \\|) =
- \\left( 1 - \\frac{\\| \\boldsymbol{x} \\|}{r} \\right)^4 +
- \\left( 4 \\frac{\\| \\boldsymbol{x} \\|}{r} + 1 \\right)
-
- :param numpy.ndarray X: l2-norm between given inputs of a function
- and the locations to perform rbf approximation to that function.
- :param float r: smoothing length, also called the cut-off radius.
-
- :return: result: the result of the formula above.
- :rtype: float
- """
- arg = X / r
- first = np.where((1 - arg) > 0, np.power((1 - arg), 4), 0)
- second = (4 * arg) + 1
- return first * second
-
- def weights_matrix(self, X1, X2):
- """
- This method returns the following matrix:
-
- .. math::
- \\boldsymbol{D_{ij}} = \\varphi(\\| \\boldsymbol{x_i} -
- \\boldsymbol{y_j} \\|)
-
- :param numpy.ndarray X1: the vector x in the formula above.
- :param numpy.ndarray X2: the vector y in the formula above.
-
- :return: matrix: the matrix D.
- :rtype: numpy.ndarray
- """
- if X1.size == X1.shape[0]:
- X1 = X1.reshape(-1, 1)
- if X2.size == X2.shape[0]:
- X2 = X2.reshape(-1, 1)
- return self.basis(cdist(X1, X2), self.radius)
-
-
-def reconstruct_f(original_input, original_output, rbf_input, rbf_output, basis,
- radius):
- """
- Reconstruct a function by using the radial basis function approximations.
-
- :param array_like original_input: the original values of function inputs.
- :param array_like original_output: the original values of function output.
- :param array_like rbf_input: the input data for RBF approximation.
- :param array_like rbf_output: the array elements to be updated with the RBF
- interpolated outputs after the approximation.
- :param string basis: radial basis function.
- :param float radius: smoothing length, also called the cut-off radius.
-
- :Example:
- >>> import numpy as np
- >>> from bladex.ndinterpolator import reconstruct_f
- >>> x = np.arange(10)
- >>> y = np.square(x)
- >>> radius = 10
- >>> n_interp = 50
- >>> x_rbf = np.linspace(x[0], x[-1], num=n_interp)
- >>> y_rbf = np.zeros(n_interp)
- >>> reconstruct_f(original_input=x, original_output=y, rbf_input=x_rbf,
- rbf_output=y_rbf, radius=radius, basis='beckert_wendland_c2_basis')
-
- """
- radial = RBF(basis=basis, radius=radius)
-
- weights_coeff = np.linalg.solve(
- radial.weights_matrix(original_input, original_input), original_output)
-
- weights_rbf = radial.weights_matrix(rbf_input, original_input)
-
- for i in range(rbf_input.shape[0]):
- for j in range(original_input.shape[0]):
- rbf_output[i] += weights_coeff[j] * weights_rbf[i][j]
-
-
-def scipy_bspline(cv, npoints, degree):
- """
- Construct B-Spline curve via the control points.
-
- :param array_like cv: control points vector (spline coefficients).
- :param int npoints: number of points on the curve.
- :param int degree: BSpline degree.
- """
- c = cv.shape[0]
- # calculating BSpline knots
- kv = np.clip(np.arange(c+degree+1)-degree, 0, c-degree)
- # u is the array of points at which to return the value of the smoothed spline
- u = np.linspace(0, c-degree, npoints)
- # Calculate resulting spline
- # splev requires u, and a tuple which is a sequence of length 3 containing
- # the knots, coefficients, and degree of the spline.
- return np.array(splev(u, (kv, cv.T, degree))).T
diff --git a/bladex/parameter_files/default.prm b/bladex/parameter_files/default.prm
deleted file mode 100644
index 7de1c02..0000000
--- a/bladex/parameter_files/default.prm
+++ /dev/null
@@ -1,184 +0,0 @@
-
-[Original parameters]
-# This section describes the radial distributions of the parameters:
-# "chord lengths", "pitch", "rake", "skew angles", and "camber"
-# at given radial sections.
-
-Radial sections = 0.3
- 0.4
- 0.5
- 0.6000000000000001
- 0.7000000000000002
- 0.8000000000000003
- 0.9000000000000001
- 1.0000000000000002
-
-Radial distribution of chord = 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
-
-Radial distribution of pitch = 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
-
-Radial distribution of rake = 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
-
-Radial distribution of skew = 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
-
-Radial distribution of camber = 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
-
-
-[Chord B-Spline]
-# This section describes the B-Spline construction of the RADII -- CHORD curve.
-
-# degree of the B-Spline curve
-spline degree: 3
-
-# number of points to be evaluated with the B-Spline interpolation
-spline npoints: 500
-
-# number of the control points
-number of control points: 10
-
-# Y-deformations of the control points.
-control points Y-deformations = 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
-
-
-[Pitch B-Spline]
-# This section describes the B-Spline construction of the RADII -- PITCH curve.
-
-# degree of the B-Spline curve
-spline degree: 3
-
-# number of points to be evaluated with the B-Spline interpolation
-spline npoints: 500
-
-# number of the control points
-number of control points: 10
-
-# Y-deformations of the control points.
-control points Y-deformations = 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
-
-
-[Rake B-Spline]
-# This section describes the B-Spline construction of the RADII -- RAKE curve.
-
-# degree of the B-Spline curve
-spline degree: 3
-
-# number of points to be evaluated with the B-Spline interpolation
-spline npoints: 500
-
-# number of the control points
-number of control points: 10
-
-# Y-deformations of the control points.
-control points Y-deformations = 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
-
-
-[Skew B-Spline]
-# This section describes the B-Spline construction of the RADII -- SKEW curve.
-
-# degree of the B-Spline curve
-spline degree: 3
-
-# number of points to be evaluated with the B-Spline interpolation
-spline npoints: 500
-
-# number of the control points
-number of control points: 10
-
-# Y-deformations of the control points.
-control points Y-deformations = 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
-
-
-[Camber B-Spline]
-# This section describes the B-Spline construction of the RADII -- CAMBER curve.
-
-# degree of the B-Spline curve
-spline degree: 3
-
-# number of points to be evaluated with the B-Spline interpolation
-spline npoints: 500
-
-# number of the control points
-number of control points: 10
-
-# Y-deformations of the control points.
-control points Y-deformations = 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
diff --git a/bladex/parameter_files/pptc.prm b/bladex/parameter_files/pptc.prm
deleted file mode 100644
index c00e1f7..0000000
--- a/bladex/parameter_files/pptc.prm
+++ /dev/null
@@ -1,208 +0,0 @@
-
-[Original parameters]
-# This section describes the radial distributions of the parameters:
-# "chord lengths", "pitch", "rake", "skew angles", and "camber"
-# at given radial sections.
-
-Radial sections = 0.3
- 0.35
- 0.4
- 0.5
- 0.6
- 0.7
- 0.8
- 0.85
- 0.9
- 0.95
- 0.975
- 1.0
-
-Radial distribution of chord = 0.18
- 0.225
- 0.26168
- 0.325
- 0.37668
- 0.41668
- 0.42832
- 0.42616
- 0.41668
- 0.37668
- 0.31468
- 0.1
-
-Radial distribution of pitch = 1.4
- 1.455
- 1.505
- 1.578
- 1.62
- 1.635
- 1.614
- 1.582
- 1.531
- 1.458
- 1.411
- 1.355
-
-Radial distribution of rake = 0.0
- 0.002
- 0.005
- 0.0134
- 0.0235
- 0.03
- 0.0295
- 0.0265
- 0.0218
- 0.016132
- 0.0132
- 0.01
-
-Radial distribution of skew = 3.6262795
- -1.188323
- -4.4654502
- -7.440779
- -7.3840979
- -5.0367916
- -1.3257914
- 1.0856404
- 4.1448947
- 7.697235
- 9.5368917
- 11.397609
-
-Radial distribution of camber = 0.015
- 0.02
- 0.02399878
- 0.02899692
- 0.03012637
- 0.02969185
- 0.02850205
- 0.02784869
- 0.02565038
- 0.02329829
- 0.02179992
- 0.02
-
-
-[Chord B-Spline]
-# This section describes the B-Spline construction of the RADII -- CHORD curve.
-
-# degree of the B-Spline curve
-spline degree: 3
-
-# number of points to be evaluated with the B-Spline interpolation
-spline npoints: 500
-
-# number of the control points
-number of control points: 10
-
-# Y-deformations of the control points.
-control points Y-deformations = 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
-
-
-[Pitch B-Spline]
-# This section describes the B-Spline construction of the RADII -- PITCH curve.
-
-# degree of the B-Spline curve
-spline degree: 3
-
-# number of points to be evaluated with the B-Spline interpolation
-spline npoints: 500
-
-# number of the control points
-number of control points: 10
-
-# Y-deformations of the control points.
-control points Y-deformations = 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
-
-
-[Rake B-Spline]
-# This section describes the B-Spline construction of the RADII -- RAKE curve.
-
-# degree of the B-Spline curve
-spline degree: 3
-
-# number of points to be evaluated with the B-Spline interpolation
-spline npoints: 500
-
-# number of the control points
-number of control points: 10
-
-# Y-deformations of the control points.
-control points Y-deformations = 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
-
-
-[Skew B-Spline]
-# This section describes the B-Spline construction of the RADII -- SKEW curve.
-
-# degree of the B-Spline curve
-spline degree: 3
-
-# number of points to be evaluated with the B-Spline interpolation
-spline npoints: 500
-
-# number of the control points
-number of control points: 10
-
-# Y-deformations of the control points.
-control points Y-deformations = 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
-
-
-[Camber B-Spline]
-# This section describes the B-Spline construction of the RADII -- CAMBER curve.
-
-# degree of the B-Spline curve
-spline degree: 3
-
-# number of points to be evaluated with the B-Spline interpolation
-spline npoints: 500
-
-# number of the control points
-number of control points: 10
-
-# Y-deformations of the control points.
-control points Y-deformations = 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
- 0.0
diff --git a/bladex/params.py b/bladex/params.py
deleted file mode 100644
index cf5d5e8..0000000
--- a/bladex/params.py
+++ /dev/null
@@ -1,290 +0,0 @@
-"""
-Module to read and write a parameter file
-which can be used for parameters deformations.
-"""
-try:
- import configparser as configparser
-except ImportError:
- import ConfigParser as configparser
-import os
-import numpy as np
-
-
-class ParamFile(object):
- """
- Read and Write a parameter file
-
- :cvar array_like radii: contains radii values of the blade sectional
- profiles, starting from the hub. Default value is None
- :cvar dict parameters: dictionary that contains the radial distribution
- of parameters `chord`, `pitch`, `rake`, `skew`, `camber` at specific
- blade sections. Each element of the dictionary is an array_like of
- length equals to that of the array radii. Both parameters `chord` and
- `camber` descibes the chord length and the camber of the 2D foil
- representing the blade section. Possible dictionary keys are `chord`,
- `pitch`, `rake`, `skew`, `camber`. Default values are None
- :cvar dict nbasis: dictionary that contains number of control points for
- each parameter. Possible dictionary keys are: `chord`, `pitch`, `rake`,
- `skew`, `camber`
- :cvar dict degree: dictionary that contains degree of the BSpline to be
- constructed according to the parameter radial distribution. Possible
- dictionary keys are: `chord`, `pitch`, `rake`, `skew`, `camber`
- :cvar dict npoints: dictionary that contains number of points to be
- evaluated using the BSpline interpolation, for each of the parameter
- curves. Possible dictionary keys for the parameters are: `chord`,
- `pitch`, `rake`, `skew`, `camber`
- :cvar dict deformations: dictionary that contains the control points
- Y-deformations of the parameter BSpline curve. Possible dictionary
- keys are: `chord`, `pitch`, `rake`, `skew`, `camber`
- """
-
- def __init__(self):
- self.radii = None
- self.parameters = {
- 'chord': None,
- 'pitch': None,
- 'rake': None,
- 'skew': None,
- 'camber': None
- }
- self.nbasis = {
- 'chord': 10,
- 'pitch': 10,
- 'rake': 10,
- 'skew': 10,
- 'camber': 10
- }
- self.degree = {
- 'chord': 3,
- 'pitch': 3,
- 'rake': 3,
- 'skew': 3,
- 'camber': 3
- }
- self.npoints = {
- 'chord': 500,
- 'pitch': 500,
- 'rake': 500,
- 'skew': 500,
- 'camber': 500
- }
- self.deformations = {
- 'chord': np.zeros(self.nbasis['chord']),
- 'pitch': np.zeros(self.nbasis['chord']),
- 'rake': np.zeros(self.nbasis['chord']),
- 'skew': np.zeros(self.nbasis['chord']),
- 'camber': np.zeros(self.nbasis['chord'])
- }
-
- def _check_params(self):
- """
- Private method that is called while writing a parameter file.
-
- 1. The method checks if the user specifies a radii array, otherwise it
- raises exception.
-
- 2. In case no values assigned to any of the remaining parameter arrays
- then an array of zeros is assigned, in which its length is equal
- to the radii array.
-
- 3. Any array that is not numpy is converted to be one. Finally, in case
- the user specifies the parameter array values but not with same length,
- then an exception is raised.
- """
- if self.radii is None:
- raise ValueError('Array radii can not have a None value.')
-
- if not isinstance(self.radii, np.ndarray):
- self.radii = np.asarray(self.radii)
-
- for param in ['chord', 'pitch', 'rake', 'skew', 'camber']:
- # If any parameter is not inserted then assign that parameter
- # with array of zeros. This is useful in case the user is
- # interested in only one or few parameters, while not interested
- # in (or does have information about) the remaining ones.
- if self.parameters[param] is None:
- self.parameters[param] = np.zeros(self.radii.shape[0])
-
- # In case inserted parameters are not numpy arrays
- if not isinstance(self.parameters[param], np.ndarray):
- self.parameters[param] = np.asarray(self.parameters[param])
-
- # check the case if user inserts inhomogeneous radial distributions
- if not self.parameters[param].shape == self.radii.shape:
- raise ValueError(
- 'Array ' + param + ' must have same shape of array radii.')
-
- # If inserted deformations array not correspond to nbasis
- if not self.nbasis[param] == len(self.deformations[param]):
- raise ValueError(
- param + ' deformations must correspond to nbasis.')
-
- def read_parameters(self, filename='parameters.prm'):
- """
- Reads in the parameters file and fill the self structure.
-
- :param str filename: parameters file to be read in. Default value is
- parameters.prm
- """
- if not isinstance(filename, str):
- raise TypeError('filename must be a string')
-
- # Checks if the parameters file exists. If not it writes a default
- # parameters file with zero deformations for all parameters at uniform
- # radial sections.
- if not os.path.isfile(filename):
- self.radii = np.arange(0.3, 1.1, 0.1)
- self.write_parameters(filename=filename)
-
- config = configparser.RawConfigParser()
- config.read(filename)
-
- radii = config.get('Original parameters', 'Radial sections')
- lines = radii.split('\n')
- self.radii = np.zeros(len(lines))
- for j, line in enumerate(lines):
- if len(line.split()) > 1:
- raise ValueError(
- 'Radial sections must have single value at each section.')
- self.radii[j] = float(line)
-
- params = ['chord', 'pitch', 'rake', 'skew', 'camber']
- for param in params:
- parameters = config.get('Original parameters',
- 'Radial distribution of ' + param)
- lines = parameters.split('\n')
- self.parameters[param] = np.zeros(len(lines))
- for j, line in enumerate(lines):
- if len(line.split()) > 1:
- raise ValueError(
- param +
- ' radial distribution must have single value at each'\
- ' radial section.'
- )
- self.parameters[param][j] = float(line)
-
- if not (len(self.radii) ==
- len(self.parameters['chord']) ==
- len(self.parameters['pitch']) ==
- len(self.parameters['rake']) ==
- len(self.parameters['skew']) ==
- len(self.parameters['camber'])):
- raise ValueError(
- 'Arrays "radii", "chord", "pitch", "rake", "skew", "camber"'\
- ' must have same length.'
- )
-
- section_all = [
- 'Chord B-Spline', 'Pitch B-Spline', 'Rake B-Spline',
- 'Skew B-Spline', 'Camber B-Spline'
- ]
-
- for section, param in zip(section_all, params):
- self.degree[param] = config.getint(section, 'spline degree')
- self.npoints[param] = config.getint(section, 'spline npoints')
- self.nbasis[param] = config.getint(section,
- 'number of control points')
-
- deformations = config.get(section, 'control points Y-deformations')
- if bool(deformations) is False:
- raise ValueError('control points Y-deformations in section [' +
- section + '] must be non-empty.')
- lines = deformations.split('\n')
- self.deformations[param] = np.zeros(len(lines))
- for j, line in enumerate(lines):
- if len(line.split()) > 1:
- raise ValueError(
- 'You can pass only one value for each control point',
- ' Y-deformation of the ' + param)
- self.deformations[param][j] = float(line)
- if not len(self.deformations[param]) == self.nbasis[param]:
- raise ValueError(param + ' has nbasis not equal deformations.')
-
- def write_parameters(self, filename='parameters.prm'):
- """
- This method writes a parameters file (.prm) called `filename` and fills
- it with all the parameters class members. Default value is
- parameters.prm.
-
- :param str filename: parameters file to be written out.
- :param bool param_pptc: if True, then the parameter arrays are replaced
- with that of the benchmark PPTC propeller.
- """
- if not isinstance(filename, str):
- raise TypeError("filename must be a string")
-
- self._check_params()
-
- output_string = ""
-
- output_string += '\n[Original parameters]\n'
- output_string += '# This section describes the radial distributions'\
- ' of the parameters:\n'
- output_string += '# "chord lengths", "pitch", "rake", "skew angles",'\
- ' and "camber"\n'
- output_string += '# at given radial sections.\n'
-
- output_string += '\nRadial sections = '
- offset = 1
- for radius in self.radii:
- output_string += offset * ' ' + str(radius) + '\n'
- offset = 19
-
- params = ['chord', 'pitch', 'rake', 'skew', 'camber']
- gaps = [0, 0, 1, 1, -1]
-
- for param, gap in zip(params, gaps):
- offset = 1 + gap
- output_string += '\nRadial distribution of ' + param + ' = '
- for parameter in self.parameters[param]:
- output_string += offset * ' ' + str(parameter) + '\n'
- offset = 32
-
- sections = [
- '[Chord B-Spline]', '[Pitch B-Spline]', '[Rake B-Spline]',
- '[Skew B-Spline]', '[Camber B-Spline]'
- ]
-
- for section, param in zip(sections, params):
- output_string += '\n\n' + section + '\n'
- output_string += '# This section describes the B-Spline'\
- ' construction of the RADII -- ' + param.upper() + ' curve.\n'
- output_string += '\n# degree of the B-Spline curve\n'
- output_string += 'spline degree: {}\n'.format(
- str(self.degree[param]))
- output_string += '\n# number of points to be evaluated with the'\
- ' B-Spline interpolation\n'
- output_string += 'spline npoints: {}\n'.format(
- str(self.npoints[param]))
- output_string += '\n# number of the control points\n'
- output_string += 'number of control points: {}\n'.format(
- str(self.nbasis[param]))
- output_string += '\n# Y-deformations of the control points.\n'
- output_string += 'control points Y-deformations = '
- offset = 1
- for i in range(self.nbasis[param]):
- output_string += offset * ' ' + str(
- self.deformations[param][i]) + '\n'
- offset = 33
-
- with open(filename, 'w') as f:
- f.write(output_string)
-
- def __str__(self):
- """
- This method prints all the parameters on the screen. Its purpose is
- for debugging.
- """
- string = ''
- string += 'radii = {}'.format(self.radii)
- params = ['chord', 'pitch', 'rake', 'skew', 'camber']
- for param in params:
- string += '\n\n' + param + ' = {}'.format(self.parameters[param])
- string += '\n' + param + ' degree = {}'.format(
- self.degree[param])
- string += '\n' + param + ' npoints = {}'.format(
- self.npoints[param])
- string += '\n' + param + ' nbasis = {}'.format(self.nbasis[param])
- string += '\n' + param + ' control points deformations = '
- string += '{}'.format(self.deformations[param])
- return string
diff --git a/bladex/profile/__init__.py b/bladex/profile/__init__.py
deleted file mode 100644
index 3b44d32..0000000
--- a/bladex/profile/__init__.py
+++ /dev/null
@@ -1,8 +0,0 @@
-"""
-Profile init
-"""
-__all__ = ['ProfileInterface', 'NacaProfile', 'CustomProfile']
-
-from .profileinterface import ProfileInterface
-from .nacaprofile import NacaProfile
-from .customprofile import CustomProfile
diff --git a/bladex/profile/baseprofile.py b/bladex/profile/baseprofile.py
deleted file mode 100644
index b307d8d..0000000
--- a/bladex/profile/baseprofile.py
+++ /dev/null
@@ -1,829 +0,0 @@
-"""
-Base module that provides essential tools and transformations on airfoils.
-"""
-import numpy as np
-import matplotlib.pyplot as plt
-from scipy.optimize import newton
-from ..ndinterpolator import reconstruct_f
-from scipy.interpolate import RBFInterpolator
-
-from .profileinterface import ProfileInterface
-
-
-class BaseProfile(ProfileInterface):
- """
- Base sectional profile of the propeller blade.
-
- Each sectional profile is a 2D airfoil that is split into two parts: the
- upper and lower parts. The coordinates of each part is represented by two
- arrays corresponding to the X and Y components in the 2D coordinate system.
- Such coordinates can be either generated using NACA functions, or be
- inserted directly by the user as custom profiles.
-
- :param numpy.ndarray xup_coordinates: 1D array that contains the
- X-components of the airfoil upper-half surface. Default value is None
- :param numpy.ndarray xdown_coordinates: 1D array that contains the
- X-components of the airfoil lower-half surface. Default value is None
- :param numpy.ndarray yup_coordinates: 1D array that contains the
- Y-components of the airfoil upper-half surface. Default value is None
- :param numpy.ndarray ydown_coordinates: 1D array that contains the
- Y-components of the airfoil lower-half surface. Default value is None
- :param numpy.ndarray chord_line: contains the X and Y coordinates of the
- straight line joining between the leading and trailing edges. Default
- value is None
- :param numpy.ndarray camber_line: contains the X and Y coordinates of the
- curve passing through all the mid-points between the upper and lower
- surfaces of the airfoil. Default value is None
- :param numpy.ndarray leading_edge: 2D coordinates of the airfoil's
- leading edge. Default values are zeros
- :param numpy.ndarray trailing_edge: 2D coordinates of the airfoil's
- trailing edge. Default values are zeros
- """
- def generate_parameters(self, convention='british'):
- """
- Abstract method that generates the airfoil parameters based on the
- given coordinates.
-
- The method generates the airfoil's chord length, chord percentages,
- maximum camber, camber percentages, maximum thickness, thickness
- percentages.
-
- :param str convention: convention of the airfoil coordinates. Default
- value is 'british'
- """
- self._update_edges()
- # compute chord parameters
- self._chord_length = np.linalg.norm(self.leading_edge -
- self.trailing_edge)
- self._chord_percentage = (self.xup_coordinates - np.min(
- self.xup_coordinates))/self._chord_length
- # compute camber parameters
- _camber = (self.yup_coordinates + self.ydown_coordinates)/2
- self._camber_max = abs(np.max(_camber))
- if self._camber_max == 0:
- self._camber_percentage = np.zeros(self.xup_coordinates.shape[0])
- elif self.camber_max != 0:
- self._camber_percentage = _camber/self._camber_max
- # compute thickness parameters
- if convention == 'british' or self._camber_max==0:
- _thickness = abs(self.yup_coordinates - self.ydown_coordinates)
- elif convention == 'american':
- _thickness = self._compute_thickness_american()
- self._thickness_max = np.max(_thickness)
- if self._thickness_max == 0:
- self._thickness_percentage = np.zeros(self.xup_coordinates.shape[0])
- elif self._thickness_max != 0:
- self._thickness_percentage = _thickness/self._thickness_max
-
- @property
- def xup_coordinates(self):
- """
- X-coordinates of the upper surface of the airfoil.
- """
- return self._xup_coordinates
-
- @xup_coordinates.setter
- def xup_coordinates(self, xup_coordinates):
- self._xup_coordinates = xup_coordinates
-
- @property
- def xdown_coordinates(self):
- """
- X-coordinates of the lower surface of the airfoil.
- """
- return self._xdown_coordinates
-
- @xdown_coordinates.setter
- def xdown_coordinates(self, xdown_coordinates):
- self._xdown_coordinates = xdown_coordinates
-
- @property
- def yup_coordinates(self):
- """
- Y-coordinates of the upper surface of the airfoil.
- """
- return self._yup_coordinates
-
- @yup_coordinates.setter
- def yup_coordinates(self, yup_coordinates):
- self._yup_coordinates = yup_coordinates
-
- @property
- def ydown_coordinates(self):
- """
- Y-coordinates of the lower surface of the airfoil.
- """
- return self._ydown_coordinates
-
- @ydown_coordinates.setter
- def ydown_coordinates(self, ydown_coordinates):
- self._ydown_coordinates = ydown_coordinates
-
- @property
- def chord_length(self):
- """
- Chord length of the airfoil.
- """
- return self._chord_length
-
- @chord_length.setter
- def chord_length(self, chord_length):
- self._chord_length = chord_length
-
- @property
- def chord_percentage(self):
- """
- Chord percentages of the airfoil.
- """
- return self._chord_percentage
-
- @chord_percentage.setter
- def chord_percentage(self, chord_percentage):
- self._chord_percentage = chord_percentage
-
- @property
- def camber_max(self):
- """
- Maximum camber of the airfoil.
- """
- return self._camber_max
-
- @camber_max.setter
- def camber_max(self, camber_max):
- self._camber_max = camber_max
-
- @property
- def camber_percentage(self):
- """
- Camber percentages of the airfoil.
- """
- return self._camber_percentage
-
- @camber_percentage.setter
- def camber_percentage(self, camber_percentage):
- self._camber_percentage = camber_percentage
-
- @property
- def thickness_max(self):
- """
- Maximum thickness of the airfoil.
- """
- return self._thickness_max
-
- @thickness_max.setter
- def thickness_max(self, thickness_max):
- self._thickness_max = thickness_max
-
- @property
- def thickness_percentage(self):
- """
- Thickness percentages of the airfoil.
- """
- return self._thickness_percentage
-
- @thickness_percentage.setter
- def thickness_percentage(self, thickness_percentage):
- self._thickness_percentage = thickness_percentage
-
- def _update_edges(self):
- """
- Private method that identifies and updates the airfoil's leading and
- trailing edges.
-
- Given the airfoil coordinates from the leading to the trailing edge,
- if the trailing edge has a non-zero thickness, then the average value
- between the upper and lower trailing edges is taken as the true
- trailing edge, hence both the leading and the trailing edges are always
- unique.
- """
- self.leading_edge = np.zeros(2)
- self.trailing_edge = np.zeros(2)
- if np.fabs(self.xup_coordinates[0] - self.xdown_coordinates[0]) > 1e-4:
- raise ValueError('Airfoils must have xup_coordinates[0] '\
- 'almost equal to xdown_coordinates[0]')
- if np.fabs(
- self.xup_coordinates[-1] - self.xdown_coordinates[-1]) > 1e-4:
- raise ValueError('Airfoils must have xup_coordinates[-1] '\
- 'almost equal to xdown_coordinates[-1]')
-
- self.leading_edge[0] = self.xup_coordinates[0]
- self.leading_edge[1] = self.yup_coordinates[0]
- self.trailing_edge[0] = self.xup_coordinates[-1]
-
- if self.yup_coordinates[-1] == self.ydown_coordinates[-1]:
- self.trailing_edge[1] = self.yup_coordinates[-1]
- else:
- self.trailing_edge[1] = 0.5 * (
- self.yup_coordinates[-1] + self.ydown_coordinates[-1])
-
- def interpolate_coordinates(self, num=500, radius=1.0):
- """
- Interpolate the airfoil coordinates from the given data set of
- discrete points.
-
- The interpolation applies the Radial Basis Function (RBF) method,
- to construct approximations of the two functions that correspond to the
- airfoil upper half and lower half coordinates. The RBF implementation
- is present in :ref:`RBF ndinterpolator `.
-
- References:
-
- Buhmann, Martin D. (2003), Radial Basis Functions: Theory
- and Implementations.
- http://www.cs.bham.ac.uk/~jxb/NN/l12.pdf
- https://www.cc.gatech.edu/~isbell/tutorials/rbf-intro.pdf
-
- :param int num: number of interpolated points. Default value is 500
- :param float radius: range of the cut-off radius necessary for the RBF
- interpolation. Default value is 1.0. It is quite necessary to
- adjust the value properly so as to ensure a smooth interpolation
- :return: interpolation points for the airfoil upper half X-component,
- interpolation points for the airfoil lower half X-component,
- interpolation points for the airfoil upper half Y-component,
- interpolation points for the airfoil lower half Y-component
- :rtype: numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray
- :raises TypeError: if num is not of type int
- :raises ValueError: if num is not positive, or if radius is not
- positive
- """
- if not isinstance(num, int):
- raise TypeError('Inserted value must be of type integer.')
- if num <= 0 or radius <= 0:
- raise ValueError('Inserted value must be positive.')
-
- xx_up = np.linspace(
- self.xup_coordinates[0], self.xup_coordinates[-1], num=num)
- yy_up = np.zeros(num)
- reconstruct_f(
- basis='beckert_wendland_c2_basis',
- radius=radius,
- original_input=self.xup_coordinates,
- original_output=self.yup_coordinates,
- rbf_input=xx_up,
- rbf_output=yy_up)
- xx_down = np.linspace(
- self.xdown_coordinates[0], self.xdown_coordinates[-1], num=num)
- yy_down = np.zeros(num)
- reconstruct_f(
- basis='beckert_wendland_c2_basis',
- radius=radius,
- original_input=self.xdown_coordinates,
- original_output=self.ydown_coordinates,
- rbf_input=xx_down,
- rbf_output=yy_down)
-
- return xx_up, xx_down, yy_up, yy_down
-
- def compute_chord_line(self, n_interpolated_points=None):
- """
- Compute the 2D coordinates of the chord line. Also updates
- the chord_line class member.
-
- The chord line is the straight line that joins between the leading edge
- and the trailing edge. It is simply computed from the equation of
- a line passing through two points, the LE and TE.
-
- :param int n_interpolated_points: number of points to be used for the
- equally-spaced sample computations. If None then there is no
- interpolation, unless the arrays x_up != x_down elementwise which
- implies that the corresponding y_up and y_down can not be
- comparable, hence a uniform interpolation is required. Default
- value is None
- """
- self._update_edges()
- aratio = ((self.trailing_edge[1] - self.leading_edge[1]) /
- (self.trailing_edge[0] - self.leading_edge[0]))
- if not (self.xup_coordinates == self.xdown_coordinates
- ).all() and n_interpolated_points is None:
- # If x_up != x_down element-wise, then the corresponding y_up and
- # y_down can not be comparable, hence a uniform interpolation is
- # required. Also in case the interpolated_points is None,
- # then we assume a default number of interpolated points
- n_interpolated_points = 500
-
- if n_interpolated_points:
- cl_x_coordinates = np.linspace(
- self.leading_edge[0],
- self.trailing_edge[0],
- num=n_interpolated_points)
- cl_y_coordinates = (aratio *
- (cl_x_coordinates - self.leading_edge[0]) +
- self.leading_edge[1])
- self.chord_line = np.array([cl_x_coordinates, cl_y_coordinates])
- else:
- cl_y_coordinates = (aratio *
- (self.xup_coordinates - self.leading_edge[0]) +
- self.leading_edge[1])
- self.chord_line = np.array([self.xup_coordinates, cl_y_coordinates])
-
- def compute_camber_line(self, n_interpolated_points=None):
- """
- Compute the 2D coordinates of the camber line. Also updates the
- camber_line class member.
-
- The camber line is defined by the curve passing through all the mid
- points between the upper surface and the lower surface of the airfoil.
-
- :param int n_interpolated_points: number of points to be used for the
- equally-spaced sample computations. If None then there is no
- interpolation, unless the arrays x_up != x_down elementwise which
- implies that the corresponding y_up and y_down can not be
- comparable, hence a uniform interpolation is required. Default
- value is None
-
- We note that a uniform interpolation becomes necessary for the cases
- when the X-coordinates of the upper and lower surfaces do not
- correspond to the same vertical sections, since this would imply
- inaccurate measurements for obtaining the camber line.
- """
- if not (self.xup_coordinates == self.xdown_coordinates
- ).all() and n_interpolated_points is None:
- # If x_up != x_down element-wise, then the corresponding y_up and
- # y_down can not be comparable, hence a uniform interpolation is
- # required. Also in case the interpolated_points is None,
- # then we assume a default number of interpolated points
- n_interpolated_points = 500
-
- if n_interpolated_points:
- cl_x_coordinates, yy_up, yy_down = (
- self.interpolate_coordinates(num=n_interpolated_points)[1:])
- cl_y_coordinates = 0.5 * (yy_up + yy_down)
- self.camber_line = np.array([cl_x_coordinates, cl_y_coordinates])
- else:
- cl_y_coordinates = (0.5 *
- (self.ydown_coordinates + self.yup_coordinates))
- self.camber_line = np.array(
- [self.xup_coordinates, cl_y_coordinates])
-
- def deform_camber_line(self, percent_change, n_interpolated_points=None):
- """
- Deform camber line according to a given percentage of change of the
- maximum camber. Also reconstructs the deformed airfoil's coordinates.
-
- The percentage of change is defined as follows:
-
- .. math::
- \\frac{\\text{new magnitude of max camber - old magnitude of
- maximum \
- camber}}{\\text{old magnitude of maximum camber}} * 100
-
- A positive percentage means the new camber is larger than the max
- camber value, while a negative percentage indicates the new value
- is smaller.
-
- We note that the method works only for airfoils in the reference
- position, i.e. chord line lies on the X-axis and the foil is not
- rotated, since the measurements are based on the Y-values of the
- airfoil coordinates, hence any measurements or scalings will be
- inaccurate for the foils not in their reference position.
-
- :param float percent_change: percentage of change of the
- maximum camber. Default value is None
- :param int n_interpolated_points: number of points to be used for the
- equally-spaced sample computations. If None then there is no
- interpolation, unless the arrays x_up != x_down elementwise which
- implies that the corresponding y_up and y_down can not be
- comparable, hence a uniform interpolation is required. Default
- value is None
- """
- # Updating camber line
- self.compute_camber_line(n_interpolated_points=n_interpolated_points)
- scaling_factor = percent_change / 100. + 1.
- self.camber_line[1] *= scaling_factor
-
- if not (self.xup_coordinates == self.xdown_coordinates
- ).all() and n_interpolated_points is None:
- # If x_up != x_down element-wise, then the corresponding y_up and
- # y_down can not be comparable, hence a uniform interpolation is
- # required. Also in case the interpolated_points is None,
- # then we assume a default number of interpolated points
- n_interpolated_points = 500
-
- # Evaluating half-thickness of the undeformed airfoil,
- # which should hold same values for the deformed foil.
- if n_interpolated_points:
- (self.xup_coordinates, self.xdown_coordinates, self.yup_coordinates,
- self.ydown_coordinates
- ) = self.interpolate_coordinates(num=n_interpolated_points)
-
- half_thickness = 0.5 * np.fabs(
- self.yup_coordinates - self.ydown_coordinates)
-
- self.yup_coordinates = self.camber_line[1] + half_thickness
- self.ydown_coordinates = self.camber_line[1] - half_thickness
-
- def set_camber_line_max(self, camber_max):
- """
- Deform camber line according to a given maximum value.
- The percentage of camber wrt to the x/c coordinate does not change, i.e.,
- we rescale the camber value by a scalar
- Also reconstructs the deformed airfoil's coordinates.
-
- Thus, the percentage of change is defined as follows:
-
- .. math::
- \\frac{\\text{new magnitude of max camber - old magnitude of
- maximum \
- camber}}{\\text{old magnitude of maximum camber}} * 100
-
- A positive percentage means the new camber is larger than the max
- camber value, while a negative percentage indicates the new value
- is smaller.
-
- We note that the method works only for airfoils in the reference
- position, i.e. chord line lies on the X-axis and the foil is not
- rotated, since the measurements are based on the Y-values of the
- airfoil coordinates, hence any measurements or scalings will be
- inaccurate for the foils not in their reference position.
-
- :param float camber_max: maximum camber to be set.
- """
- old_camber_max = self.max_camber()
- percent_scaling_factor = 100*(camber_max - old_camber_max) / (old_camber_max)
- # print(percent_scaling_factor)
- self.deform_camber_line(percent_scaling_factor)
-
-
- def set_thickness_max(self, thickness_max):
- """
- Deform y_up and y_down coordinates to have the desired thickness max value.
- To do so, we compute the ratio between olt thickness and new one
-
- :param float thickness_max: maximum thickness to be set.
- """
- old_thickness = self.max_thickness()
- ratio_thickness = thickness_max / old_thickness if old_thickness != 0. else 0.
- self.yup_coordinates *= ratio_thickness
- self.ydown_coordinates *= ratio_thickness
-
- @property
- def yup_curve(self):
- """
- Return the spline function corresponding to the upper profile
- of the airfoil
-
- :return: a spline function
- :rtype: scipy interpolation object
-
- .. todo::
- generalize the interpolation function
- """
- spline = RBFInterpolator(self.xup_coordinates.reshape(-1,1),
- self.yup_coordinates.reshape(-1,1))
- return spline
-
- @property
- def ydown_curve(self):
- """
- Return the spline function corresponding to the lower profile
- of the airfoil
-
- :return: a spline function
- :rtype: scipy interpolation object
-
- .. todo::
- generalize the interpolation function
- """
- spline = RBFInterpolator(self.xdown_coordinates.reshape(-1,1),
- self.ydown_coordinates.reshape(-1,1))
- return spline
-
- @property
- def reference_point(self):
- """
- Return the coordinates of the chord's mid point.
-
- :return: reference point in 2D
- :rtype: numpy.ndarray
- """
- self._update_edges()
- reference_point = [
- 0.5 * (self.leading_edge[0] + self.trailing_edge[0]),
- 0.5 * (self.leading_edge[1] + self.trailing_edge[1])
- ]
- return np.asarray(reference_point)
-
- def _compute_thickness_american(self):
- """
- Compute the thickness of the airfoil using the American standard
- definition.
- """
- n_pos = self.xup_coordinates.shape[0]
- m = np.zeros(n_pos)
- for i in range(1, n_pos, 1):
- m[i] = (self._camber_percentage[i]-
- self._camber_percentage[i-1])/(self._chord_percentage[i]-
- self._chord_percentage[i-1])*self._camber_max/self._chord_length
- m_angle = np.arctan(m)
-
- # generating temporary profile coordinates orthogonal to the camber
- # line
- camber = self._camber_max*self._camber_percentage
- ind_horizontal_camber = np.sin(m_angle)==0
- def eq_to_solve(x):
- spline_curve = self.ydown_curve(x.reshape(-1,1)).reshape(
- x.shape[0],)
- line_orth_camber = (camber[~ind_horizontal_camber] +
- np.cos(m_angle[~ind_horizontal_camber])/
- np.sin(m_angle[~ind_horizontal_camber])*(
- self._chord_percentage[~ind_horizontal_camber]
- *self._chord_length-x))
- return spline_curve - line_orth_camber
-
- xdown_tmp = self.xdown_coordinates.copy()
- xdown_tmp[~ind_horizontal_camber] = newton(eq_to_solve,
- xdown_tmp[~ind_horizontal_camber])
- xup_tmp = 2*self._chord_percentage*self._chord_length - xdown_tmp
- ydown_tmp = self.ydown_curve(xdown_tmp.reshape(-1,1)).reshape(
- xdown_tmp.shape[0],)
- yup_tmp = 2*self._camber_max*self._camber_percentage - ydown_tmp
- if xup_tmp[1]= ydown_coordinates must be satisfied
- # element-wise to the whole elements in the mentioned arrays.
- if not all(
- np.greater_equal(self.yup_coordinates[1:-1],
- self.ydown_coordinates[1:-1])):
- raise ValueError('yup is not >= ydown elementwise.')
-
- if not np.isclose(self.xdown_coordinates[0], self.xup_coordinates[0],
- atol=1e-6):
- raise ValueError('(xdown[0]=xup[0]) not satisfied.')
-
- if not np.isclose(self.xdown_coordinates[-1], self.xup_coordinates[-1],
- atol=1e-6):
- raise ValueError('(xdown[-1]=xup[-1]) not satisfied.')
-
- if not np.isclose(self.ydown_coordinates[0], self.yup_coordinates[0],
- atol=1e-6):
- raise ValueError('(ydown[0]=yup[0]) not satisfied.')
-
- if not np.isclose(self.ydown_coordinates[-1], self.yup_coordinates[-1],
- atol=1e-6):
- raise ValueError('(ydown[-1]=yup[-1]) not satisfied.')
-
diff --git a/bladex/profile/nacaprofile.py b/bladex/profile/nacaprofile.py
deleted file mode 100644
index f18e4b7..0000000
--- a/bladex/profile/nacaprofile.py
+++ /dev/null
@@ -1,222 +0,0 @@
-"""
-Derived module from profilebase.py to provide the airfoil coordinates for
-standard Naca profiles.
-"""
-from scipy.interpolate import splev, splrep
-import numpy as np
-from .baseprofile import BaseProfile
-
-class NacaProfile(BaseProfile):
- """
- Generate 4- and 5-digit NACA profiles.
-
- The NACA airfoils are airfoil shapes for aircraft wings developed by the
- National Advisory Committee for Aeronautics (NACA). The shape of the NACA
- airfoils is described using a series of digits following the word "NACA".
- The parameters in the numerical code can be entered into equations to
- precisely generate the cross-section of the airfoil and calculate its
- properties.
-
- The NACA four-digit series describes airfoil by the format MPTT, where:
-
- - M/100: indicates the maximum camber in percentage, with respect to the
- chord length.
-
- - P/10: indicates the location of the maximum camber measured from the
- leading edge. The location is normalized by the chord length.
-
- - TT/100: the maximum thickness as fraction of the chord length.
-
- The profile 00TT refers to a symmetrical NACA airfoil.
-
- The NACA five-digit series describes more complex airfoil shapes.
- Its format is: LPSTT, where:
-
- - L: the theoretical optimum lift coefficient at ideal
- angle-of-attack = 0.15*L
-
- - P: the x-coordinate of the point of maximum camber
- (max camber at x = 0.05*P)
-
- - S: indicates whether the camber is simple (S=0) or reflex (S=1)
- TT/100: the maximum thickness in percent of chord, as in a four-digit
- NACA airfoil code
-
- References:
-
- - Moran, Jack (2003). An introduction to theoretical and computational
- aerodynamics. Dover. p. 7. ISBN 0-486-42879-6.
-
- - Abbott, Ira (1959). Theory of Wing Sections: Including a Summary of
- Airfoil Data. New York: Dover Publications. p. 115. ISBN 978-0486605869.
-
- :param str digits: 4 or 5 digits that describes the NACA profile
- :param int n_points: number of discrete points that represents the
- airfoil profile. Default value is 240
- :param bool cosine_spacing: if True, then a cosine spacing is used for the
- airfoil coordinate distribution, otherwise linear spacing is used.
- Default value is True
- :raises ValueError: if n_points is not positive
- :raises TypeError: if n_points is not of type int
- :raises SyntaxError: if digits is not a string
- :raises Exception: if digits is not of length 4 or 5
- """
-
- def __init__(self, digits, n_points=240, cosine_spacing=True):
- super(NacaProfile, self).__init__()
- self.digits = digits
- self.n_points = n_points
- self.cosine_spacing = cosine_spacing
- self._check_args()
- self.generate_coordinates()
- self.generate_parameters(convention='british')
-
- def _check_args(self):
- """
- Private method to check that the number of the airfoil discrete points
- is a positive integer.
- """
- if not isinstance(self.digits, str):
- raise TypeError('digits must be of type string.')
- if isinstance(self.n_points, float):
- self.n_points = int(self.n_points)
- if not isinstance(self.n_points, int):
- raise TypeError('n_points must be of type integer.')
- if self.n_points < 0:
- raise ValueError('n_points must be positive.')
-
- def generate_parameters(self, convention='british'):
- return super().generate_parameters(convention)
-
- def generate_coordinates(self):
- """
- Private method that generates the coordinates of the NACA 4 or 5 digits
- airfoil profile. The method assumes a zero-thickness trailing edge, and
- no half-cosine spacing.
- """
- a0 = +0.2969
- a1 = -0.1260
- a2 = -0.3516
- a3 = +0.2843
- a4 = -0.1036 # zero thickness TE
-
- x = np.linspace(0.0, 1.0, num=self.n_points)
-
- if len(self.digits) == 4:
- # Returns n+1 points in [0 1] for the given 4-digits NACA string
- m = float(self.digits[0]) / 100.0
- p = float(self.digits[1]) / 10.0
- t = float(self.digits[2:]) / 100.0
-
- # half-thickness distribution
- yt = 5 * t * (a0 * np.sqrt(x) + a1 * x + a2 * np.power(x, 2) +
- a3 * np.power(x, 3) + a4 * np.power(x, 4))
-
- if p == 0:
- # Symmetric foil
- self.xup_coordinates = np.linspace(0.0, 1.0, num=self.n_points)
- self.yup_coordinates = yt
- self.xdown_coordinates = np.linspace(
- 0.0, 1.0, num=self.n_points)
- self.ydown_coordinates = -yt
- else:
- # Cambered foil
- xc1 = np.asarray([xx for xx in x if xx <= p])
- xc2 = np.asarray([xx for xx in x if xx > p])
- yc1 = m / np.power(p, 2) * xc1 * (2 * p - xc1)
- yc2 = m / np.power(1 - p, 2) * (1 - 2 * p + xc2) * (1 - xc2)
- # Y-coordinates of camber line
- yc = np.append(yc1, yc2)
-
- if self.cosine_spacing:
- # points are generated according to cosine distribution of
- # the X-coordinates of the chord
- dyc1_dx = m / np.power(p, 2) * (2 * p - 2 * xc1)
- dyc2_dx = m / np.power(1 - p, 2) * (2 * p - 2 * xc2)
- dyc_dx = np.append(dyc1_dx, dyc2_dx)
- theta = np.arctan(dyc_dx)
- self.xup_coordinates = x - yt * np.sin(theta)
- self.yup_coordinates = yc + yt * np.cos(theta)
- self.xdown_coordinates = x + yt * np.sin(theta)
- self.ydown_coordinates = yc - yt * np.cos(theta)
- else:
- # Linear spacing distribution of the foil coordinates
- self.xup_coordinates = np.linspace(
- 0.0, 1.0, num=self.n_points)
- self.xdown_coordinates = np.linspace(
- 0.0, 1.0, num=self.n_points)
- self.yup_coordinates = yc + yt
- self.ydown_coordinates = yc - yt
-
- elif len(self.digits) == 5:
- # Returns n+1 points in [0 1] for the given 5-digits NACA string
- cld = float(self.digits[0]) * 0.15
- p = 5.0 * float(self.digits[1]) / 100.0
- s = float(self.digits[2])
- t = float(self.digits[3:]) / 100.0
-
- # half-thickness distribution
- yt = 5 * t * (a0 * np.sqrt(x) + a1 * x + a2 * np.power(x, 2) +
- a3 * np.power(x, 3) + a4 * np.power(x, 4))
-
- if s == 1:
- # Relfex camber
- P = np.array([0.1, 0.15, 0.2, 0.25])
- M = np.array([0.13, 0.2170, 0.318, 0.441])
- K = np.array([51.99, 15.793, 6.520, 3.191])
- elif s == 0:
- # Standard camber
- P = np.array([0.05, 0.1, 0.15, 0.2, 0.25])
- M = np.array([0.0580, 0.1260, 0.2025, 0.2900, 0.3910])
- K = np.array([361.4, 51.64, 15.957, 6.643, 3.230])
- else:
- raise ValueError(
- 'For NACA "LPSTT" the value of "S" can be either 0 or 1.')
-
- if p == 0:
- # Symmetric foil
- self.xup_coordinates = np.linspace(0.0, 1.0, num=self.n_points)
- self.yup_coordinates = yt
- self.xdown_coordinates = np.linspace(
- 0.0, 1.0, num=self.n_points)
- self.ydown_coordinates = -yt
- else:
- # Cambered foil
- spl_m = splrep(P, M)
- spl_k = splrep(M, K)
- m = splev(p, spl_m)
- k1 = splev(m, spl_k)
- xc1 = np.asarray([xx for xx in x if xx <= m])
- xc2 = np.asarray([xx for xx in x if xx > m])
- yc1 = k1 / 6.0 * (np.power(xc1, 3) - 3 * m * np.power(xc1, 2) +
- np.power(m, 2) * (3 - m) * xc1)
- yc2 = k1 / 6.0 * np.power(m, 3) * (1 - xc2)
- yc = np.append(yc1, yc2)
-
- if self.cosine_spacing:
- # points are generated according to cosine distribution of
- # the X-coordinates of the chord
- zc = cld / 0.3 * yc
- dyc1_dx = 1.0 / 6.0 * k1 * (
- 3 * np.power(xc1, 2) - 6 * m * xc1 + np.power(m, 2) *
- (3 - m))
- dyc2_dx = np.tile(-1.0 / 6.0 * k1 * np.power(m, 3),
- len(xc2))
- dyc_dx = np.append(dyc1_dx, dyc2_dx)
- theta = np.arctan(dyc_dx)
- self.xup_coordinates = x - yt * np.sin(theta)
- self.yup_coordinates = zc + yt * np.cos(theta)
- self.xdown_coordinates = x + yt * np.sin(theta)
- self.ydown_coordinates = zc - yt * np.cos(theta)
- else:
- # Linear spacing distribution of the foil coordinates
- self.xup_coordinates = np.linspace(
- 0.0, 1.0, num=self.n_points)
- self.xdown_coordinates = np.linspace(
- 0.0, 1.0, num=self.n_points)
- self.yup_coordinates = yc + yt
- self.ydown_coordinates = yc - yt
-
- else:
- raise Exception
-
diff --git a/bladex/profile/profileinterface.py b/bladex/profile/profileinterface.py
deleted file mode 100644
index b519ada..0000000
--- a/bladex/profile/profileinterface.py
+++ /dev/null
@@ -1,54 +0,0 @@
-"""
-Interface module that provides essential tools and transformations on airfoils.
-"""
-
-from abc import ABC, abstractmethod
-
-
-class ProfileInterface(ABC):
- """
- Interface for profile of the propeller blade.
-
- Each sectional profile is a 2D airfoil that is split into two parts: the
- upper and lower parts. The coordinates of each part is represented by two
- arrays corresponding to the X and Y components in the 2D coordinate system.
- Such coordinates can be either generated using NACA functions, or be
- inserted directly by the user as custom profiles.
- """
- @abstractmethod
- def generate_parameters(self, convention='british'):
- """
- Abstract method that generates the airfoil parameters based on the
- given coordinates.
-
- The method generates the airfoil's chord length, maximum camber and
- maximum thickness, along with their corresponding percentages. The
- method is called automatically when the airfoil coordinates are
- inserted by the user.
-
- """
- pass
-
- @abstractmethod
- def generate_coordinates(self):
- """
- Abstract method that generates the airfoil coordinates based on the
- given parameters.
-
- The method generates the airfoil's upper and lower surfaces
- coordinates. The method is called automatically when the airfoil
- parameters are inserted by the user.
-
- """
- pass
-
- @abstractmethod
- def plot(self):
- """
- Abstract method that plots the airfoil coordinates.
-
- The method creates a 2D plot of the airfoil's upper and lower
- surfaces using Matplotlib.
-
- """
- pass
\ No newline at end of file
diff --git a/bladex/propeller.py b/bladex/propeller.py
deleted file mode 100644
index 9a4e09c..0000000
--- a/bladex/propeller.py
+++ /dev/null
@@ -1,311 +0,0 @@
-"""
-Module for the propeller with shaft bottom-up parametrized construction.
-"""
-import numpy as np
-from OCC.Core.IGESControl import IGESControl_Writer
-from OCC.Core.BRepBuilderAPI import BRepBuilderAPI_Sewing
-from OCC.Core.BRepAlgoAPI import BRepAlgoAPI_Fuse
-from OCC.Extend.DataExchange import write_stl_file
-from OCC.Display.SimpleGui import init_display
-from smithers.io.obj import ObjHandler, WavefrontOBJ
-from smithers.io.stlhandler import STLHandler
-
-from OCC.Core.BRep import BRep_Builder
-from OCC.Core.TopoDS import TopoDS_Compound
-import copy
-
-def make_compound(shapes):
- builder = BRep_Builder()
- comp = TopoDS_Compound()
- builder.MakeCompound(comp)
-
- for s in shapes:
- if s is None:
- raise ValueError("make_compound: shape is None")
- builder.Add(comp, s)
-
- return comp
-
-class Propeller(object):
- """
- Bottom-up parametrized propeller (including shaft) construction.
- The constructor requires PythonOCC to be installed.
-
- :param shaft.Shaft shaft: shaft to be added to the propeller
- :param blade.Blade blade: blade of the propeller
- :param int n_blades: number of blades composing the propeller
- :cvar OCC.Core.TopoDS.TopoDS_Solid shaft_solid: solid shaft
- :cvar OCC.Core.TopoDS.TopoDS_Shell sewed_full_body: propeller with shaft shell
- """
-
- def __init__(self, shaft, blade, n_blades, reflect_blade=False):
- self.shaft = shaft
-
- blade.build(reflect=reflect_blade)
-
- self.blades = [copy.deepcopy(blade) for _ in range(n_blades)]
- [
- blade.rotate(rad_angle=i * 2.0 * np.pi / float(n_blades))
- for i, blade in enumerate(self.blades)
- ]
-
-
- def tmp_stl(self, filename, linear_deflection=0.1):
- """
-
- """
- from OCC.Core.BRepMesh import BRepMesh_IncrementalMesh
- from OCC.Core.StlAPI import StlAPI_Writer
- shapes = []
- for blade_ in self.blades:
-
- sewer = BRepBuilderAPI_Sewing(1e-2)
- sewer.Add(blade_.upper_face)
- sewer.Add(blade_.lower_face)
- sewer.Add(blade_.root_face)
- sewer.Add(blade_.tip_face)
- sewer.Perform()
- sewed_shape = sewer.SewedShape()
- shapes.append(sewed_shape)
-
- blades_compound = make_compound(shapes)
- triangulation = BRepMesh_IncrementalMesh(blades_compound, linear_deflection, True)
- triangulation.Perform()
-
- writer = StlAPI_Writer()
- writer.SetASCIIMode(False)
- writer.Write(blades_compound, filename)
-
- @property
- def shape(self):
- if hasattr(self, '_shape'):
- return self._shape
-
- solid = self.solid
-
- sewer = BRepBuilderAPI_Sewing(1e-2)
- sewer.Add(solid)
- sewer.Perform()
-
- self._shape = sewer.SewedShape()
- return self._shape
-
- @property
- def solid(self):
- """
- Docstring for build
-
- :param self: Description
- """
- if hasattr(self, '_solid'):
- return self._solid
-
- shaft_solid = self.shaft.generate_solid()
- blade_solids = [blade_.generate_solid() for blade_ in self.blades]
- blades_compound = make_compound(blade_solids)
-
- fuse = BRepAlgoAPI_Fuse(shaft_solid, blades_compound)
- # fuse.SetRunParallel(True) # if available in your build
- fuse.SetFuzzyValue(1e-4)
-
- fuse.Build()
- if not fuse.IsDone():
- raise RuntimeError("Fuse shaft + blades failed")
-
- self._solid = fuse.Shape()
- return self._solid
-
-
- def export_iges(self, filename):
- """
- Export the .iges CAD for the propeller with shaft.
-
- :param string filename: path (with the file extension) where to store
- the .iges CAD for the propeller and shaft
- :raises RuntimeError: if the solid assembling of blades is not
- completed successfully
- """
- iges_writer = IGESControl_Writer()
- iges_writer.AddShape(self.shape)
- iges_writer.Write(filename)
-
- def export_stl(self, filename):
- """
- Export the .stl CAD for the propeller with shaft.
-
- :param string filename: path (with the file extension) where to store
- the .stl CAD for the propeller and shaft
- :raises RuntimeError: if the solid assembling of blades is not
- completed successfully
- """
- write_stl_file(self.shape, filename)
-
- def generate_obj(self, filename, region_selector="by_coords", **kwargs):
- """
- Export the .obj CAD for the propeller with shaft. The resulting
- file contains two regions: `propellerTip` and `propellerStem`, selected
- according to the criteria passed in the parameter `region_selector`.
-
- :param string filename: path (with the file extension).
- :param string region_selector: Two selectors available:
-
- * `by_coords`: We compute :math:`x`, the smallest X coordinate of
- the solid which represents the blades of the propeller. Then all
- the polygons (belonging to both blades and shaft) composed of
- points whose X coordinate is greater than :math:`x` are
- considered to be part of the region `propellerTip`. The rest
- belongs to `propellerStem`;
- * `blades_and_stem`: The two regions are simply given by the two
- solids which are used in :func:`__init__`.
- :raises RuntimeError: if the solid assembling of blades is not
- completed successfully
- """
-
- # we write the propeller to STL, then re-open it to obtain the points
- write_stl_file(self.shaft_solid, "/tmp/temp_shaft.stl")
- shaft = STLHandler.read("/tmp/temp_shaft.stl")
- write_stl_file(self.blades_solid, "/tmp/temp_blades.stl")
- blades = STLHandler.read("/tmp/temp_blades.stl")
-
- obj_instance = WavefrontOBJ()
-
- # add vertexes. first of all we check for duplicated vertexes
- all_vertices = np.concatenate(
- [shaft["points"], blades["points"]], axis=0
- )
-
- # unique_mapping maps items in all_vertices to items in unique_vertices
- unique_vertices, unique_mapping = np.unique(
- all_vertices, return_inverse=True, axis=0
- )
- obj_instance.vertices = unique_vertices
-
- def cells_to_np(cells):
- cells = np.asarray(cells)
- return unique_mapping[cells.flatten()].reshape(-1, cells.shape[1])
-
- # append a list of cells to obj_instance.polygons, possibly with a
- # region name
- def append_cells(cells, region_name=None):
- if region_name is not None:
- obj_instance.regions_change_indexes.append(
- (
- np.asarray(obj_instance.polygons).shape[0],
- len(obj_instance.regions),
- )
- )
- obj_instance.regions.append(region_name)
-
- if len(obj_instance.polygons) == 0:
- obj_instance.polygons = np.array(cells_to_np(cells))
- else:
- obj_instance.polygons = np.concatenate(
- [obj_instance.polygons, cells_to_np(cells)], axis=0
- )
-
- shaft_cells = np.asarray(shaft["cells"])
- # the 0th point in blades if the last+1 point in shaft
- blades_cells = np.asarray(blades["cells"]) + len(shaft["points"])
-
- if region_selector == "blades_and_stem":
- defaultKwargs = {'blades_name' : 'blades', 'shaft_name' : 'shaft'}
- kwargs = {**defaultKwargs, **kwargs}
- append_cells(blades_cells, region_name=kwargs['blades_name'])
- append_cells(shaft_cells, region_name=kwargs['shaft_name'])
-
- elif region_selector == "by_coords":
- defaultKwargs = {'blades_name' : 'blades', 'shafthead_name' : 'shaftHead', 'shafttail_name' : 'shaftTail'}
- kwargs = {**defaultKwargs, **kwargs}
- minimum_blades_x = np.min(blades["points"][:, 0])
- maximum_blades_x = np.max(blades["points"][:, 0])
- shaft_x = shaft["points"][:, 0]
-
- if np.count_nonzero(shaft_x > maximum_blades_x) >= np.count_nonzero(shaft_x < maximum_blades_x):
- tip_boolean_array = shaft["points"][:, 0] <= maximum_blades_x
-
- elif np.count_nonzero(shaft_x < maximum_blades_x) > np.count_nonzero(shaft_x > maximum_blades_x):
- tip_boolean_array = shaft["points"][:, 0] >= minimum_blades_x
-
- shaft_cells_tip = np.all(
- tip_boolean_array[shaft_cells.flatten()].reshape(
- -1, shaft_cells.shape[1]
- ),
- axis=1,
- )
-
- append_cells(
- shaft_cells[shaft_cells_tip],
- region_name=kwargs['shafthead_name'],
- )
- append_cells(
- shaft_cells[np.logical_not(shaft_cells_tip)],
- region_name=kwargs['shafttail_name'],
- )
- append_cells(
- blades_cells,
- region_name=kwargs['blades_name'],
- )
- else:
- raise ValueError("This selector is not supported at the moment")
-
- # this is needed because indexes start at 1
- obj_instance.polygons += 1
-
- ObjHandler.write(obj_instance, filename)
-
- def generate_obj_blades(self, filename):
- """
- Export the .obj CAD for the blades.
-
- :param string filename: path (with the file extension).
- """
-
- # we write the propeller to STL, then re-open it to obtain the points
- write_stl_file(self.blades_solid, "/tmp/temp_blades.stl")
- blades = STLHandler.read("/tmp/temp_blades.stl")
-
- obj_instance = WavefrontOBJ()
-
- # add vertexes. first of all we check for duplicated vertexes
- all_vertices = blades["points"]
- # unique_mapping maps items in all_vertices to items in unique_vertices
- unique_vertices, unique_mapping = np.unique(
- all_vertices, return_inverse=True, axis=0
- )
- obj_instance.vertices = unique_vertices
-
- def cells_to_np(cells):
- cells = np.asarray(cells)
- return unique_mapping[cells.flatten()].reshape(-1, cells.shape[1])
- # append a list of cells to obj_instance.polygons, possibly with a
- # region name
- def append_cells(cells):
- obj_instance.regions_change_indexes.append(
- (
- np.asarray(obj_instance.polygons).shape[0],
- len(obj_instance.regions),
- )
- )
- obj_instance.regions.append('blades')
-
- if len(obj_instance.polygons) == 0:
- obj_instance.polygons = np.array(cells_to_np(cells))
- else:
- obj_instance.polygons = np.concatenate(
- [obj_instance.polygons, cells_to_np(cells)], axis=0
- )
-
- blades_cells = np.asarray(blades["cells"])
-
- append_cells(blades_cells)
- obj_instance.polygons += 1
-
- ObjHandler.write(obj_instance, filename)
-
- def display(self):
- """
- Display the propeller with shaft.
- """
- display, start_display = init_display()[:2]
- display.DisplayShape(self.shape, update=True)
- start_display()
\ No newline at end of file
diff --git a/bladex/reversepropeller/__init__.py b/bladex/reversepropeller/__init__.py
deleted file mode 100644
index 904f92b..0000000
--- a/bladex/reversepropeller/__init__.py
+++ /dev/null
@@ -1,10 +0,0 @@
-"""
-Profile init
-"""
-__all__ = ['ReversePropellerInterface', 'BaseReversePropeller',
- 'ReversePropeller', 'ReversePropellerBladeX']
-
-from .reversepropellerinterface import ReversePropellerInterface
-from .basereversepropeller import BaseReversePropeller
-from .reversepropeller import ReversePropeller
-from .reversepropellerbladex import ReversePropellerBladeX
diff --git a/bladex/reversepropeller/basereversepropeller.py b/bladex/reversepropeller/basereversepropeller.py
deleted file mode 100644
index 49cb34a..0000000
--- a/bladex/reversepropeller/basereversepropeller.py
+++ /dev/null
@@ -1,385 +0,0 @@
-import sys
-import numpy as np
-import csv
-from bladex import CustomProfile, Blade, Propeller, Shaft
-from .reversepropellerinterface import ReversePropellerInterface
-from OCC.Core.IGESControl import (IGESControl_Reader)
-from OCC.Core.BRepBuilderAPI import BRepBuilderAPI_MakeVertex,\
- BRepBuilderAPI_MakeEdge, BRepBuilderAPI_MakeWire, BRepBuilderAPI_MakeSolid, \
- BRepBuilderAPI_Sewing, BRepBuilderAPI_NurbsConvert
-from OCC.Core.BRep import BRep_Tool
-import OCC.Core.TopoDS
-from OCC.Core.TopTools import TopTools_ListOfShape
-from OCC.Core.TopExp import TopExp_Explorer
-from OCC.Core.TopAbs import TopAbs_VERTEX, TopAbs_EDGE, TopAbs_FACE, TopAbs_WIRE, TopAbs_SHELL
-from OCC.Core.gp import gp_Pnt, gp_Dir, gp_Ax2, gp_Vec, gp_Pln
-from OCC.Core.TColgp import TColgp_Array1OfPnt
-from OCC.Core.BRepAdaptor import BRepAdaptor_Curve
-from OCC.Core.GCPnts import GCPnts_AbscissaPoint
-from OCC.Core.BRep import BRep_Tool
-from OCC.Core.TopoDS import topods
-from OCC.Display.SimpleGui import init_display
-from OCC.Core.BRepPrimAPI import BRepPrimAPI_MakeCylinder
-from OCC.Core.GeomLProp import GeomLProp_SLProps
-from OCC.Core.GCPnts import GCPnts_AbscissaPoint
-from OCC.Core.BRepAdaptor import (BRepAdaptor_Curve,
- BRepAdaptor_CompCurve)
-from OCC.Core.GeomAPI import GeomAPI_PointsToBSpline
-from OCC.Core.GeomAbs import GeomAbs_C2
-from OCC.Core.Bnd import Bnd_Box
-from OCC.Core.BRepBndLib import brepbndlib
-from OCC.Core.BRepAlgoAPI import BRepAlgoAPI_Section
-from OCC.Core.Geom import Geom_Plane
-from OCC.Core.BRepBuilderAPI import BRepBuilderAPI_MakeFace
-from scipy.interpolate import interp1d
-import matplotlib.pyplot as plt
-
-
-class BaseReversePropeller(ReversePropellerInterface):
- """
- Base class for the extraction of the parameters of a blade and reconstruction of the parametrized
- blade and of the entire propeller.
-
- Depending on the source code of the generated blade, different child classes can be chosen.
-
-
- Given the IGES file of the blade, the following parameters are extracted:
-
- - :math:`(X, Y)` coordinates of the blade cylindrical sections after
- being expanded in 2D to create airfoils.
-
- - Chord length, for each cylindrical section.
-
- - Pitch :math:`(P)`, for each cylindrical section.
-
- - Rake :math:`(k)`, in distance units, for each cylindrical section.
-
- - Skew angle :math:`(\\theta_s)`, for each cylindrical section, expressed
- in degrees.
-
- The parameters can be saved in a csv file with the method
- 'save_global_parameters' and used to reconstruct the blade, which is saved
- in a IGES file (method 'reconstruct_blade').
- The coordinates of each section can be extracted with the method
- 'reconstruct_sections'.
- Given the shaft, the whole propeller can be reconstructed and saved in a
- IGES file with the method 'reconstruct_propeller'.
-
- --------------------------
-
- :param filename: path to the IGES file of the blade.
- :param list radii_list: list which contains the radii values of the
- sectional profiles.
- :param num_points_top_bottom: number of points used to interpolate each
- sectional profile.
- """
- def __init__(self, filename, radii_list, num_points_top_bottom):
-
- self.iges_file = filename #filename is the path to the file iges
- self.radii_list = radii_list #radii at which we want to measure properties
- self.section_points_number = 1200 #number of points for each section profile
- self.airfoil_points_number = 1000
- self.num_points_top_bottom = num_points_top_bottom #number of points used to reconstruct the profile, equal for top and lower parts of the profile
- # self.num_sections = len(self.radii_list)
- # Initialize things we want to compute from the blade IGES file
- self.pitch_angles_list = []
- self.pitch_list = []
- self.skew_angles_list = []
- self.skew_list = []
- self.rake_list = []
- self.chord_length_list = []
- self.blade_solid = None
- self.blade_compound = None
- self.tolerance_solid = 5e-2
- self._extract_solid_from_file()
- num_sections = len(radii_list)
- self.xup = np.zeros((num_sections, self.num_points_top_bottom))
- self.xdown = np.zeros((num_sections, self.num_points_top_bottom))
- self.yup = np.zeros((num_sections, self.num_points_top_bottom))
- self.ydown = np.zeros((num_sections, self.num_points_top_bottom))
- # Lists of OCC objects used for plotting in display_* methods
- self.cylinder_lateral_faces_list = []
- self.section_wires_list = []
- self.camber_wires_list = []
-
- def _extract_solid_from_file(self):
- """
- Private method that reads the IGES file of the blade and constructs
- the correspondent solid object
- """
- # Extract the blade from the IGES file; build it as a solid with OCC
- iges_reader = IGESControl_Reader()
- iges_reader.ReadFile(self.iges_file)
- iges_reader.TransferRoots()
- sewer = BRepBuilderAPI_Sewing(self.tolerance_solid)
- # Case where we have Faces and not closed surface.
- # This is the case for BladeX generated blade
- if iges_reader.Shape().ShapeType() == 4:
- self.blade_compound = iges_reader.OneShape()
- exp = TopExp_Explorer(self.blade_compound, TopAbs_FACE)
- while exp.More():
- sewer.Add(exp.Current())
- exp.Next()
- else:
- self.blade_compound = iges_reader.Shape()
- sewer.Add(self.blade_compound)
- sewer.Perform()
- result_sewed_blade = sewer.SewedShape()
- blade_solid_maker = BRepBuilderAPI_MakeSolid()
- if result_sewed_blade.ShapeType() == 0:
- exp = TopExp_Explorer(result_sewed_blade, TopAbs_SHELL)
- while exp.More():
- shell = topods.Shell(exp.Current())
- blade_solid_maker.Add(shell)
- exp.Next()
- else:
- blade_solid_maker.Add(OCC.Core.TopoDS.topods.Shell(result_sewed_blade))
- if (blade_solid_maker.IsDone()):
- self.blade_solid = blade_solid_maker.Solid()
- else:
- self.blade_solid = result_sewed_blade
-
- def _build_cylinder(self, radius):
- """
- Private method that builds the cylinder which intersects the blade
- at a specific cylindrical section.
- Argument 'radius' is the radius value corresponding to the cylindrical
- section taken into account. This method is applied to all the radii in
- list 'radii_list' given as input.
- """
- # Base point such that cylinder intersect all section
- bbox = Bnd_Box()
- brepbndlib.Add(self.blade_solid, bbox)
- xmin, _, _, xmax, _, _ = bbox.Get()
-
- axis = gp_Ax2(gp_Pnt(xmin-0.2*abs(xmin), 0.0, 0.0),
- gp_Dir(1.0, 0.0, 0.0))
- self.cylinder = BRepPrimAPI_MakeCylinder(axis, radius, 1.2*(xmax-xmin)).Shape()
- faceCount = 0
- faces_explorer = TopExp_Explorer(self.cylinder, TopAbs_FACE)
-
- while faces_explorer.More():
- face = OCC.Core.TopoDS.topods.Face(faces_explorer.Current())
- faceCount += 1
- # Convert the cylinder faces into Non Uniform Rational Basis-Splines geometry (NURBS)
- nurbs_converter = BRepBuilderAPI_NurbsConvert(face)
- nurbs_converter.Perform(face)
- nurbs_face_converter = nurbs_converter.Shape()
- nurbs_face = OCC.Core.TopoDS.topods.Face(nurbs_face_converter)
-
- surface = BRep_Tool.Surface(OCC.Core.TopoDS.topods.Face(nurbs_face))
- self.bounds = 0.0
- self.bounds = surface.Bounds()
-
- # Compute the normal curve to the surfaces, specifying the bounds considered,
- # the maximum order of the derivative we want to compute, the linear tolerance
- normal = GeomLProp_SLProps(surface,
- (self.bounds[0] + self.bounds[1]) / 2.0,
- (self.bounds[2] + self.bounds[3]) / 2.0,
- 1, self.linear_tolerance).Normal()
- if (normal * axis.Direction() == 0):
- self.cylinder_lateral_face = face
- self.cylinder_lateral_surface = surface
- self.cylinder_lateral_faces_list.append(surface)
- faces_explorer.Next()
-
- def _extract_parameters_and_transform_profile(self, radius):
- """
- Private method which extracts the parameters (pitch, rake, skew ,...) related
- to a specific section of the blade, and then transforms the camber points
- initialized in _initial_camber_points_plane and the prile points initialized
- in _initial_airfoil_points_plane according to the parameters found.
- This method trasforms the leading and trailing edges initialed in
- _initial_leading_trailing_edges and the mid chord point as well.
-
- Basically all points and edges of the profile section are transformed
- to fulfill the properties of the specific sectionwe are considering.
- """
- self.pitch_angle = np.arctan2(
- self.leading_edge_point_on_plane[1] -
- self.trailing_edge_point_on_plane[1],
- self.leading_edge_point_on_plane[0] -
- self.trailing_edge_point_on_plane[0])
- self.skew = self.mid_chord_point_on_plane[1]
- self.rake_induced_by_skew = self.skew / np.tan(self.pitch_angle)
-
- self.airfoil_points_on_plane[:, 1:2] -= self.skew
- self.camber_points_on_plane[:, 1:2] -= self.skew
- self.leading_edge_point_on_plane[1] -= self.skew
- self.trailing_edge_point_on_plane[1] -= self.skew
- self.mid_chord_point_on_plane[1] -= self.skew
-
-
- self.airfoil_points_on_plane[:, 0:1] -= self.rake_induced_by_skew
- self.camber_points_on_plane[:, 0:1] -= self.rake_induced_by_skew
- self.leading_edge_point_on_plane[0] -= self.rake_induced_by_skew
- self.trailing_edge_point_on_plane[0] -= self.rake_induced_by_skew
- self.mid_chord_point_on_plane[0] -= self.rake_induced_by_skew
-
-
- self.rake = self.mid_chord_point_on_plane[0]
-
- self.airfoil_points_on_plane[:, 0:1] -= self.rake
- self.camber_points_on_plane[:, 0:1] -= self.rake
- self.leading_edge_point_on_plane[0] -= self.rake
- self.trailing_edge_point_on_plane[0] -= self.rake
- self.mid_chord_point_on_plane[0] -= self.rake
-
- self.rotation_matrix = np.zeros((2, 2))
- self.rotation_matrix[0][0] = np.cos(-self.pitch_angle)
- self.rotation_matrix[0][1] = -np.sin(-self.pitch_angle)
- self.rotation_matrix[1][0] = np.sin(-self.pitch_angle)
- self.rotation_matrix[1][1] = np.cos(-self.pitch_angle)
-
- self.airfoil_points_on_plane = self.airfoil_points_on_plane.dot(
- self.rotation_matrix.transpose())
- self.camber_points_on_plane = self.camber_points_on_plane.dot(
- self.rotation_matrix.transpose())
- self.leading_edge_point_on_plane = self.leading_edge_point_on_plane.dot(
- self.rotation_matrix.transpose())
- self.trailing_edge_point_on_plane = self.trailing_edge_point_on_plane.dot(
- self.rotation_matrix.transpose())
- self.mid_chord_point_on_plane = self.mid_chord_point_on_plane.dot(
- self.rotation_matrix.transpose())
-
-
- self.chord_length = ((self.leading_edge_point_on_plane[0] -
- self.trailing_edge_point_on_plane[0])**2 +
- (self.leading_edge_point_on_plane[1] -
- self.trailing_edge_point_on_plane[1])**2)**.5
-
- self.airfoil_points_on_plane[:, 0:2] /= self.chord_length
- self.camber_points_on_plane[:, 0:2] /= self.chord_length
- self.leading_edge_point_on_plane[0:1] /= self.chord_length
- self.trailing_edge_point_on_plane[0:1] /= self.chord_length
- self.mid_chord_point_on_plane[0:1] /= self.chord_length
-
- self.airfoil_points_on_plane[:, 0:1] *= -1.0
- self.camber_points_on_plane[:, 0:1] *= -1.0
- self.leading_edge_point_on_plane[0] *= -1.0
- self.trailing_edge_point_on_plane[0] *= -1.0
- self.mid_chord_point_on_plane[0] *= -1.0
-
- self.airfoil_points_on_plane[:, 0:1] += 0.5
- self.camber_points_on_plane[:, 0:1] += 0.5
- self.leading_edge_point_on_plane[0] += 0.5
- self.trailing_edge_point_on_plane[0] += 0.5
- self.mid_chord_point_on_plane[0] += 0.5
-
- self.camber_points_on_plane = np.matrix(self.camber_points_on_plane)
- self.camber_points_on_plane[0, 0] = 0.0
- self.camber_points_on_plane[-1, 0] = 1.0
-
- self.camber_points_on_plane = np.sort(
- self.camber_points_on_plane.view('float64,float64'),
- order=['f0'],
- axis=0).view(np.float64)
- self.f_camber = interp1d(
- np.squeeze(np.asarray(self.camber_points_on_plane[:, 0])),
- np.squeeze(np.asarray(self.camber_points_on_plane[:, 1])),
- kind='cubic')
-
- def save_global_parameters(self, filename_csv):
- """
- Method that writes all blade properties and points of the sections
- in a csv file named filename_csv
- """
-
- # open the file in the write mode
- with open(filename_csv, 'w') as f:
- # create the csv writer
- writer = csv.writer(f)
- # write a row to the csv file
- writer.writerow(("Radii list: ", self.radii_list))
- writer.writerow(("Pitch angles list: ", self.pitch_angles_list))
- writer.writerow(("Pitch list: ", self.pitch_list))
- writer.writerow(("Skew angles list: ", self.skew_angles_list))
- writer.writerow(("Rake list: ", self.rake_list))
- writer.writerow(("Chord length list: ", self.chord_length_list))
- for j in range(len(self.radii_list)):
- writer.writerow(("x section" + str(j) + " upper coordinates: ",
- self.xup[j, :]))
- writer.writerow(("x section" + str(j) + " lower coordinates: ",
- self.xdown[j, :]))
- writer.writerow(("y section" + str(j) + " upper coordinates: ",
- self.yup[j, :]))
- writer.writerow(("y section" + str(j) + " lower coordinates: ",
- self.ydown[j, :]))
-
- def reconstruct_sections(self):
- """
- Method that reconstructs single sections of the blade starting from the
- points computed from the original IGES file.
- If sections are not enough to reconstruct the blade, one can just export sections
- and then reconstruct the blade in a dedicated script.
- """
-
- for j in range(self.num_sections):
- self.recons_sections[j] = CustomProfile(
- xup=self.xup[j, :],
- yup=self.yup[j, :],
- xdown=self.xdown[j, :],
- ydown=self.ydown[j, :])
- return self.recons_sections
-
- def reconstruct_blade(self):
- """
- Method that reconstructs the blade starting from the sections
- computed from the original IGES file, and then reconstruct the 4 parts
- of the blade (upper, lower face, tip, root).
- """
-
- for j in range(self.num_sections):
- self.recons_sections[j] = CustomProfile(
- xup=self.xup[j, :],
- yup=self.yup[j, :],
- xdown=self.xdown[j, :],
- ydown=self.ydown[j, :])
- radii = np.array(self.radii_list) / 1000
- self.recons_blade = Blade(sections=self.recons_sections,
- radii=radii,
- chord_lengths=self.chord_length_list,
- pitch=self.pitch_list,
- rake=self.rake_list,
- skew_angles=self.skew_angles_list)
- self.recons_blade.apply_transformations()
- self.recons_blade.generate_iges_blade('iges_reconstructed.iges')
-
- def reconstruct_propeller(self, propeller_iges, shaft_iges, n_blades):
- """
- Method which reconstructs the whole propeller with shaft starting from
- the iges file of the shaft and the number of blades. The whole propeller
- is saved in an IGES file named filename_iges (must be given as input).
- """
- shaft_path = shaft_iges
- prop_shaft = Shaft(shaft_path)
- prop = Propeller(prop_shaft, self.recons_blade, n_blades)
- prop.generate_iges(propeller_iges)
- prop.display()
-
- def display_cylinder(self, radius):
- """
- Method that displays the cylinder and the blade intersecting each others.
- If the radius is not in self.radii_list, error is raised
- """
- if radius not in self.radii_list:
- raise ValueError("The radius must be among the ones passed in the constructor of the object. The unit is mm.")
- index_radius = np.where(self.radii_list == radius)[0][0]
- display, start_display, add_menu, add_function_to_menu = init_display()
- display.DisplayShape(self.blade_solid, update=True)
- display.DisplayShape(self.cylinder_lateral_faces_list[index_radius], update=True)
- display.DisplayShape(self.section_wires_list[index_radius], update=True)
- start_display()
-
- def display_section(self, radius):
- """
- Method that displays a section profile over the cylinder with its camber line.
- """
- if radius not in self.radii_list:
- raise ValueError("The radius must be among the ones passed in the constructor of the object. The unit is mm.")
- index_radius = np.where(self.radii_list == radius)[0][0]
- display, start_display, add_menu, add_function_to_menu = init_display()
- display.DisplayShape(self.cylinder_lateral_faces_list[index_radius], update=True)
- display.DisplayShape(self.section_wires_list[index_radius], update=True)
- display.DisplayShape(self.camber_wires_list[index_radius], color="GREEN", update=True)
- start_display()
diff --git a/bladex/reversepropeller/reversepropeller.py b/bladex/reversepropeller/reversepropeller.py
deleted file mode 100644
index 1bc98e2..0000000
--- a/bladex/reversepropeller/reversepropeller.py
+++ /dev/null
@@ -1,554 +0,0 @@
-"""
-Module for the extraction of the parameters of a blade and for the
-approximated reconstruction of the blade and the whole propeller.
-"""
-
-import numpy as np
-from bladex import CustomProfile, Blade, Propeller, Shaft
-from .basereversepropeller import BaseReversePropeller
-from OCC.Core.IGESControl import (IGESControl_Reader)
-from OCC.Core.BRepBuilderAPI import BRepBuilderAPI_MakeVertex,\
- BRepBuilderAPI_MakeEdge, BRepBuilderAPI_MakeWire, BRepBuilderAPI_MakeSolid, \
- BRepBuilderAPI_Sewing, BRepBuilderAPI_NurbsConvert
-from OCC.Core.BRep import BRep_Tool
-import OCC.Core.TopoDS
-from OCC.Core.TopTools import TopTools_ListOfShape
-from OCC.Core.TopExp import TopExp_Explorer
-from OCC.Core.TopAbs import TopAbs_VERTEX, TopAbs_EDGE, TopAbs_FACE, TopAbs_WIRE
-from OCC.Core.gp import gp_Pnt, gp_Dir, gp_Ax2, gp_Vec
-from OCC.Core.TColgp import TColgp_Array1OfPnt
-from OCC.Core.BRepAdaptor import BRepAdaptor_Curve
-from OCC.Core.GCPnts import GCPnts_AbscissaPoint
-from OCC.Core.BRep import BRep_Tool
-from OCC.Core.BRepExtrema import BRepExtrema_DistShapeShape
-from OCC.Core.TopoDS import topods
-from OCC.Display.SimpleGui import init_display
-from OCC.Core.BRepPrimAPI import BRepPrimAPI_MakeCylinder
-from OCC.Core.GeomLProp import GeomLProp_SLProps
-from OCC.Core.GCPnts import GCPnts_AbscissaPoint
-from OCC.Core.BRepAdaptor import (BRepAdaptor_Curve,
- BRepAdaptor_CompCurve)
-from OCC.Core.GeomAPI import GeomAPI_PointsToBSpline
-from OCC.Core.GeomAbs import GeomAbs_C2
-from OCC.Core.Bnd import Bnd_Box
-from OCC.Core.BRepBndLib import brepbndlib
-from OCC.Core.BRepAlgoAPI import BRepAlgoAPI_Section
-from OCC.Display.SimpleGui import init_display
-
-from scipy.spatial import Voronoi
-from scipy.interpolate import interp1d
-
-def distance(P1, P2):
- """
- distance between two points
- """
- return ((P1[0] - P2[0])**2 + (P1[1] - P2[1])**2)**0.5
-
-
-def optimized_path(coords, start=None):
- if start is None:
- start = coords[0]
- pass_by = coords
- path = [start]
- pass_by.remove(start)
- while pass_by:
- nearest = min(pass_by, key=lambda x: distance(path[-1], x))
- path.append(nearest)
- pass_by.remove(nearest)
- return path
-
-def point_inside_polygon(x, y, poly, include_edges=True):
- """
- Test if point (x,y) is inside polygon poly.
-
- poly is N-vertices polygon defined as
- [(x1,y1),...,(xN,yN)] or [(x1,y1),...,(xN,yN),(x1,y1)]
- (function works fine in both cases)
-
- Geometrical idea: point is inside polygon if horisontal beam
- to the right from point crosses polygon even number of times.
- Works fine for non-convex polygons.
- """
- n = len(poly)
- inside = False
-
- p1x, p1y = poly[0]
- for i in range(1, n + 1):
- p2x, p2y = poly[i % n]
- if p1y == p2y:
- if y == p1y:
- if min(p1x, p2x) <= x <= max(p1x, p2x):
- # point is on horisontal edge
- inside = include_edges
- break
- elif x < min(p1x,
- p2x): # point is to the left from current edge
- inside = not inside
- else: # p1y!= p2y
- if min(p1y, p2y) <= y <= max(p1y, p2y):
- xinters = (y - p1y) * (p2x - p1x) / float(p2y - p1y) + p1x
-
- if x == xinters: # point is right on the edge
- inside = include_edges
- break
-
- if x < xinters: # point is to the left from current edge
- inside = not inside
-
- p1x, p1y = p2x, p2y
-
- return inside
-
-
-class ReversePropeller(BaseReversePropeller):
- """
-
- :param filename: path to the IGES file of the blade.
- :param list radii_list: list which contains the radii values of the
- sectional profiles.
- :param num_points_top_bottom: number of points used to interpolate each
- sectional profile.
- """
- def __init__(self, filename, radii_list, num_points_top_bottom):
-
- super().__init__(filename, radii_list, num_points_top_bottom)
- ind_sec = 0
- for radius in self.radii_list:
- self.cylinder = None
- self.bounds = None
- self.cylinder_lateral_face = None
- self.cylinder_lateral_surface = None
- self.linear_tolerance = 1e-3
- self.conversion_unit = 1000
- self._build_cylinder(radius)
- self._build_intersection_cylinder_blade()
- self.leading_edge_point = []
- self.trailing_edge_point = []
- self.edge_3d = None
- self.camber_curve_edge = None
- self.first_edge = None
- self.last_edge = None
- self.firstSegment = None
- self.lastSegment = None
- self.camber_points_on_plane = None
- self.leading_edge_point_on_plane = []
- self.trailing_edge_point_on_plane = []
- # Compute a number section_points_number of points on the parametric curve
- # at a equal relative distance (taken on the curvilinear ascissa)
- self.param_plane_points = []
- self.orig_param_plane_points = []
- self._camber_points(radius)
- self._voronoi_points(radius)
- self._camber_curve(radius)
- self._initial_leading_trailing_edges_plane(radius)
- self._initial_camber_points_plane(radius)
- self._initial_airfoil_points_plane(radius)
- self._extract_parameters_and_transform_profile(radius)
- self._store_properties(radius)
- self._airfoil_top_and_bottom_points()
- self.xup[ind_sec, :] = self.ascissa
- self.xdown[ind_sec, :] = self.ascissa
- self.yup[ind_sec, :] = self.int_airfoil_top
- self.ydown[ind_sec, :] = self.int_airfoil_bottom
- ind_sec = ind_sec + 1
-
-
- def _build_intersection_cylinder_blade(self):
- """
- Private method that constructs the section lines which are the intersections
- between the cylinder at a fixed radius and the blade, and the camber points.
- """
- # Construction of the section lines between two shapes (in this case the
- # blade and the lateral face of the cylinder)
- section_builder = BRepAlgoAPI_Section(self.blade_solid,
- self.cylinder_lateral_face, False)
- # Define and build the parametric 2D curve (pcurve) for the section lines defined above
- section_builder.ComputePCurveOn2(True)
- section_builder.Build()
- self.section = section_builder.Shape()
- edgeExplorer = TopExp_Explorer(self.section, TopAbs_EDGE)
- wire_maker = BRepBuilderAPI_MakeWire()
-
- edgeCount = 0
- self.total_section_length = 0.0
- edgeList = TopTools_ListOfShape()
- while edgeExplorer.More():
- edgeCount = edgeCount + 1 # Numbering from 1 in OCC
- edge = topods.Edge(edgeExplorer.Current())
- edgeList.Append(edge)
- edgeExplorer.Next()
- wire_maker.Add(edgeList)
- self.wire = wire_maker.Wire()
- self.section_wires_list.append(self.wire)
- self.curve_adaptor = BRepAdaptor_CompCurve(
- OCC.Core.TopoDS.topods.Wire(self.wire))
- # Length of the curve section (ascissa curvilinea)
- self.total_section_length = GCPnts_AbscissaPoint.Length(
- self.curve_adaptor)
-
-
- def _camber_points(self, radius):
- """
- Private method which computes the single points of the camber curve and
- collects them in param_plane_points and in orig_plane_points.
- """
- firstParam = self.curve_adaptor.FirstParameter()
- for i in range(self.section_points_number):
- rel_distance = float(i) / float(
- self.section_points_number) * self.total_section_length
- point_generator = GCPnts_AbscissaPoint(1e-7, self.curve_adaptor,
- rel_distance, firstParam)
- param = point_generator.Parameter()
- point = self.curve_adaptor.Value(param)
- # Compute the angle for polar reference system
- theta = np.arctan2(point.Y(), point.Z())
- if theta < 0:
- theta += 2.0 * np.pi
- # Param_plane_points is the list of all points parametrized in cylindric coordinates,
- # i.e., the coordinate along X (the axis of the cylinder) and the
- # radius multiplying the polar angle.
- self.orig_param_plane_points.append([point.X(), radius * theta])
- self.param_plane_points.append([point.X(), radius * theta])
-
- def _voronoi_points(self, radius):
- """
- Private method which computes the points of the Voronoi map for each
- section of the blade.
-
- """
- # update the bounds of the section
- self.bounds = [0.0, 0.0, 0.0, 0.0]
- for p in self.param_plane_points:
- self.bounds[0] = min(self.bounds[0], p[0])
- self.bounds[1] = max(self.bounds[1], p[0])
- self.bounds[2] = min(self.bounds[2], p[1])
- self.bounds[3] = max(self.bounds[3], p[1])
- # Create the Voronoi diagram for the 2D points
- vor = Voronoi(self.param_plane_points)
- vor_points = []
- # Find in an iterative way the Voronoi points
- for i in range(len(vor.vertices)):
- p = [vor.vertices[i][0], vor.vertices[i][1]]
- if (point_inside_polygon(p[0],
- p[1],
- self.param_plane_points,
- include_edges=True)):
- vor_points.append(p)
- optimized_vor_points = sorted(vor_points, key=lambda x: x[0])
- #vor_us includes the X coordinates and vor_vs the Z coordinates
- self.vor_us = []
- self.vor_vs = []
- for p in optimized_vor_points:
- # coordinates of the points of the Voronoi map
- self.vor_us.append(p[0])
- self.vor_vs.append(p[1])
-
- def _camber_curve(self, radius):
- """
- Private method which constructs the camber curve by interpolating the
- points found with the method _camber_points. Also the leading and the
- trailing edge are found and assembled with the camber line in a unique
- object.
- """
- # Create objects for the points of the Voronoi map, construct Splines
- # to construct the camber line, the upper and lower part of each section profile.
- Pnts = TColgp_Array1OfPnt(1, len(self.vor_us))
- for i in range(len(self.vor_us)):
- # from cartesian to cylindric coordinates
- Pnts.SetValue(
- i + 1,
- gp_Pnt(self.vor_us[i], radius * np.sin(self.vor_vs[i] / radius),
- radius * np.cos(self.vor_vs[i] / radius)))
-
- # Build the spline curve of degree 3 from Voronoi points, which are those on the camber line
- # with tolerance 1e-1
- spline_builder = GeomAPI_PointsToBSpline(Pnts, 3, 3, GeomAbs_C2, 1e-1)
- camber_curve = spline_builder.Curve()
- # Build the camber line from 3D edges
- self.edge_3d = BRepBuilderAPI_MakeEdge(camber_curve).Edge()
- camber_curve_adaptor = BRepAdaptor_Curve(
- OCC.Core.TopoDS.topods.Edge(self.edge_3d))
- # Converting camber edge into wire for plotting purposes
- wire_maker = BRepBuilderAPI_MakeWire()
- wire_maker.Add(self.edge_3d)
- self.camber_wires_list.append(wire_maker.Wire())
- # Compute the length of the camber curve for each section
- camber_curve_length = GCPnts_AbscissaPoint.Length(camber_curve_adaptor)
- relative_tolerance = 2.5e-3
- absolute_tolerance = relative_tolerance * camber_curve_length
- firstPoint = gp_Pnt(0.0, 0.0, 0.0)
- lastPoint = gp_Pnt(0.0, 0.0, 0.0)
- firstTangent = gp_Vec(0.0, 0.0, 0.0)
- lastTangent = gp_Vec(0.0, 0.0, 0.0)
- # Compute the first and last points and the related derivative of the camber curve w.r.t.
- camber_curve_adaptor.D1(camber_curve_adaptor.FirstParameter(),
- firstPoint, firstTangent)
- camber_curve_adaptor.D1(camber_curve_adaptor.LastParameter(), lastPoint,
- lastTangent)
- dummyFirstPoint = gp_Pnt(0.0, 0.0, 0.0)
- dummyLastPoint = gp_Pnt(0.0, 0.0, 0.0)
- usedFirstTangent = gp_Vec(0.0, 0.0, 0.0)
- usedLastTangent = gp_Vec(0.0, 0.0, 0.0)
- camber_curve_adaptor.D1(
- camber_curve_adaptor.FirstParameter() + 0.005 *
- (camber_curve_adaptor.LastParameter() -
- camber_curve_adaptor.FirstParameter()), dummyFirstPoint,
- usedFirstTangent)
- camber_curve_adaptor.D1(
- camber_curve_adaptor.FirstParameter() + 0.985 *
- (camber_curve_adaptor.LastParameter() -
- camber_curve_adaptor.FirstParameter()), dummyLastPoint,
- usedLastTangent)
- firstTangent = gp_Dir(usedFirstTangent)
- lastTangent = gp_Dir(usedLastTangent)
- firstPoint = dummyFirstPoint
- lastPoint = dummyLastPoint
- self.camber_curve_edge = BRepBuilderAPI_MakeEdge(
- camber_curve,
- camber_curve_adaptor.FirstParameter() + 0.005 *
- (camber_curve_adaptor.LastParameter() -
- camber_curve_adaptor.FirstParameter()),
- camber_curve_adaptor.FirstParameter() + 0.985 *
- (camber_curve_adaptor.LastParameter() -
- camber_curve_adaptor.FirstParameter())).Edge()
- # Set of the leading edges
- self.firstSegment = BRepBuilderAPI_MakeEdge(
- firstPoint,
- gp_Pnt(
- firstPoint.X() - 10.0 * firstTangent.X() * absolute_tolerance,
- firstPoint.Y() - 10.0 * firstTangent.Y() * absolute_tolerance,
- firstPoint.Z() -
- 10.0 * firstTangent.Z() * absolute_tolerance)).Edge()
-
- # Set of trailing edges
- self.lastSegment = BRepBuilderAPI_MakeEdge(
- lastPoint,
- gp_Pnt(lastPoint.X() + 10.0 * lastTangent.X() * absolute_tolerance,
- lastPoint.Y() + 10.0 * lastTangent.Y() * absolute_tolerance,
- lastPoint.Z() +
- 10.0 * lastTangent.Z() * absolute_tolerance)).Edge()
- # Visiting the vertices of the chord line and storing the leading edges
- vertexExplorer = TopExp_Explorer(self.wire, TopAbs_VERTEX)
- found = False
- while vertexExplorer.More():
- vertex = topods.Vertex(vertexExplorer.Current())
- point = BRep_Tool.Pnt(vertex)
- if (point.Distance(firstPoint) <
- camber_curve_length * relative_tolerance):
- self.leading_edge_point = point
- found = True
- vertexExplorer.Next()
- if found == False:
- distSS = BRepExtrema_DistShapeShape(self.wire, self.firstSegment)
- minDist = 1e8
- for k in range(distSS.NbSolution()):
- if firstPoint.Distance(distSS.PointOnShape1(k + 1)) < minDist:
- minDist = firstPoint.Distance(distSS.PointOnShape1(k + 1))
- self.leading_edge_point = distSS.PointOnShape1(k + 1)
-
- # Visiting the vertices of the chord line and storing the trailing edges
- found = False
- while vertexExplorer.More():
- vertex = topods.Vertex(vertexExplorer.Current())
- point = BRep_Tool.Pnt(vertex)
- if (point.Distance(lastPoint) <
- camber_curve_length * relative_tolerance):
- self.trailing_edge_point = point
- found = True
- vertexExplorer.Next()
- if found == False:
- distSS = BRepExtrema_DistShapeShape(self.wire, self.lastSegment)
- minDist = 1e8
-
- for k in range(distSS.NbSolution()):
- if lastPoint.Distance(distSS.PointOnShape1(k + 1)) < minDist:
- minDist = lastPoint.Distance(distSS.PointOnShape1(k + 1))
- self.trailing_edge_point = distSS.PointOnShape1(k + 1)
-
- if (self.trailing_edge_point.X() > self.leading_edge_point.X()):
- serv_point = self.trailing_edge_point
- self.trailing_edge_point = self.leading_edge_point
- self.leading_edge_point = serv_point
- serv_point = lastPoint
- lastPoint = firstPoint
- firstPoint = serv_point
-
- # Edges
- self.first_edge = BRepBuilderAPI_MakeEdge(self.trailing_edge_point,
- lastPoint).Edge()
- self.last_edge = BRepBuilderAPI_MakeEdge(self.leading_edge_point,
- firstPoint).Edge()
-
- # Storing the "full" camber line (camber line = leading and trailing edges)
- # in a unique object with OCC wire
- wire_maker = BRepBuilderAPI_MakeWire()
- wire_maker.Add(self.first_edge)
- wire_maker.Add(self.camber_curve_edge)
- wire_maker.Add(self.last_edge)
-
- full_camber_wire = wire_maker.Wire()
- self.full_camber_curve_adaptor = BRepAdaptor_CompCurve(
- OCC.Core.TopoDS.topods.Wire(full_camber_wire))
- self.full_camber_length = GCPnts_AbscissaPoint.Length(
- self.full_camber_curve_adaptor)
-
- def _initial_leading_trailing_edges_plane(self, radius):
- """
- Private method which computes the coordinates of the leading and trailing
- edges of each section, as were in the initial blade. Thenm transformations
- will be applied in order to plot the points of the profiles on a plane
- and to map the X coordinates in the interval [0,1].
- """
-
- leading_edge_theta = np.arctan2(self.leading_edge_point.Y(),
- self.leading_edge_point.Z())
- if leading_edge_theta < 0:
- leading_edge_theta += 2.0 * np.pi
- self.leading_edge_point_on_plane = np.array(
- [self.leading_edge_point.X(), radius * leading_edge_theta])
-
- trailing_edge_theta = np.arctan2(self.trailing_edge_point.Y(),
- self.trailing_edge_point.Z())
- if trailing_edge_theta < 0:
- trailing_edge_theta += 2.0 * np.pi
- self.trailing_edge_point_on_plane = np.array(
- [self.trailing_edge_point.X(), radius * trailing_edge_theta])
-
- def _initial_camber_points_plane(self, radius):
- """
- Private method that defines the points of the camber line projected on
- plane, in 2D coordinates.
- """
- camber_points_number = int(round(self.airfoil_points_number / 2))
-
- self.camber_points_on_plane = np.zeros((camber_points_number, 2))
-
- for i in range(camber_points_number):
- firstParam = self.full_camber_curve_adaptor.FirstParameter()
- rel_distance = float(i) / float(camber_points_number -
- 1) * self.full_camber_length
- param = GCPnts_AbscissaPoint(1e-7, self.full_camber_curve_adaptor,
- rel_distance, firstParam).Parameter()
- point = self.full_camber_curve_adaptor.Value(param)
- theta = np.arctan2(point.Y(), point.Z())
- if theta < 0:
- theta += 2.0 * np.pi
- self.camber_points_on_plane[i][0] = point.X()
- self.camber_points_on_plane[i][1] = radius * theta
-
- def _initial_airfoil_points_plane(self, radius):
- """
- Private method that evaluates the airfoil points on a plane (the points of
- the profile of a single section, which will be then distinguished into
- upper and lower part). Those points are defined in a plane, in 2D coordinates.
- """
-
- self.airfoil_points_on_plane = np.zeros((self.airfoil_points_number, 2))
-
- for i in range(self.airfoil_points_number):
- firstParam = self.curve_adaptor.FirstParameter()
- rel_distance = float(i) / float(self.airfoil_points_number -
- 1) * self.total_section_length
- param = GCPnts_AbscissaPoint(1e-7, self.curve_adaptor, rel_distance,
- firstParam).Parameter()
- point = self.curve_adaptor.Value(param)
- theta = np.arctan2(point.Y(), point.Z())
- if theta < 0:
- theta += 2.0 * np.pi
-
- self.airfoil_points_on_plane[i][0] = point.X()
- self.airfoil_points_on_plane[i][1] = radius * theta
-
- # Compute the mid point of the chord line
- self.mid_chord_point_on_plane = (
- self.leading_edge_point_on_plane +
- self.trailing_edge_point_on_plane) / 2.0
-
- def _store_properties(self, radius):
- """
- Private method which extracts the parameters (pitch, rake, skew ,...) related
- to a specific section of the blade, and then transforms the camber points
- initialized in _initial_camber_points_plane and the prile points initialized
- in _initial_airfoil_points_plane according to the parameters found.
- This method trasforms the leading and trailing edges initialed in
- _initial_leading_trailing_edges and the mid chord point as well.
-
- Basically all points and edges of the profile section are transformed
- to fulfill the properties of the specific sectionwe are considering.
- """
- # Save the properties we wanted for each section
- self.pitch_angles_list.append(self.pitch_angle)
- self.pitch_list.append(
- abs(2 * np.pi * radius / np.tan(self.pitch_angle)) / 1000.0)
- self.skew_angles_list.append((self.skew / radius - np.pi) * 180 / np.pi)
- self.skew_list.append((self.skew - np.pi * radius) / 1000.0)
- total_rake = self.rake + self.rake_induced_by_skew
- self.rake = total_rake - (self.skew - np.pi * radius) / np.tan(
- self.pitch_angle)
- self.rake = -self.rake / 1000.0
- self.rake_list.append(self.rake)
- self.chord_length_list.append(self.chord_length / 1000.0)
-
- def _airfoil_top_and_bottom_points(self):
- """
- Private method that finds the points of the airfoil belonging to the upper
- and lower profiles of each section.
- """
- self.airfoil_top = []
- self.airfoil_top.append(self.leading_edge_point_on_plane)
- self.airfoil_top.append(self.trailing_edge_point_on_plane)
- self.airfoil_bottom = []
- self.airfoil_bottom.append(self.leading_edge_point_on_plane)
- self.airfoil_bottom.append(self.trailing_edge_point_on_plane)
- for i in range(len(self.airfoil_points_on_plane)):
- # points close to the leading and trailing edges are not considered for
- # the construction of the upper and lower profiles of sections
- if ((self.airfoil_points_on_plane[i, 0] > 0.005)
- and (self.airfoil_points_on_plane[i, 0] < 0.995)):
- if (self.airfoil_points_on_plane[i, 1] > self.f_camber(
- min(max(self.airfoil_points_on_plane[i, 0], 0.0),
- 1.0))):
- self.airfoil_top.append([
- self.airfoil_points_on_plane[i, 0],
- self.airfoil_points_on_plane[i, 1]
- ])
- else:
- self.airfoil_bottom.append([
- self.airfoil_points_on_plane[i, 0],
- self.airfoil_points_on_plane[i, 1]
- ])
- # Storing the upper and lower points in matrices and rescaling in the interval [0,1]
- self.airfoil_top = np.matrix(self.airfoil_top)
- self.airfoil_top = np.sort(self.airfoil_top.view('float64,float64'),
- order=['f0'],
- axis=0).view(np.float64)
- self.airfoil_bottom = np.matrix(self.airfoil_bottom)
- self.airfoil_bottom = np.sort(
- self.airfoil_bottom.view('float64,float64'), order=['f0'],
- axis=0).view(np.float64)
-
- self.airfoil_top[0, 0] = 0.0
- self.airfoil_top[-1, 0] = 1.0
- self.airfoil_bottom[0, 0] = 0.0
- self.airfoil_bottom[-1, 0] = 1.0
-
- self.ascissa = np.linspace(0,
- 1,
- num=self.num_points_top_bottom,
- endpoint=True)
- self.f_top = interp1d(np.squeeze(np.asarray(self.airfoil_top[:, 0])),
- np.squeeze(np.asarray(self.airfoil_top[:, 1])),
- kind='cubic')
- self.f_bottom = interp1d(
- np.squeeze(np.asarray(self.airfoil_bottom[:, 0])),
- np.squeeze(np.asarray(self.airfoil_bottom[:, 1])),
- kind='cubic')
- # Plot points of camber line, trailing and leading edges, upper and lower profiles
- # of each blade section
- self.int_airfoil_top = self.f_top(self.ascissa)
- self.int_airfoil_top[0] = 0.0
- self.int_airfoil_top[-1] = 0.0
- self.int_airfoil_bottom = self.f_bottom(self.ascissa)
- self.int_airfoil_bottom[0] = 0.0
- self.int_airfoil_bottom[-1] = 0.0
-
diff --git a/bladex/reversepropeller/reversepropellerbladex.py b/bladex/reversepropeller/reversepropellerbladex.py
deleted file mode 100644
index 08ee028..0000000
--- a/bladex/reversepropeller/reversepropellerbladex.py
+++ /dev/null
@@ -1,448 +0,0 @@
-"""
-Module for the extraction of the parameters of a blade and for the
-approximated reconstruction of the blade and the whole propeller.
-"""
-
-import numpy as np
-from bladex import CustomProfile, Blade, Propeller, Shaft
-from .basereversepropeller import BaseReversePropeller
-from OCC.Core.IGESControl import (IGESControl_Reader)
-from OCC.Core.BRepBuilderAPI import BRepBuilderAPI_MakeVertex,\
- BRepBuilderAPI_MakeEdge, BRepBuilderAPI_MakeWire, BRepBuilderAPI_MakeSolid, \
- BRepBuilderAPI_Sewing, BRepBuilderAPI_NurbsConvert
-from OCC.Core.BRep import BRep_Tool
-import OCC.Core.TopoDS
-from OCC.Core.TopTools import TopTools_ListOfShape
-from OCC.Core.TopExp import TopExp_Explorer
-from OCC.Core.TopAbs import TopAbs_VERTEX, TopAbs_EDGE, TopAbs_FACE, TopAbs_WIRE
-from OCC.Core.gp import gp_Pnt, gp_Dir, gp_Ax2, gp_Vec, gp_Pln
-from OCC.Core.TColgp import TColgp_Array1OfPnt
-from OCC.Core.BRepAdaptor import BRepAdaptor_Curve
-from OCC.Core.GCPnts import GCPnts_AbscissaPoint
-from OCC.Core.BRep import BRep_Tool
-from OCC.Core.TopoDS import topods
-from OCC.Display.SimpleGui import init_display
-from OCC.Core.BRepPrimAPI import BRepPrimAPI_MakeCylinder
-from OCC.Core.GeomLProp import GeomLProp_SLProps
-from OCC.Core.GCPnts import GCPnts_AbscissaPoint
-from OCC.Core.BRepAdaptor import (BRepAdaptor_Curve,
- BRepAdaptor_CompCurve)
-from OCC.Core.GeomAPI import GeomAPI_PointsToBSpline
-from OCC.Core.GeomAbs import GeomAbs_C2
-from OCC.Core.Bnd import Bnd_Box
-from OCC.Core.BRepBndLib import brepbndlib
-from OCC.Core.BRepAlgoAPI import BRepAlgoAPI_Section
-from OCC.Core.Geom import Geom_Plane
-from OCC.Core.BRepBuilderAPI import BRepBuilderAPI_MakeFace
-from scipy.interpolate import interp1d
-import matplotlib.pyplot as plt
-
-
-class ReversePropellerBladeX(BaseReversePropeller):
- """
-
- :param filename: path to the IGES file of the blade.
- :param list radii_list: list which contains the radii values of the
- sectional profiles.
- :param num_points_top_bottom: number of points used to interpolate each
- sectional profile.
- """
- def __init__(self, filename, radii_list, num_points_top_bottom):
-
- super().__init__(filename, radii_list, num_points_top_bottom)
- ind_sec = 0
- for radius in self.radii_list:
- self.cylinder = None
- self.bounds = None
- self.cylinder_lateral_face = None
- self.cylinder_lateral_surface = None
- self.linear_tolerance = 1e-3
- self.conversion_unit = 1000
- self._build_cylinder(radius)
- self._build_intersection_cylinder_blade()
- self.leading_edge_point = []
- self.trailing_edge_point = []
- self.edge_3d = None
- self.camber_curve_edge = None
- self.first_edge = None
- self.last_edge = None
- self.firstSegment = None
- self.lastSegment = None
- self.camber_points_on_plane = None
- self.leading_edge_point_on_plane = []
- self.trailing_edge_point_on_plane = []
- self.param_plane_points = []
- self.orig_param_plane_points = []
- # points = []
- self._camber_curve(radius)
- # for i in range(len(self.vor_us)):
- # x, y, z = self.vor_us[i], radius*np.sin(self.vor_vs[i]/radius), radius*np.cos(self.vor_vs[i]/radius)
- # pnt = gp_Pnt(float(x), float(y), float(z))
- # points.append(BRepBuilderAPI_MakeVertex(pnt).Vertex())
- # self._camber_curve(radius)
- if False:
- display, start_display, add_menu, add_function_to_menu = init_display()
- # display.DisplayShape(self.blade_solid, update=True)
- display.DisplayShape(self.cylinder, update=True)
- display.DisplayShape(self.wire_top, color="RED", update=True)
- display.DisplayShape(self.wire_bottom, color="BLUE", update=True)
- # display.DisplayShape(self.chord_wire, color="ORANGE", update=True)
- display.DisplayShape(self.full_camber_wire, color="GREEN", update=True)
- display.DisplayShape(self.leading_edge, color="BLACK", update=True)
- display.DisplayShape(self.trailing_edge, color="MAGENTA", update=True)
- # display.DisplayShape(self.chord_plane, update=True)
- display.DisplayShape(self.chord_point, update=True)
- display.DisplayShape(self.trimmed_edge, color="BLACK", update=True)
- # display.DisplayShape(points, update=True)
- start_display()
- self._initial_leading_trailing_edges_plane(radius)
- self._initial_camber_points_plane(radius)
- self._initial_airfoil_points_plane(radius)
- self._airfoil_top_and_bottom_points_before_transformations(radius)
- self._extract_parameters_and_transform_profile(radius)
- self._store_properties(radius)
- self._transform_top_and_bottom()
- self._airfoil_top_and_bottom_points_after_transformations()
- self.xup[ind_sec, :] = self.ascissa
- self.xdown[ind_sec, :] = self.ascissa
- self.yup[ind_sec, :] = self.int_airfoil_top
- self.ydown[ind_sec, :] = self.int_airfoil_bottom
- ind_sec = ind_sec + 1
-
-
- def _build_intersection_cylinder_blade(self):
- """
- Private method that constructs the section lines which are the intersections
- between the cylinder at a fixed radius and the blade, and the camber points.
- """
- # Construction of the section lines between two shapes (in this case the
- # blade and the lateral face of the cylinder)
- section_builder = BRepAlgoAPI_Section(self.blade_solid,
- self.cylinder_lateral_face, False)
- # Define and build the parametric 2D curve (pcurve) for the section lines defined above
- section_builder.ComputePCurveOn2(True)
- section_builder.Build()
- self.section = section_builder.Shape()
- wire_maker = BRepBuilderAPI_MakeWire()
- wire_maker_top = BRepBuilderAPI_MakeWire()
- wire_maker_bottom = BRepBuilderAPI_MakeWire()
-
- edgeList = TopTools_ListOfShape()
- edgeList_top = TopTools_ListOfShape()
- edgeList_bottom = TopTools_ListOfShape()
- edgeExplorer = TopExp_Explorer(self.section, TopAbs_EDGE)
- edgeCount = 0
- while edgeExplorer.More():
- edgeCount = edgeCount + 1 # Numbering from 1 in OCC
- edge = edgeExplorer.Current()
- edgeList.Append(edge)
- if edgeCount % 2 == 1:
- edgeList_top.Append(edge)
- else:
- edgeList_bottom.Append(edge)
- edgeExplorer.Next()
-
- # Total sectional curve
- wire_maker.Add(edgeList)
- self.wire = wire_maker.Wire()
- self.section_wires_list.append(self.wire)
- self.curve_adaptor = BRepAdaptor_CompCurve(
- OCC.Core.TopoDS.topods.Wire(self.wire))
- self.total_section_length = GCPnts_AbscissaPoint.Length(
- self.curve_adaptor)
- # Top part
- wire_maker_top.Add(edgeList_top)
- self.wire_top = wire_maker_top.Wire()
- self.curve_adaptor_top = BRepAdaptor_CompCurve(
- OCC.Core.TopoDS.topods.Wire(self.wire_top))
- self.total_section_top_length = GCPnts_AbscissaPoint.Length(
- self.curve_adaptor_top)
- # Bottom part
- wire_maker_bottom.Add(edgeList_bottom)
- self.wire_bottom = wire_maker_bottom.Wire()
- self.curve_adaptor_bottom = BRepAdaptor_CompCurve(
- OCC.Core.TopoDS.topods.Wire(self.wire_bottom))
- self.total_section_bottom_length = GCPnts_AbscissaPoint.Length(
- self.curve_adaptor_bottom)
-
-
- def _camber_curve(self, radius):
- """
- Computation of the camber points. We get the chord, move along it and fint the intersection
- of the othogonal plane to the chord-curvilinear absissa and the top-bottom wires
- """
- self.trailing_edge = self.curve_adaptor_top.Value(0.0)
- self.leading_edge = self.curve_adaptor_top.Value(self.curve_adaptor_top.LastParameter())
- # Equation of generic geodesic from leading to trailing edge:
- # x = lambda*s + mu, y = R*sin(a*s+b), z = R*cos(a*s+b)
- # with s parametrization of curve and lambda, mu, a, b to be found
- # for s=0 we habe leading edge and s=1 we have trailing edge
- mu = self.leading_edge.X()
- lam = self.trailing_edge.X() - mu
- b = np.arcsin(self.leading_edge.Y()/radius)
- a = np.arcsin(self.trailing_edge.Y()/radius) - b
- # Thus, the new a chord point is, given any s \in [0,1]
- # gp_Pnt(lam*s + mu, radius * np.sin(a*s+b), radius * np.cos(a*s+b)))
-
- # Now, for N chord points, we compute the tangent vector to it,
- # define the plane passing to the point and with normal direction equal to the tangent
- # and compute the intersecting curve between cylinder and plane. The midpoint is the camber point
- self.n_camber_points = 500
- n_plot_point = int (self.n_camber_points/2)
- s_values = np.linspace(0, 1, self.n_camber_points)
- self.camber_Pnts = TColgp_Array1OfPnt(1, len(s_values))
- for i, s in enumerate(s_values):
- if i == 0:
- self.camber_Pnts.SetValue(i+1, self.leading_edge)
- elif i == len(s_values)-1:
- self.camber_Pnts.SetValue(i+1, self.trailing_edge)
- else:
- chord_point = gp_Pnt(lam*s + mu, radius * np.sin(a*s+b), radius * np.cos(a*s+b))
- # Equation of tangent vector is: x = lam, y = a*R*cos(a*s+b), z = -a*R*sin(a*s+b)
- tangent_vector = gp_Vec(lam, a*radius*np.cos(a*s+b), -a*radius*np.sin(a*s+b))
- chord_plane = gp_Pln(chord_point, gp_Dir(tangent_vector))
- chord_plane_face = BRepBuilderAPI_MakeFace(chord_plane, -1e8, 1e8, -1e8, 1e8).Face()
- if i == n_plot_point:
- self.chord_plane = chord_plane_face
- # self.chord_plane = chord_plane
- self.chord_point = chord_point
- # Now we intersect the plane with the cylinder
- section_pc = BRepAlgoAPI_Section(self.cylinder_lateral_face, chord_plane_face)
- section_pc.Build()
- curve_shape = section_pc.Shape()
- exp = TopExp_Explorer(curve_shape, TopAbs_EDGE)
- curve_edge = exp.Current()
- # Find the intersection of the curve with top and bottom faces of the blade's section
- int_top = BRepAlgoAPI_Section(curve_edge, self.wire_top)
- int_top.Build()
- int_bottom = BRepAlgoAPI_Section(curve_edge, self.wire_bottom)
- int_bottom.Build()
- exp = TopExp_Explorer(int_top.Shape(), TopAbs_VERTEX)
- from OCC.Core.TopoDS import TopoDS_Vertex
- while exp.More():
- point_top = exp.Current()
- if isinstance(int_top, TopoDS_Vertex):
- break
- exp.Next()
- exp = TopExp_Explorer(int_bottom.Shape(), TopAbs_VERTEX)
- while exp.More():
- point_bottom= exp.Current()
- if isinstance(int_bottom, TopoDS_Vertex):
- break
- exp.Next()
- # Now we trim the curve to only have inside the two intersection points
- curve_handle, u1, u2 = BRep_Tool.Curve(curve_edge)
- from OCC.Core.GeomAPI import GeomAPI_ProjectPointOnCurve
- proj = GeomAPI_ProjectPointOnCurve(BRep_Tool.Pnt(point_top), curve_handle)
- u_top = proj.LowerDistanceParameter()
- proj = GeomAPI_ProjectPointOnCurve(BRep_Tool.Pnt(point_bottom), curve_handle)
- u_bot = proj.LowerDistanceParameter()
- u_min = min(u_top, u_bot)
- u_max = max(u_top, u_bot)
- trimmed_edge = BRepBuilderAPI_MakeEdge(curve_handle, u_min, u_max).Edge()
- if i == n_plot_point:
- wire_maker = BRepBuilderAPI_MakeWire()
- wire_maker.Add(trimmed_edge)
- self.trimmed_edge= wire_maker.Wire()
- trimmed_adaptor = BRepAdaptor_Curve(trimmed_edge)
- u0 = trimmed_adaptor.FirstParameter()
- u1 = trimmed_adaptor.LastParameter()
- total_length = GCPnts_AbscissaPoint.Length(trimmed_adaptor, u0, u1)
- absc = GCPnts_AbscissaPoint(trimmed_adaptor, 0.5*total_length, u0)
- u_mid = absc.Parameter()
- self.camber_Pnts.SetValue(i+1, trimmed_adaptor.Value(u_mid))
- # Building an edge from points
- spline_builder = GeomAPI_PointsToBSpline(self.camber_Pnts, 3, 3, GeomAbs_C2, 1e-1)
- camber_curve = spline_builder.Curve()
- # Build the camber line from 3D edges
- self.edge_3d = BRepBuilderAPI_MakeEdge(camber_curve).Edge()
- # Building wire from edge
- wire_maker = BRepBuilderAPI_MakeWire()
- wire_maker.Add(self.edge_3d)
-
- self.full_camber_wire = wire_maker.Wire()
- self.full_camber_curve_adaptor = BRepAdaptor_CompCurve(
- OCC.Core.TopoDS.topods.Wire(self.full_camber_wire))
- self.full_camber_length = GCPnts_AbscissaPoint.Length(
- self.full_camber_curve_adaptor)
- self.camber_wires_list.append(self.full_camber_wire)
-
- def _initial_leading_trailing_edges_plane(self, radius):
- """
- Private method which computes the coordinates of the leading and trailing
- edges of each section, as were in the initial blade. Thenm transformations
- will be applied in order to plot the points of the profiles on a plane
- and to map the X coordinates in the interval [0,1].
- """
-
- self.trailing_edge_point = self.trailing_edge
- self.leading_edge_point = self.leading_edge
- leading_edge_theta = np.arctan2(self.leading_edge_point.Y(),
- self.leading_edge_point.Z())
- self.leading_edge_point_on_plane = np.array(
- [self.leading_edge_point.X(), radius * leading_edge_theta])
-
- trailing_edge_theta = np.arctan2(self.trailing_edge_point.Y(),
- self.trailing_edge_point.Z())
- self.trailing_edge_point_on_plane = np.array(
- [self.trailing_edge_point.X(), radius * trailing_edge_theta])
-
- def _initial_camber_points_plane(self, radius):
- """
- Private method that defines the points of the camber line projected on
- plane, in 2D coordinates.
- """
- self.camber_points_on_plane = np.zeros((self.num_points_top_bottom, 2))
-
- for i in range(self.num_points_top_bottom):
- point = self.camber_Pnts.Value(i+1)
- theta = np.arctan2(point.Y(), point.Z())
- if theta < 0:
- theta += 2.0 * np.pi
- self.camber_points_on_plane[i][0] = point.X()
- self.camber_points_on_plane[i][1] = radius * theta
-
- def _initial_airfoil_points_plane(self, radius):
- """
- Private method that evaluates the airfoil points on a plane (the points of
- the profile of a single section, which will be then distinguished into
- upper and lower part). Those points are defined in a plane, in 2D coordinates.
- """
-
- self.airfoil_points_on_plane = np.zeros((self.airfoil_points_number, 2))
-
- for i in range(self.airfoil_points_number):
- firstParam = self.curve_adaptor.FirstParameter()
- rel_distance = float(i) / float(self.airfoil_points_number -
- 1) * self.total_section_length
- param = GCPnts_AbscissaPoint(1e-7, self.curve_adaptor, rel_distance,
- firstParam).Parameter()
- point = self.curve_adaptor.Value(param)
- theta = np.arctan2(point.Y(), point.Z())
- if theta < 0:
- theta += 2.0 * np.pi
-
- self.airfoil_points_on_plane[i][0] = point.X()
- self.airfoil_points_on_plane[i][1] = radius * theta
-
- # Compute the mid point of the chord line
- self.mid_chord_point_on_plane = (
- self.leading_edge_point_on_plane +
- self.trailing_edge_point_on_plane) / 2.0
-
- def _airfoil_top_and_bottom_points_before_transformations(self, radius):
- """
- Private method that finds the points of the airfoil belonging to the upper
- and lower profiles of each section.
- """
- self.airfoil_top = []
- u0_top = self.curve_adaptor_top.FirstParameter()
- u1_top = self.curve_adaptor_top.LastParameter()
- total_length = GCPnts_AbscissaPoint.Length(self.curve_adaptor_top, u0_top, u1_top)
- for i in range(self.num_points_top_bottom):
- point_generator = GCPnts_AbscissaPoint(1e-7, self.curve_adaptor_top,
- float(i)/(self.num_points_top_bottom-1)*total_length, u0_top)
- param = point_generator.Parameter()
- point = self.curve_adaptor_top.Value(param)
- theta = np.arctan2(point.Y(), point.Z())
- self.airfoil_top.append([point.X(), radius*theta])
- self.airfoil_bottom = []
- u0_bottom = self.curve_adaptor_bottom.FirstParameter()
- u1_bottom = self.curve_adaptor_bottom.LastParameter()
- total_length = GCPnts_AbscissaPoint.Length(self.curve_adaptor_bottom, u0_bottom, u1_bottom)
- for i in range(self.num_points_top_bottom):
- point_generator = GCPnts_AbscissaPoint(1e-7, self.curve_adaptor_bottom,
- float(i)/(self.num_points_top_bottom-1)*total_length, u0_bottom)
- param = point_generator.Parameter()
- point = self.curve_adaptor_bottom.Value(param)
- theta = np.arctan2(point.Y(), point.Z())
- self.airfoil_bottom.append([point.X(), radius*theta])
-
- self.airfoil_top = np.array(self.airfoil_top)
- self.airfoil_bottom = np.array(self.airfoil_bottom)
-
- def _store_properties(self, radius):
- # Save the properties we wanted for each section
- self.pitch_angles_list.append(self.pitch_angle)
- self.pitch_list.append(
- abs(2 * np.pi * radius / np.tan(self.pitch_angle)) / 1000.0)
- self.skew_angles_list.append(-(self.skew / radius) * 180 / np.pi)
- self.skew_list.append(self.skew / 1000.0)
- total_rake = self.rake + self.rake_induced_by_skew
- rake = total_rake - (self.skew) / np.tan(
- self.pitch_angle)
- rake = -rake / 1000.0
- self.rake_list.append(rake)
- self.chord_length_list.append(self.chord_length / 1000.0)
-
- def _transform_top_and_bottom(self):
- """
- Method that transforms the top and bottom coordinates from physical coordinates
- to 2D planar with chord aligned to x-axis
- skew, pitch, rake etc. have been already compute in _extract_parameters_and_transform_profile()
- """
- self.airfoil_top[:, 1] -= self.skew
- self.airfoil_bottom[:, 1] -= self.skew
-
- self.airfoil_top[:, 0] -= self.rake_induced_by_skew
- self.airfoil_bottom[:, 0] -= self.rake_induced_by_skew
-
- self.airfoil_top[:, 0] -= self.rake
- self.airfoil_bottom[:, 0] -= self.rake
-
- self.airfoil_top = self.airfoil_top.dot(
- self.rotation_matrix.transpose())
- self.airfoil_bottom = self.airfoil_bottom.dot(
- self.rotation_matrix.transpose())
-
- self.airfoil_top /= self.chord_length
- self.airfoil_bottom /= self.chord_length
-
- self.airfoil_top[:, 0] *= -1.0
- self.airfoil_bottom[:, 0] *= -1.0
-
- self.airfoil_top[:, 0] += 0.5
- self.airfoil_bottom[:, 0] += 0.5
-
- # Final check on y components to see which one is really top
- if self.airfoil_top[np.abs(self.airfoil_top[:, 1]).argmax(), 1] < 0:
- self.airfoil_top[:, 1] *= -1
- self.airfoil_bottom[:, 1] *= -1
-
- def _airfoil_top_and_bottom_points_after_transformations(self):
- # Now we create two interpolating functions fitting bottom e up points
- # In this way we can retrieve as many bottom/up points as we want
- self.airfoil_top = np.matrix(self.airfoil_top)
- self.airfoil_top = np.sort(self.airfoil_top.view('float64,float64'),
- order=['f0'],
- axis=0).view(np.float64)
- self.airfoil_bottom = np.matrix(self.airfoil_bottom)
- self.airfoil_bottom = np.sort(
- self.airfoil_bottom.view('float64,float64'), order=['f0'],
- axis=0).view(np.float64)
-
- self.airfoil_top[0, 0] = 0.0
- self.airfoil_top[-1, 0] = 1.0
- self.airfoil_bottom[0, 0] = 0.0
- self.airfoil_bottom[-1, 0] = 1.0
-
- self.ascissa = np.linspace(0,
- 1,
- num=self.num_points_top_bottom,
- endpoint=True)
- self.f_top = interp1d(np.squeeze(np.asarray(self.airfoil_top[:, 0])),
- np.squeeze(np.asarray(self.airfoil_top[:, 1])),
- kind='cubic')
- self.f_bottom = interp1d(
- np.squeeze(np.asarray(self.airfoil_bottom[:, 0])),
- np.squeeze(np.asarray(self.airfoil_bottom[:, 1])),
- kind='cubic')
- # Plot points of camber line, trailing and leading edges, upper and lower profiles
- # of each blade section
- self.int_airfoil_top = self.f_top(self.ascissa)
- self.int_airfoil_top[0] = 0.0
- self.int_airfoil_top[-1] = 0.0
- self.int_airfoil_bottom = self.f_bottom(self.ascissa)
- self.int_airfoil_bottom[0] = 0.0
- self.int_airfoil_bottom[-1] = 0.0
-
diff --git a/bladex/reversepropeller/reversepropellerinterface.py b/bladex/reversepropeller/reversepropellerinterface.py
deleted file mode 100644
index afd6e19..0000000
--- a/bladex/reversepropeller/reversepropellerinterface.py
+++ /dev/null
@@ -1,52 +0,0 @@
-"""
-Interface module that provides essential tools for the reversepropeller.
-"""
-
-from abc import ABC, abstractmethod
-
-
-class ReversePropellerInterface(ABC):
- """
- Interface for reverse problem propeller blade.
-
- Given an iges file that has the blade's geometry, we solve an inverse problem
- to retrieve the properties of the blades both in terms of:
- - sectional properties (chord length, thickness, camber);
- - sections location in the space (skew angle, pitch and rake)
- """
- @abstractmethod
- def _extract_solid_from_file(self):
- """
- Abstract method that extract the solid object from the IGES file
- """
- pass
-
- @abstractmethod
- def _build_cylinder(self, radius):
- """
- Abstract method that, given a radius, it builds the cylinder with specified radius
- and main axis along x direction. This cylinder will be intersected with the blade
- """
- pass
-
- @abstractmethod
- def _build_intersection_cylinder_blade(self):
- """
- Abstract method that computes the intersection between the blade and the cylinder
- created by _build_cylinder() method
- """
- pass
-
- @abstractmethod
- def _camber_curve(self, radius):
- """
- Abstract method that retrieves the camber curve once the intersection is computed
- """
- pass
-
- @abstractmethod
- def save_global_parameters(self, filename_csv):
- """
- Abstract method to store the retrieved properties and section into a csv file
- """
-
diff --git a/bladex/shaft/cylinder_shaft.py b/bladex/shaft/cylinder_shaft.py
deleted file mode 100644
index c99732c..0000000
--- a/bladex/shaft/cylinder_shaft.py
+++ /dev/null
@@ -1,57 +0,0 @@
-""" Cylinder Shaft """
-from OCC.Display.SimpleGui import init_display
-from OCC.Core.BRepPrimAPI import BRepPrimAPI_MakeCylinder
-from OCC.Core.gp import gp_Pnt, gp_Dir, gp_Ax2
-
-
-class CylinderShaft:
- """
- Cylinder shaft construction.
-
- :param float radius: radius of the cylinder shaft. Defaults to 1.0.
- :param float height: height of the cylinder shaft. Defaults to 1.0.
- :param list orientation: orientation vector of the cylinder shaft. Defaults
- to [1.0, 0.0, 0.0], so along X axis.
- :param list origin: origin point of the cylinder shaft. Defaults to
- [0.0, 0.0, 0.0].
- """
-
- def __init__(self, radius=1.0, height=1.0, orientation=None, origin=None):
- self.radius = radius
- self.height = height
-
- if orientation is None:
- self.orientation = [1.0, 0.0, 0.0] # default orientation along X
- else:
- self.orientation = orientation
-
- if origin is None:
- self.origin = [0.0, 0.0, 0.0] # default origin at (0,0,0)
- else:
- self.origin = origin
-
- def generate_solid(self):
- """
- Generate a cylindrical shaft using the BRepBuilderAPI_MakeCylinder
- algorithm. This method requires PythonOCC to be installed.
-
- :return: solid shaft
- :rtype: OCC.Core.TopoDS.TopoDS_Solid
- """
-
- origin = gp_Pnt(*self.origin)
- orientation = gp_Dir(*self.orientation)
- ax2 = gp_Ax2(origin, orientation)
-
- shape = BRepPrimAPI_MakeCylinder(ax2, self.radius, self.height).Shape()
-
- return shape
-
- def display(self):
- """
- Display the shaft.
- """
- shaft_solid = self.generate_solid()
- display, start_display = init_display()[:2]
- display.DisplayShape(shaft_solid, update=True)
- start_display()
diff --git a/bladex/shaft/shaft.py b/bladex/shaft/shaft.py
deleted file mode 100644
index 2677f90..0000000
--- a/bladex/shaft/shaft.py
+++ /dev/null
@@ -1,60 +0,0 @@
-import os
-from OCC.Core.IGESControl import IGESControl_Reader
-from OCC.Extend.DataExchange import read_stl_file
-from OCC.Core.BRepBuilderAPI import BRepBuilderAPI_MakeSolid, BRepBuilderAPI_Sewing
-import OCC.Core.TopoDS
-from OCC.Display.SimpleGui import init_display
-
-class Shaft(object):
- """
- Bottom-up parametrized shaft construction.
-
- :param string filename: path (with the file extension) of a .stl or .iges file with
- stored shaft information.
- :cvar string filename: path (with the file extension) of a .stl or .iges file with
- stored shaft information.
- :raises Exception: if the extension in the filename is not in .stl or .iges formats.
- """
-
- def __init__(self, filename):
- self.filename = filename
-
- def generate_solid(self):
- """
- Generate an assembled solid shaft using the BRepBuilderAPI_MakeSolid
- algorithm. This method requires PythonOCC to be installed.
-
- :raises RuntimeError: if the assembling of the solid shaft is not
- completed successfully
- :return: solid shaft
- :rtype: OCC.Core.TopoDS.TopoDS_Solid
- """
- ext = os.path.splitext(self.filename)[1][1:]
- if ext == 'stl':
- shaft_compound = read_stl_file(self.filename)
- elif ext == 'iges':
- iges_reader = IGESControl_Reader()
- iges_reader.ReadFile(self.filename)
- iges_reader.TransferRoots()
- shaft_compound = iges_reader.Shape()
- else:
- raise Exception('The shaft file is not in iges/stl formats')
- sewer = BRepBuilderAPI_Sewing(1e-2)
- sewer.Add(shaft_compound)
- sewer.Perform()
- result_sewed_shaft = sewer.SewedShape()
- shaft_solid_maker = BRepBuilderAPI_MakeSolid()
- shaft_solid_maker.Add(OCC.Core.TopoDS.topods.Shell(result_sewed_shaft))
- if not shaft_solid_maker.IsDone():
- raise RuntimeError('Unsuccessful assembling of solid shaft')
- shaft_solid = shaft_solid_maker.Solid()
- return shaft_solid
-
- def display(self):
- """
- Display the shaft.
- """
- shaft_solid = self.generate_solid()
- display, start_display = init_display()[:2]
- display.DisplayShape(shaft_solid, update=True)
- start_display()
diff --git a/code.html b/code.html
new file mode 100644
index 0000000..ecee9ef
--- /dev/null
+++ b/code.html
@@ -0,0 +1,296 @@
+
+
+
+
+
+
+ Code Documentation — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
Contact — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
How to contribute — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
How to contribute
+
We’d love to accept your patches and contributions to this project. There are
+just a few small guidelines you need to follow.
+
Submitting a patch:
+
+
+It’s generally best to start by opening a new issue describing the bug or
+feature you’re intending to fix. Even if you think it’s relatively minor,
+it’s helpful to know what people are working on. Mention in the initial
+issue that you are planning to work on that bug or feature so that it can
+be assigned to you.
+Follow the normal process of forking the project, and setup a new
+branch to work in. It’s important that each group of changes be done in
+separate branches in order to ensure that a pull request only includes the
+commits related to that bug or feature.
+To ensure properly formatted code, please make sure to use 4
+spaces to indent the code. You should also run pylint over your code.
+It’s not strictly necessary that your code be completely “lint-free”,
+but this will help you find common style issues.
+Any significant changes should almost always be accompanied by tests. The
+project already has good test coverage, so look at some of the existing
+tests if you’re unsure how to go about it. We’re using coveralls that
+is an invaluable tools for seeing which parts of your code aren’t being
+exercised by your tests.
+Do your best to have well-formed commit messages for each change.
+This provides consistency throughout the project, and ensures that commit
+messages are able to be formatted properly by various git tools.
+Finally, push the commits to your fork and submit a pull request. Please,
+remember to rebase properly in order to maintain a clean, linear git history.
+
+
+
+
+
+
+
+
+
+
+
+
+
Deformation — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
' where is one of"
- @echo " html to make standalone HTML files"
- @echo " dirhtml to make HTML files named index.html in directories"
- @echo " singlehtml to make a single large HTML file"
- @echo " pickle to make pickle files"
- @echo " json to make JSON files"
- @echo " htmlhelp to make HTML files and a HTML help project"
- @echo " qthelp to make HTML files and a qthelp project"
- @echo " applehelp to make an Apple Help Book"
- @echo " devhelp to make HTML files and a Devhelp project"
- @echo " epub to make an epub"
- @echo " latex to make LaTeX files, you can set PAPER=a4 or PAPER=letter"
- @echo " latexpdf to make LaTeX files and run them through pdflatex"
- @echo " latexpdfja to make LaTeX files and run them through platex/dvipdfmx"
- @echo " text to make text files"
- @echo " man to make manual pages"
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- @echo " doctest to run all doctests embedded in the documentation (if enabled)"
- @echo " coverage to run coverage check of the documentation (if enabled)"
- @echo " rst to generate the .rst file for documentation"
-
-clean:
- rm -rf $(BUILDDIR)/*
-
-html:
- $(SPHINXBUILD) -b html $(ALLSPHINXOPTS) $(BUILDDIR)/html
- @echo
- @echo "Build finished. The HTML pages are in $(BUILDDIR)/html."
-
-dirhtml:
- $(SPHINXBUILD) -b dirhtml $(ALLSPHINXOPTS) $(BUILDDIR)/dirhtml
- @echo
- @echo "Build finished. The HTML pages are in $(BUILDDIR)/dirhtml."
-
-singlehtml:
- $(SPHINXBUILD) -b singlehtml $(ALLSPHINXOPTS) $(BUILDDIR)/singlehtml
- @echo
- @echo "Build finished. The HTML page is in $(BUILDDIR)/singlehtml."
-
-pickle:
- $(SPHINXBUILD) -b pickle $(ALLSPHINXOPTS) $(BUILDDIR)/pickle
- @echo
- @echo "Build finished; now you can process the pickle files."
-
-json:
- $(SPHINXBUILD) -b json $(ALLSPHINXOPTS) $(BUILDDIR)/json
- @echo
- @echo "Build finished; now you can process the JSON files."
-
-htmlhelp:
- $(SPHINXBUILD) -b htmlhelp $(ALLSPHINXOPTS) $(BUILDDIR)/htmlhelp
- @echo
- @echo "Build finished; now you can run HTML Help Workshop with the" \
- ".hhp project file in $(BUILDDIR)/htmlhelp."
-
-qthelp:
- $(SPHINXBUILD) -b qthelp $(ALLSPHINXOPTS) $(BUILDDIR)/qthelp
- @echo
- @echo "Build finished; now you can run "qcollectiongenerator" with the" \
- ".qhcp project file in $(BUILDDIR)/qthelp, like this:"
- @echo "# qcollectiongenerator $(BUILDDIR)/qthelp/active_subspaces.qhcp"
- @echo "To view the help file:"
- @echo "# assistant -collectionFile $(BUILDDIR)/qthelp/active_subspaces.qhc"
-
-applehelp:
- $(SPHINXBUILD) -b applehelp $(ALLSPHINXOPTS) $(BUILDDIR)/applehelp
- @echo
- @echo "Build finished. The help book is in $(BUILDDIR)/applehelp."
- @echo "N.B. You won't be able to view it unless you put it in" \
- "~/Library/Documentation/Help or install it in your application" \
- "bundle."
-
-devhelp:
- $(SPHINXBUILD) -b devhelp $(ALLSPHINXOPTS) $(BUILDDIR)/devhelp
- @echo
- @echo "Build finished."
- @echo "To view the help file:"
- @echo "# mkdir -p $$HOME/.local/share/devhelp/active_subspaces"
- @echo "# ln -s $(BUILDDIR)/devhelp $$HOME/.local/share/devhelp/active_subspaces"
- @echo "# devhelp"
-
-epub:
- $(SPHINXBUILD) -b epub $(ALLSPHINXOPTS) $(BUILDDIR)/epub
- @echo
- @echo "Build finished. The epub file is in $(BUILDDIR)/epub."
-
-latex:
- $(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) $(BUILDDIR)/latex
- @echo
- @echo "Build finished; the LaTeX files are in $(BUILDDIR)/latex."
- @echo "Run \`make' in that directory to run these through (pdf)latex" \
- "(use \`make latexpdf' here to do that automatically)."
-
-latexpdf:
- $(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) $(BUILDDIR)/latex
- @echo "Running LaTeX files through pdflatex..."
- $(MAKE) -C $(BUILDDIR)/latex all-pdf
- @echo "pdflatex finished; the PDF files are in $(BUILDDIR)/latex."
-
-latexpdfja:
- $(SPHINXBUILD) -b latex $(ALLSPHINXOPTS) $(BUILDDIR)/latex
- @echo "Running LaTeX files through platex and dvipdfmx..."
- $(MAKE) -C $(BUILDDIR)/latex all-pdf-ja
- @echo "pdflatex finished; the PDF files are in $(BUILDDIR)/latex."
-
-text:
- $(SPHINXBUILD) -b text $(ALLSPHINXOPTS) $(BUILDDIR)/text
- @echo
- @echo "Build finished. The text files are in $(BUILDDIR)/text."
-
-man:
- $(SPHINXBUILD) -b man $(ALLSPHINXOPTS) $(BUILDDIR)/man
- @echo
- @echo "Build finished. The manual pages are in $(BUILDDIR)/man."
-
-texinfo:
- $(SPHINXBUILD) -b texinfo $(ALLSPHINXOPTS) $(BUILDDIR)/texinfo
- @echo
- @echo "Build finished. The Texinfo files are in $(BUILDDIR)/texinfo."
- @echo "Run \`make' in that directory to run these through makeinfo" \
- "(use \`make info' here to do that automatically)."
-
-info:
- $(SPHINXBUILD) -b texinfo $(ALLSPHINXOPTS) $(BUILDDIR)/texinfo
- @echo "Running Texinfo files through makeinfo..."
- make -C $(BUILDDIR)/texinfo info
- @echo "makeinfo finished; the Info files are in $(BUILDDIR)/texinfo."
-
-gettext:
- $(SPHINXBUILD) -b gettext $(I18NSPHINXOPTS) $(BUILDDIR)/locale
- @echo
- @echo "Build finished. The message catalogs are in $(BUILDDIR)/locale."
-
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- @echo
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-
-linkcheck:
- $(SPHINXBUILD) -b linkcheck $(ALLSPHINXOPTS) $(BUILDDIR)/linkcheck
- @echo
- @echo "Link check complete; look for any errors in the above output " \
- "or in $(BUILDDIR)/linkcheck/output.txt."
-
-doctest:
- $(SPHINXBUILD) -b doctest $(ALLSPHINXOPTS) $(BUILDDIR)/doctest
- @echo "Testing of doctests in the sources finished, look at the " \
- "results in $(BUILDDIR)/doctest/output.txt."
-
-coverage:
- $(SPHINXBUILD) -b coverage $(ALLSPHINXOPTS) $(BUILDDIR)/coverage
- @echo "Testing of coverage in the sources finished, look at the " \
- "results in $(BUILDDIR)/coverage/python.txt."
-
-xml:
- $(SPHINXBUILD) -b xml $(ALLSPHINXOPTS) $(BUILDDIR)/xml
- @echo
- @echo "Build finished. The XML files are in $(BUILDDIR)/xml."
-
-pseudoxml:
- $(SPHINXBUILD) -b pseudoxml $(ALLSPHINXOPTS) $(BUILDDIR)/pseudoxml
- @echo
- @echo "Build finished. The pseudo-XML files are in $(BUILDDIR)/pseudoxml."
-
-rst:
- @./make_rst.sh
- @echo
- @echo "Created new .RST files."
- @echo "Run \`sphinx-autogen\` in order to populate the summary directory."
diff --git a/docs/make.bat b/docs/make.bat
deleted file mode 100755
index 12875d6..0000000
--- a/docs/make.bat
+++ /dev/null
@@ -1,263 +0,0 @@
-@ECHO OFF
-
-REM Command file for Sphinx documentation
-
-if "%SPHINXBUILD%" == "" (
- set SPHINXBUILD=sphinx-build
-)
-set BUILDDIR=build
-set ALLSPHINXOPTS=-d %BUILDDIR%/doctrees %SPHINXOPTS% source
-set I18NSPHINXOPTS=%SPHINXOPTS% source
-if NOT "%PAPER%" == "" (
- set ALLSPHINXOPTS=-D latex_paper_size=%PAPER% %ALLSPHINXOPTS%
- set I18NSPHINXOPTS=-D latex_paper_size=%PAPER% %I18NSPHINXOPTS%
-)
-
-if "%1" == "" goto help
-
-if "%1" == "help" (
- :help
- echo.Please use `make ^` where ^ is one of
- echo. html to make standalone HTML files
- echo. dirhtml to make HTML files named index.html in directories
- echo. singlehtml to make a single large HTML file
- echo. pickle to make pickle files
- echo. json to make JSON files
- echo. htmlhelp to make HTML files and a HTML help project
- echo. qthelp to make HTML files and a qthelp project
- echo. devhelp to make HTML files and a Devhelp project
- echo. epub to make an epub
- echo. latex to make LaTeX files, you can set PAPER=a4 or PAPER=letter
- echo. text to make text files
- echo. man to make manual pages
- echo. texinfo to make Texinfo files
- echo. gettext to make PO message catalogs
- echo. changes to make an overview over all changed/added/deprecated items
- echo. xml to make Docutils-native XML files
- echo. pseudoxml to make pseudoxml-XML files for display purposes
- echo. linkcheck to check all external links for integrity
- echo. doctest to run all doctests embedded in the documentation if enabled
- echo. coverage to run coverage check of the documentation if enabled
- goto end
-)
-
-if "%1" == "clean" (
- for /d %%i in (%BUILDDIR%\*) do rmdir /q /s %%i
- del /q /s %BUILDDIR%\*
- goto end
-)
-
-
-REM Check if sphinx-build is available and fallback to Python version if any
-%SPHINXBUILD% 2> nul
-if errorlevel 9009 goto sphinx_python
-goto sphinx_ok
-
-:sphinx_python
-
-set SPHINXBUILD=python -m sphinx.__init__
-%SPHINXBUILD% 2> nul
-if errorlevel 9009 (
- echo.
- echo.The 'sphinx-build' command was not found. Make sure you have Sphinx
- echo.installed, then set the SPHINXBUILD environment variable to point
- echo.to the full path of the 'sphinx-build' executable. Alternatively you
- echo.may add the Sphinx directory to PATH.
- echo.
- echo.If you don't have Sphinx installed, grab it from
- echo.http://sphinx-doc.org/
- exit /b 1
-)
-
-:sphinx_ok
-
-
-if "%1" == "html" (
- %SPHINXBUILD% -b html %ALLSPHINXOPTS% %BUILDDIR%/html
- if errorlevel 1 exit /b 1
- echo.
- echo.Build finished. The HTML pages are in %BUILDDIR%/html.
- goto end
-)
-
-if "%1" == "dirhtml" (
- %SPHINXBUILD% -b dirhtml %ALLSPHINXOPTS% %BUILDDIR%/dirhtml
- if errorlevel 1 exit /b 1
- echo.
- echo.Build finished. The HTML pages are in %BUILDDIR%/dirhtml.
- goto end
-)
-
-if "%1" == "singlehtml" (
- %SPHINXBUILD% -b singlehtml %ALLSPHINXOPTS% %BUILDDIR%/singlehtml
- if errorlevel 1 exit /b 1
- echo.
- echo.Build finished. The HTML pages are in %BUILDDIR%/singlehtml.
- goto end
-)
-
-if "%1" == "pickle" (
- %SPHINXBUILD% -b pickle %ALLSPHINXOPTS% %BUILDDIR%/pickle
- if errorlevel 1 exit /b 1
- echo.
- echo.Build finished; now you can process the pickle files.
- goto end
-)
-
-if "%1" == "json" (
- %SPHINXBUILD% -b json %ALLSPHINXOPTS% %BUILDDIR%/json
- if errorlevel 1 exit /b 1
- echo.
- echo.Build finished; now you can process the JSON files.
- goto end
-)
-
-if "%1" == "htmlhelp" (
- %SPHINXBUILD% -b htmlhelp %ALLSPHINXOPTS% %BUILDDIR%/htmlhelp
- if errorlevel 1 exit /b 1
- echo.
- echo.Build finished; now you can run HTML Help Workshop with the ^
-.hhp project file in %BUILDDIR%/htmlhelp.
- goto end
-)
-
-if "%1" == "qthelp" (
- %SPHINXBUILD% -b qthelp %ALLSPHINXOPTS% %BUILDDIR%/qthelp
- if errorlevel 1 exit /b 1
- echo.
- echo.Build finished; now you can run "qcollectiongenerator" with the ^
-.qhcp project file in %BUILDDIR%/qthelp, like this:
- echo.^> qcollectiongenerator %BUILDDIR%\qthelp\active_subspaces.qhcp
- echo.To view the help file:
- echo.^> assistant -collectionFile %BUILDDIR%\qthelp\active_subspaces.ghc
- goto end
-)
-
-if "%1" == "devhelp" (
- %SPHINXBUILD% -b devhelp %ALLSPHINXOPTS% %BUILDDIR%/devhelp
- if errorlevel 1 exit /b 1
- echo.
- echo.Build finished.
- goto end
-)
-
-if "%1" == "epub" (
- %SPHINXBUILD% -b epub %ALLSPHINXOPTS% %BUILDDIR%/epub
- if errorlevel 1 exit /b 1
- echo.
- echo.Build finished. The epub file is in %BUILDDIR%/epub.
- goto end
-)
-
-if "%1" == "latex" (
- %SPHINXBUILD% -b latex %ALLSPHINXOPTS% %BUILDDIR%/latex
- if errorlevel 1 exit /b 1
- echo.
- echo.Build finished; the LaTeX files are in %BUILDDIR%/latex.
- goto end
-)
-
-if "%1" == "latexpdf" (
- %SPHINXBUILD% -b latex %ALLSPHINXOPTS% %BUILDDIR%/latex
- cd %BUILDDIR%/latex
- make all-pdf
- cd %~dp0
- echo.
- echo.Build finished; the PDF files are in %BUILDDIR%/latex.
- goto end
-)
-
-if "%1" == "latexpdfja" (
- %SPHINXBUILD% -b latex %ALLSPHINXOPTS% %BUILDDIR%/latex
- cd %BUILDDIR%/latex
- make all-pdf-ja
- cd %~dp0
- echo.
- echo.Build finished; the PDF files are in %BUILDDIR%/latex.
- goto end
-)
-
-if "%1" == "text" (
- %SPHINXBUILD% -b text %ALLSPHINXOPTS% %BUILDDIR%/text
- if errorlevel 1 exit /b 1
- echo.
- echo.Build finished. The text files are in %BUILDDIR%/text.
- goto end
-)
-
-if "%1" == "man" (
- %SPHINXBUILD% -b man %ALLSPHINXOPTS% %BUILDDIR%/man
- if errorlevel 1 exit /b 1
- echo.
- echo.Build finished. The manual pages are in %BUILDDIR%/man.
- goto end
-)
-
-if "%1" == "texinfo" (
- %SPHINXBUILD% -b texinfo %ALLSPHINXOPTS% %BUILDDIR%/texinfo
- if errorlevel 1 exit /b 1
- echo.
- echo.Build finished. The Texinfo files are in %BUILDDIR%/texinfo.
- goto end
-)
-
-if "%1" == "gettext" (
- %SPHINXBUILD% -b gettext %I18NSPHINXOPTS% %BUILDDIR%/locale
- if errorlevel 1 exit /b 1
- echo.
- echo.Build finished. The message catalogs are in %BUILDDIR%/locale.
- goto end
-)
-
-if "%1" == "changes" (
- %SPHINXBUILD% -b changes %ALLSPHINXOPTS% %BUILDDIR%/changes
- if errorlevel 1 exit /b 1
- echo.
- echo.The overview file is in %BUILDDIR%/changes.
- goto end
-)
-
-if "%1" == "linkcheck" (
- %SPHINXBUILD% -b linkcheck %ALLSPHINXOPTS% %BUILDDIR%/linkcheck
- if errorlevel 1 exit /b 1
- echo.
- echo.Link check complete; look for any errors in the above output ^
-or in %BUILDDIR%/linkcheck/output.txt.
- goto end
-)
-
-if "%1" == "doctest" (
- %SPHINXBUILD% -b doctest %ALLSPHINXOPTS% %BUILDDIR%/doctest
- if errorlevel 1 exit /b 1
- echo.
- echo.Testing of doctests in the sources finished, look at the ^
-results in %BUILDDIR%/doctest/output.txt.
- goto end
-)
-
-if "%1" == "coverage" (
- %SPHINXBUILD% -b coverage %ALLSPHINXOPTS% %BUILDDIR%/coverage
- if errorlevel 1 exit /b 1
- echo.
- echo.Testing of coverage in the sources finished, look at the ^
-results in %BUILDDIR%/coverage/python.txt.
- goto end
-)
-
-if "%1" == "xml" (
- %SPHINXBUILD% -b xml %ALLSPHINXOPTS% %BUILDDIR%/xml
- if errorlevel 1 exit /b 1
- echo.
- echo.Build finished. The XML files are in %BUILDDIR%/xml.
- goto end
-)
-
-if "%1" == "pseudoxml" (
- %SPHINXBUILD% -b pseudoxml %ALLSPHINXOPTS% %BUILDDIR%/pseudoxml
- if errorlevel 1 exit /b 1
- echo.
- echo.Build finished. The pseudo-XML files are in %BUILDDIR%/pseudoxml.
- goto end
-)
-
-:end
diff --git a/docs/make_rst.sh b/docs/make_rst.sh
deleted file mode 100755
index c6a39a3..0000000
--- a/docs/make_rst.sh
+++ /dev/null
@@ -1,48 +0,0 @@
-#!/bin/bash
-################################################################################
-## Bash file for the automatic creation of .RST file ##
-## ##
-## This script does not work on modules that not contains class definition ##
-################################################################################
-
-module='bladex'
-
-files=`ls ../$module/[a-z]*.py`
-
-for f in $files; do
-
- filename=$(basename $f .py)
-
- classname=`grep "class.*(.*):$" $f | awk '{print $2}' | cut -d"(" -f 1`
- [[ -z $classname ]] && echo "WARNING: class not found in file $f"
-
- methodnames=`grep -e 'def .*(.*):$' $f | awk '{print $2}' | cut -d "(" -f 1`
- [[ -z $classname ]] && echo "WARNING: methods not found in file $f"
-
- methodnames=`sed -r 's/\b(__init__|__new__)\b//g' <<< $methodnames`
-
- output="source/$filename.rst"
-
- echo -e "$classname" > $output
- echo -e "=====================" >> $output
- echo -e "" >> $output
- echo -e ".. currentmodule:: $module.$filename" >> $output
- echo -e "" >> $output
- echo -e ".. automodule:: $module.$filename" >> $output
- echo -e "" >> $output
- echo -e ".. autosummary::" >> $output
- echo -e " :toctree: _summaries" >> $output
- echo -e " :nosignatures:" >> $output
- echo -e "" >> $output
- echo -e " $classname" >> $output
- for methodname in $methodnames; do
- echo -e " $classname.$methodname" >> $output
- done
- echo -e "" >> $output
- echo -e ".. autoclass:: $classname" >> $output
- echo -e " :members:" >> $output
- echo -e " :private-members:" >> $output
- echo -e " :undoc-members:" >> $output
- echo -e " :show-inheritance:" >> $output
- echo -e " :noindex:" >> $output
-done
diff --git a/docs/source/conf.py b/docs/source/conf.py
deleted file mode 100644
index 12cc9b4..0000000
--- a/docs/source/conf.py
+++ /dev/null
@@ -1,321 +0,0 @@
-# -*- coding: utf-8 -*-
-#
-# ezyrb documentation build configuration file, created by
-# sphinx-quickstart on Mon Jun 22 16:09:40 2015.
-#
-# This file is execfile()d with the current directory set to its
-# containing dir.
-#
-# Note that not all possible configuration values are present in this
-# autogenerated file.
-#
-# All configuration values have a default; values that are commented out
-# serve to show the default.
-
-import sys
-import os
-import shlex
-import sphinx
-from sphinx.errors import VersionRequirementError
-import sphinx_rtd_theme
-
-# If extensions (or modules to document with autodoc) are in another directory,
-# add these directories to sys.path here. If the directory is relative to the
-# documentation root, use os.path.abspath to make it absolute, like shown here.
-sys.path.insert(0, os.path.abspath('../..'))
-import bladex.meta as meta
-
-# -- General configuration ------------------------------------------------
-
-# If your documentation needs a minimal Sphinx version, state it here.
-needs_sphinx = '1.4'
-if needs_sphinx > sphinx.__display_version__:
- message = 'This project needs at least Sphinx v{0!s}'.format(needs_sphinx)
- raise VersionRequirementError(message)
-
-# Add any Sphinx extension module names here, as strings. They can be
-# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom
-# ones.
-extensions = [
- 'sphinx.ext.autodoc',
- 'sphinx.ext.autosummary',
- 'sphinx.ext.coverage',
- 'sphinx.ext.graphviz',
- 'sphinx.ext.doctest',
- 'sphinx.ext.intersphinx',
- 'sphinx.ext.todo',
- 'sphinx.ext.coverage',
- 'sphinx.ext.viewcode',
- 'sphinx.ext.imgmath',
- 'sphinx.ext.ifconfig',
-]
-
-intersphinx_mapping = {'python': ('http://docs.python.org/2', None),
- 'numpy': ('http://docs.scipy.org/doc/numpy/', None),
- 'scipy': ('http://docs.scipy.org/doc/scipy/reference/', None),
- 'matplotlib': ('http://matplotlib.sourceforge.net/', None)}
-
-# Add any paths that contain templates here, relative to this directory.
-templates_path = ['_templates']
-
-# The suffix(es) of source filenames.
-# You can specify multiple suffix as a list of string:
-# source_suffix = ['.rst', '.md']
-source_suffix = '.rst'
-
-# The encoding of source files.
-#source_encoding = 'utf-8-sig'
-
-# The master toctree document.
-master_doc = 'index'
-
-# General information about the project.
-project = u'BladeX'
-copyright = meta.__copyright__
-author = meta.__author__
-
-# autoclass
-autoclass_content = 'both'
-
-# The version info for the project you're documenting, acts as replacement for
-# |version| and |release|, also used in various other places throughout the
-# built documents.
-#
-# The short X.Y version.
-version = meta.__version__
-# The full version, including alpha/beta/rc tags.
-release = version
-
-# The language for content autogenerated by Sphinx. Refer to documentation
-# for a list of supported languages.
-#
-# This is also used if you do content translation via gettext catalogs.
-# Usually you set "language" from the command line for these cases.
-language = None
-
-# There are two options for replacing |today|: either, you set today to some
-# non-false value, then it is used:
-#today = ''
-# Else, today_fmt is used as the format for a strftime call.
-#today_fmt = '%B %d, %Y'
-
-# List of patterns, relative to source directory, that match files and
-# directories to ignore when looking for source files.
-exclude_patterns = []
-
-# The reST default role (used for this markup: `text`) to use for all
-# documents.
-#default_role = None
-
-# If true, '()' will be appended to :func: etc. cross-reference text.
-add_function_parentheses = True
-
-# If true, the current module name will be prepended to all description
-# unit titles (such as .. function::).
-add_module_names = False
-
-# If true, sectionauthor and moduleauthor directives will be shown in the
-# output. They are ignored by default.
-#show_authors = False
-
-# The name of the Pygments (syntax highlighting) style to use.
-pygments_style = 'sphinx'
-
-# A list of ignored prefixes for module index sorting.
-#modindex_common_prefix = []
-
-# If true, keep warnings as "system message" paragraphs in the built documents.
-keep_warnings = False
-
-# If true, `todo` and `todoList` produce output, else they produce nothing.
-todo_include_todos = True
-
-
-# -- Options for viewcode extension ---------------------------------------
-
-# Follow alias objects that are imported from another module such as functions,
-# classes and attributes. As side effects, this option ... ???
-# If false, ... ???.
-# The default is True.
-viewcode_import = True
-
-
-# -- Options for HTML output ----------------------------------------------
-
-# The theme to use for HTML and HTML Help pages. See the documentation for
-# a list of builtin themes.
-#html_theme = 'bizstyle'
-html_theme = "sphinx_rtd_theme"
-
-# Theme options are theme-specific and customize the look and feel of a theme
-# further. For a list of options available for each theme, see the
-# documentation.
-#html_theme_options = {}
-
-# Add any paths that contain custom themes here, relative to this directory.
-html_theme_path = [sphinx_rtd_theme.get_html_theme_path()]
-
-# The name for this set of Sphinx documents. If None, it defaults to
-# " v documentation".
-#html_title = None
-
-# A shorter title for the navigation bar. Default is the same as html_title.
-#html_short_title = None
-
-# The name of an image file (relative to this directory) to place at the top
-# of the sidebar.
-#html_logo = None
-
-# The name of an image file (within the static path) to use as favicon of the
-# docs. This file should be a Windows icon file (.ico) being 16x16 or 32x32
-# pixels large.
-#html_favicon = None
-
-# Add any paths that contain custom static files (such as style sheets) here,
-# relative to this directory. They are copied after the builtin static files,
-# so a file named "default.css" will overwrite the builtin "default.css".
-html_static_path = ['_static']
-
-# Add any extra paths that contain custom files (such as robots.txt or
-# .htaccess) here, relative to this directory. These files are copied
-# directly to the root of the documentation.
-html_extra_path = ['_tutorials']
-
-# If not '', a 'Last updated on:' timestamp is inserted at every page bottom,
-# using the given strftime format.
-html_last_updated_fmt = '%b %d, %Y'
-
-# If true, SmartyPants will be used to convert quotes and dashes to
-# typographically correct entities.
-#html_use_smartypants = True
-
-# Custom sidebar templates, maps document names to template names.
-#html_sidebars = {}
-
-# Additional templates that should be rendered to pages, maps page names to
-# template names.
-#html_additional_pages = {}
-
-# If false, no module index is generated.
-#html_domain_indices = True
-
-# If false, no index is generated.
-html_use_index = True
-
-# If true, the index is split into individual pages for each letter.
-#html_split_index = False
-
-# If true, links to the reST sources are added to the pages.
-html_show_sourcelink = True
-
-# If true, "Created using Sphinx" is shown in the HTML footer. Default is True.
-#html_show_sphinx = True
-
-# If true, "(C) Copyright ..." is shown in the HTML footer. Default is True.
-html_show_copyright = True
-
-# If true, an OpenSearch description file will be output, and all pages will
-# contain a Index — BladeX 0.1 documentation
+
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+ BladeX
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+
Index
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Welcome to BladeX’s documentation! — BladeX 0.1 documentation
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+ BladeX
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+
Welcome to BladeX’s documentation!
+
+
+
Description
+
BladeX is a Python package for geometrical parametrization and bottom-up construction of propeller blades. It allows to generate and deform a blade based on the radial distribution of its parameters such as pitch, rake, skew, and the sectional foils’ parameters such as chord and camber. The package is ideally suited for parametric simulations on large number of blade deformations. It provides an automated procedure for the CAD generation, hence reducing the time and effort required for modelling. The main scope of BladeX is to deal with propeller blades, however it can be flexible to be applied on further applications with analogous geometrical structures such as aircraft wings, turbomachinery, or wind turbine blades.
+
+
+
Dependencies and installation
+
BladeX requires numpy, scipy, matplotlib, sphinx (for the documentation), and nose (for the local test). They can be easily installed using pip.
+
BladeX is compatible with Python 2.7 and Python 3.6. Moreover, some of the modules require OCC to be installed for the .iges or .stl CAD generation. Please see below for instructions on how to satisfy the OCC requirements. You can also refer to pythonocc.org or github.com/tpaviot/pythonocc-core for further instructions.
+
Python2.7 OCC installation:
+
conda install - c conda - forge - c dlr - sc - c pythonocc - c oce pythonocc - core == 0.18 . 1 python = 2.7
+
+
+
Python3.6 OCC installation:
+
conda install - c conda - forge - c dlr - sc - c pythonocc - c oce pythonocc - core == 0.18 . 1 python = 3.6
+
+
+
The official distribution is on GitHub, and you can clone the repository using
+
git clone https : // github . com / mathLab / BladeX
+
+
+
To install the package just type:
+
python setup . py install
+
+
+
To uninstall the package you have to rerun the installation and record the installed files in order to remove them:
+
python setup . py install -- record installed_files . txt
+cat installed_files . txt | xargs rm - rf
+
+
+
+
+
Tutorials
+
We made some tutorial examples. Please refer to the official GitHub repository for the last updates. Here the list of the exported tutorials:
+
+Tutorial 1 - Here we show how to prepare a blade 2D sectional profile through generating legacy and custom foils.Tutorial 2 - Here we show how to proceed with preparing a blade 2D sectional profile by performing several transformation operations on the generated foils.Tutorial 3 - Here we show how to prepare a blade 3D sectional profiles by applying all the transformations due to the radial distribution of the blade parameters.Tutorial 4 - Here we show how to deform a blade and its parametric curves by using a parameter file.
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+
Ndinterpolator — BladeX 0.1 documentation
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+ BladeX
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+
Ndinterpolator
+
+
+
+class RBF( basis , radius ) [source]
+Module focused on the implementation of the Radial Basis Functions
+interpolation technique. This technique is still based on the use of
+a set of parameters, the so-called control points, as for FFD, but RBF
+is interpolatory. Another important key point of RBF strategy relies in
+the way we can locate the control points: in fact, instead of FFD where
+control points need to be placed inside a regular lattice, with RBF we
+havo no more limitations. So we have the possibility to perform localized
+control points refiniments.
+
+
+Theoretical Insight: As reference please consult M.D. Buhmann, Radial Basis Functions,
+volume 12 of Cambridge monographs on applied and computational
+mathematics. Cambridge University Press, UK, 2003. This implementation
+follows D. Forti and G. Rozza, Efficient geometrical parametrization
+techniques of interfaces for reduced order modelling: application to
+fluid-structure interaction coupling problems, International Journal
+of Computational Fluid Dynamics.
+RBF shape parametrization technique is based on the definition of a map
+
+
+
+
where
+The matrix version of the formula above is:
+
+
+
The idea is that after the computation of the weights and the
+polynomial terms from the coordinates of the control points before and
+after the deformation, we can deform all the points of the mesh
+accordingly. Among the most common used radial basis functions for
+modelling 2D and 3D shapes, we consider Gaussian splines, Multi-
+uadratic biharmonic splines, Inverted multi-quadratic biharmonic
+splines, Thin-plate splines, Beckert and Wendland
+Parameters:
+basis (string radius (float
+
+
+
+
+static beckert_wendland_c2_basis( X , r ) [source]
+It implements the following formula:
+
+
+
+
+Parameters:
+X (numpy.ndarray r (float
+Returns: result: the result of the formula above.
+Return type: float
+
+
+
+
+
+
+static gaussian_spline( X , r ) [source]
+It implements the following formula:
+
+
+
+
+Parameters:
+X (numpy.ndarray r (float
+Returns: result: the result of the formula above.
+Return type: float
+
+
+
+
+
+
+static inv_multi_quadratic_biharmonic_spline( X , r ) [source]
+It implements the following formula:
+
+
+
+
+Parameters:
+X (numpy.ndarray r (float
+Returns: result: the result of the formula above.
+Return type: float
+
+
+
+
+
+
+static multi_quadratic_biharmonic_spline( X , r ) [source]
+It implements the following formula:
+
+
+
+
+Parameters:
+X (numpy.ndarray r (float
+Returns: result: the result of the formula above.
+Return type: float
+
+
+
+
+
+
+static thin_plate_spline( X , r ) [source]
+It implements the following formula:
+
+
+
+
+Parameters:
+X (numpy.ndarray r (float
+Returns: result: the result of the formula above.
+Return type: float
+
+
+
+
+
+
+weights_matrix( X1 , X2 ) [source]
+This method returns the following matrix:
+
+
+
+
+Parameters:
+
+Returns: matrix: the matrix D.
+Return type: numpy.ndarray
+
+
+
+
+
+
+
+
+reconstruct_f( original_input , original_output , rbf_input , rbf_output , basis , radius ) [source]
+Reconstruct a function by using the radial basis function approximations.
+
+
+Parameters:
+original_input (array_like ) – the original values of function inputs.original_output (array_like ) – the original values of function output.rbf_input (array_like ) – the input data for RBF approximation.rbf_output (array_like ) – the array elements to be updated with the RBF
+interpolated outputs after the approximation.basis (string radius (float
+Example: >>> import numpy as np
+>>> from bladex.ndinterpolator import reconstruct_f
+>>> x = np . arange ( 10 )
+>>> y = np . square ( x )
+>>> radius = 10
+>>> n_interp = 50
+>>> x_rbf = np . linspace ( x [ 0 ], x [ - 1 ], num = n_interp )
+>>> y_rbf = np . zeros ( n_interp )
+>>> reconstruct_f ( original_input = x , original_output = y , rbf_input = x_rbf ,
+ rbf_output=y_rbf, radius=radius, basis='beckert_wendland_c2_basis')
+
+
+
+
+
+
+
+scipy_bspline( cv , npoints , degree ) [source]
+Construct B-Spline curve via the control points.
+
+
+Parameters:
+cv (array_like ) – control points vector (spline coefficients).npoints (int degree (int
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
ParamFile — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
ParamFile
+
Module to read and write a parameter file
+which can be used for parameters deformations.
+
+
+
+class ParamFile[source]
+Bases: object
+Read and Write a parameter file
+
+
+Variables:
+radii (array_like ) – contains radii values of the blade sectional
+profiles, starting from the hub. Default value is Noneparameters (dict chord , pitch , rake , skew , camber at specific
+blade sections. Each element of the dictionary is an array_like of
+length equals to that of the array radii. Both parameters chord and
+camber descibes the chord length and the camber of the 2D foil
+representing the blade section. Possible dictionary keys are chord ,
+pitch , rake , skew , camber . Default values are Nonenbasis (dict chord , pitch , rake ,
+skew , camber degree (dict chord , pitch , rake , skew , camber npoints (dict chord ,
+pitch , rake , skew , camber deformations (dict chord , pitch , rake , skew , camber
+
+
+
+
+_check_params( ) [source]
+Private method that is called while writing a parameter file.
+1. The method checks if the user specifies a radii array, otherwise it
+raises exception.
+2. In case no values assigned to any of the remaining parameter arrays
+then an array of zeros is assigned, in which its length is equal
+to the radii array.
+3. Any array that is not numpy is converted to be one. Finally, in case
+the user specifies the parameter array values but not with same length,
+then an exception is raised.
+
+
+
+
+read_parameters( filename='parameters.prm' ) [source]
+Reads in the parameters file and fill the self structure.
+
+
+Parameters: filename (str
+
+
+
+
+
+write_parameters( filename='parameters.prm' ) [source]
+This method writes a parameters file (.prm) called filename and fills
+it with all the parameters class members. Default value is
+parameters.prm.
+
+
+Parameters:
+filename (str param_pptc (bool
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
ProfileBase — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
ProfileBase
+
Base module that provides essential tools and transformations on airfoils.
+
+
+
+class ProfileBase[source]
+Bases: object
+Base sectional profile of the propeller blade.
+Each sectional profile is a 2D airfoil that is split into two parts: the
+upper and lower parts. The coordiates of each part is represented by two
+arrays corresponding to the X and Y components in the 2D coordinate system.
+Such coordinates can be either generated using NACA functions, or be
+inserted directly by the user as custom profiles.
+
+
+Parameters:
+xup_coordinates (numpy.ndarray xdown_coordinates (numpy.ndarray yup_coordinates (numpy.ndarray ydown_coordinates (numpy.ndarray chord_line (numpy.ndarray camber_line (numpy.ndarray leading_edge (numpy.ndarray trailing_edge (numpy.ndarray
+
+
+
+
+_update_edges( ) [source]
+Private method that identifies and updates the airfoil’s leading and
+trailing edges.
+Given the airfoil coordinates from the leading to the trailing edge,
+if the trailing edge has a non-zero thickness, then the average value
+between the upper and lower trailing edges is taken as the true
+trailing edge, hence both the leading and the trailing edges are always
+unique.
+
+
+
+
+chord_length
+Measure the l2-norm (Euclidean distance) between the leading edge
+and the trailing edge.
+
+
+Returns: chord length
+Return type: float
+
+
+
+
+
+compute_camber_line( n_interpolated_points=None ) [source]
+Compute the 2D coordinates of the camber line. Also updates the
+camber_line class member.
+The camber line is defined by the curve passing through all the mid
+points between the upper surface and the lower surface of the airfoil.
+
+
+Parameters: n_interpolated_points (int
+
+We note that a uniform interpolation becomes necessary for the cases
+when the X-coordinates of the upper and lower surfaces do not
+correspond to the same vertical sections, since this would imply
+inaccurate measurements for obtaining the camber line.
+
+
+
+
+compute_chord_line( n_interpolated_points=None ) [source]
+Compute the 2D coordinates of the chord line. Also updates
+the chord_line class member.
+The chord line is the straight line that joins between the leading edge
+and the trailing edge. It is simply computed from the equation of
+a line passing through two points, the LE and TE.
+
+
+Parameters: n_interpolated_points (int
+
+
+
+
+
+deform_camber_line( percent_change , n_interpolated_points=None ) [source]
+Deform camber line according to a given percentage of change of the
+maximum camber. Also reconstructs the deformed airfoil’s coordinates.
+The percentage of change is defined as follows:
+
+
+
A positive percentage means the new camber is larger than the max
+camber value, while a negative percentage indicates the new value
+is smaller.
+We note that the method works only for airfoils in the reference
+position, i.e. chord line lies on the X-axis and the foil is not
+rotated, since the measurements are based on the Y-values of the
+airfoil coordinates, hence any measurements or scalings will be
+inaccurate for the foils not in their reference position.
+
+
+Parameters:
+percent_change (float interpolate (bool n_interpolated_points (int
+
+
+
+
+
+
+interpolate_coordinates( num=500 , radius=1.0 ) [source]
+Interpolate the airfoil coordinates from the given data set of
+discrete points.
+The interpolation applies the Radial Basis Function (RBF) method,
+to construct approximations of the two functions that correspond to the
+airfoil upper half and lower half coordinates. The RBF implementation
+is present in RBF ndinterpolator
+References:
+Buhmann, Martin D. (2003), Radial Basis Functions: Theory
+and Implementations.
+http://www.cs.bham.ac.uk/~jxb/NN/l12.pdf
+https://www.cc.gatech.edu/~isbell/tutorials/rbf-intro.pdf
+
+
+Parameters:
+num (int radius (float
+Returns: interpolation points for the airfoil upper half X-component,
+interpolation points for the airfoil lower half X-component,
+interpolation points for the airfoil upper half Y-component,
+interpolation points for the airfoil lower half Y-component
+Return type: numpy.ndarray, numpy.ndarray, numpy.ndarray, numpy.ndarray
+Raises:
+TypeError – if num is not of type intValueError – if num is not positive, or if radius is not
+positive
+
+
+
+
+
+
+max_camber( n_interpolated_points=500 ) [source]
+Return the magnitude of the airfoil’s maximum camber.
+Camber is defined as the distance between the chord line and the mean
+camber line, and is measured along the line perpendicular to the chord
+line.
+
+
+Parameters:
+interpolate (bool n_interpolated_points (int
+Returns: maximum camber
+Return type: float
+
+
+
+
+
+
+max_thickness( n_interpolated_points=None ) [source]
+Return the airfoil’s maximum thickness.
+Thickness is defined as the distnace between the upper and lower
+surfaces of the airfoil, and can be measured in two different ways:
+
+
+American convention: measures along the line perpendicular to the mean camber line.
+British convention: measures along the line perpendicular to the chord line.
+
+
+In this implementation, the british convention is used to evaluate
+the maximum thickness.
+References:
+
+Phillips, Warren F. (2010). Mechanics of Flight (2nd ed.). Wiley & Sons. p. 27. ISBN 978-0-470-53975-0.
+
Bertin, John J.; Cummings, Russel M. (2009). Pearson Prentice Hall, ed. Aerodynamics for Engineers (5th ed.). p. 199. ISBN 978-0-13-227268-1.
+
+
+
+Parameters:
+interpolate (bool n_interpolated_points (int
+Returns: maximum thickness
+Return type: float
+
+
+
+
+
+
+plot( profile=True , chord_line=False , camber_line=False , ref_point=False , outfile=None ) [source]
+Plot the airfoil coordinates.
+
+
+Parameters:
+profile (bool chord_line (bool camber_line (bool ref_point (bool outfile (str
+
+
+
+
+
+
+reference_point
+Return the coordinates of the chord’s mid point.
+
+
+Returns: reference point in 2D
+Return type: numpy.ndarray
+
+
+
+
+
+reflect( ) [source]
+Reflect the airfoil coordinates about the origin, i.e. a mirror
+transformation is performed about both the X-axis and the Y-axis.
+
+
+
+
+rotate( rad_angle=None , deg_angle=None ) [source]
+2D counter clockwise rotation about the origin of the Cartesian
+coordinate system.
+The rotation matrix,
+
+
+
+
Given the coordinates of point
+
+
+
Then, the rotated coordinates will be:
+
+
+
If a standard right-handed Cartesian coordinate system is used, with
+the X-axis to the right and the Y-axis up, the rotation
+
+
+
+Parameters:
+rad_angle (float deg_angle (float
+Raises: ValueError – if both rad_angle and deg_angle are inserted,
+or if neither is inserted
+
+
+
+
+
+
+scale( factor ) [source]
+Scale the airfoil coordinates according to a scaling factor.
+In order to apply the scaling without affecting the position of the
+reference point, the method translates the airfoil by its refernce
+point to be centered in the origin, then the scaling is applied, and
+finally the airfoil is translated back by its reference point to the
+initial position.
+
+
+Parameters: factor (float
+
+
+
+
+
+translate( translation ) [source]
+Translate the airfoil coordinates according to a 2D translation vector.
+
+
+Parameters: translation (array_like ) – the translation vector in 2D
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Profiles — BladeX 0.1 documentation
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ BladeX
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Profiles
+
Derived module from profilebase.py to provide the airfoil coordinates.
+
+
+
+class CustomProfile( xup , yup , xdown , ydown ) [source]
+Bases: bladex.profilebase.ProfileBase
+Provide custom profile for the airfoil coordinates.
+
+
+Parameters:
+xup (numpy.ndarray xdown (numpy.ndarray yup (numpy.ndarray ydown (numpy.ndarray
+
+
+
+
+_check_coordinates( ) [source]
+Private method that checks whether the airfoil coordinates defined
+are provided correctly.
+We note that each array of coordinates must be consistent with the
+other arrays. The upper and lower surfaces should start from exactly
+the same point, the leading edge, and proceed on the way till the
+trailing edge. The trailing edge might have a non-zero thickness as
+in the case of some NACA-airfoils. In case of an open trailing edge,
+the average coordinate between upper and lower part is taken as the
+unique value.
+
+
+Raises:
+ValueError – if either xup, xdown, yup, ydown is NoneValueError – if the 1D arrays xup, yup or xdown, ydown do not
+have the same lengthValueError – if array yup not greater than or equal array ydown
+element-wiseValueError – if xdown[0] != xup[0] or ydown[0] != yup[0]
+or xdown[-1] != xup[-1]
+
+
+
+
+
+
+
+
+class NacaProfile( digits , n_points=240 , cosine_spacing=True ) [source]
+Bases: bladex.profilebase.ProfileBase
+Generate 4- and 5-digit NACA profiles.
+The NACA airfoils are airfoil shapes for aircraft wings developed by the
+National Advisory Committee for Aeronautics (NACA). The shape of the NACA
+airfoils is described using a series of digits following the word “NACA”.
+The parameters in the numerical code can be entered into equations to
+precisely generate the cross-section of the airfoil and calculate its
+properties.
+The NACA four-digit series describes airfoil by the format MPTT, where:
+
+
+M/100: indicates the maximum camber in percentage, with respect to the
+chord length.
+P/10: indicates the location of the maximum camber measured from the
+leading edge. The location is normalized by the chord length.
+TT/100: the maximum thickness as fraction of the chord length.
+
+
+The profile 00TT refers to a symmetrical NACA airfoil.
+The NACA five-digit series describes more complex airfoil shapes.
+Its format is: LPSTT, where:
+
+
+L: the theoretical optimum lift coefficient at ideal
+angle-of-attack = 0.15*L
+P: the x-coordinate of the point of maximum camber
+(max camber at x = 0.05*P)
+S: indicates whether the camber is simple (S=0) or reflex (S=1)
+TT/100: the maximum thickness in percent of chord, as in a four-digit
+NACA airfoil code
+
+
+References:
+
+Moran, Jack (2003). An introduction to theoretical and computational
+aerodynamics. Dover. p. 7. ISBN 0-486-42879-6.
+Abbott, Ira (1959). Theory of Wing Sections: Including a Summary of
+Airfoil Data. New York: Dover Publications. p. 115. ISBN 978-0486605869.
+
+
+
+Parameters:
+digits (str n_points (int cosine_spacing (bool
+Raises:
+ValueError – if n_points is not positiveTypeError – if n_points is not of type intSyntaxError – if digits is not a stringException – if digits is not of length 4 or 5
+
+
+
+
+_check_args( ) [source]
+Private method to check that the number of the airfoil discrete points
+is a positive integer.
+
+
+
+
+_generate_coordinates( ) [source]
+Private method that generates the coordinates of the NACA 4 or 5 digits
+airfoil profile. The method assumes a zero-thickness trailing edge, and
+no half-cosine spacing.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
Python Module Index — BladeX 0.1 documentation
+
+
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Python Module Index
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"
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "naca_0012 = NacaProfile(digits='0012', n_points=240, cosine_spacing=True)\n",
- "print('NACA 0012 digits: ', naca_0012.digits)\n",
- "print('NACA 0012 number of points: ', naca_0012.n_points)\n",
- "print('NACA 0012 cosine spacing distribution: ', naca_0012.cosine_spacing)\n",
- "naca_0012.plot()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Now we instantiate the object **naca_6409** which correspond to the NACA 6409 cambered foil. We generate the profile using 240 points, and cosine spacing for the coordinates distribution.\n",
- "\n",
- "For the plot we also have the possibility to plot the profile manually if we seek to style the plot by our own. The profile coordinates can be accessed through the members `xup_coordinates`, `yup_coordinates`, `xdown_coordinates`, `ydown_coordinates`."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 3,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "naca_6409 = NacaProfile(digits='6409', n_points=240, cosine_spacing=True)\n",
- "\n",
- "plt.plot(naca_6409.xup_coordinates, naca_6409.yup_coordinates, label='upper profile')\n",
- "plt.plot(naca_6409.xdown_coordinates, naca_6409.ydown_coordinates, label='lower profile')\n",
- "plt.title('NACA 6409 cambered foil')\n",
- "plt.grid(linestyle='dotted')\n",
- "plt.axis('equal')\n",
- "plt.legend()\n",
- "plt.show()\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "We note that the cosine or linear spacing for the coordinates distribution are valid for cambered foils only, since all symmetric foils are implemented only with linear spacing.\n",
- "\n",
- "In order to compare between both coordinate distributions, we instantiate another two objects, **linear_spacing_foil** and **cosine_spacing_foil**, which correspond to a NACA 2412 cambered foil with linear spacing and cosine spacing, respectively; then we print the coordinates for both objects. We generate both foils with 5 points only for each surface so that we can easily compare the data.\n",
- "\n",
- "From the resulted plots, we conclude that both coordinates distributions yield exactly the same profile, even if the coordinates of the discrete points are not the same for each coordinates distribution style."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 4,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "X_up (linear): [0. 0.25 0.5 0.75 1. ]\n",
- "X_up (cosine): [0. 0.24777378 0.50058731 0.75121259 1. ]\n",
- "\n",
- "Y_up (linear): [ 0.00000000e+00 7.65950000e-02 7.23059464e-02 4.43988349e-02\n",
- " -1.66533454e-17]\n",
- "Y_up (cosine): [ 0.00000000e+00 7.65532731e-02 7.23026837e-02 4.43752657e-02\n",
- " -1.66164608e-17]\n",
- "\n",
- "X_down (linear): [0. 0.25 0.5 0.75 1. ]\n",
- "X_down (cosine): [0. 0.25222622 0.49941269 0.74878741 1. ]\n",
- "\n",
- "Y_down (linear): [ 0.00000000e+00 -4.22200000e-02 -3.34170576e-02 -1.80099460e-02\n",
- " 1.66533454e-17]\n",
- "Y_down (cosine): [ 0.00000000e+00 -4.21782731e-02 -3.34137948e-02 -1.79863768e-02\n",
- " 1.66164608e-17]\n"
- ]
- },
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "linear_spacing_foil = NacaProfile(digits='2412', n_points=5, cosine_spacing=False)\n",
- "cosine_spacing_foil = NacaProfile(digits='2412', n_points=5, cosine_spacing=True)\n",
- "\n",
- "print('X_up (linear): ', linear_spacing_foil.xup_coordinates)\n",
- "print('X_up (cosine): ', cosine_spacing_foil.xup_coordinates)\n",
- "\n",
- "print('\\nY_up (linear): ', linear_spacing_foil.yup_coordinates)\n",
- "print('Y_up (cosine): ', cosine_spacing_foil.yup_coordinates)\n",
- "\n",
- "print('\\nX_down (linear): ', linear_spacing_foil.xdown_coordinates)\n",
- "print('X_down (cosine): ', cosine_spacing_foil.xdown_coordinates)\n",
- "\n",
- "print('\\nY_down (linear): ', linear_spacing_foil.ydown_coordinates)\n",
- "print('Y_down (cosine): ', cosine_spacing_foil.ydown_coordinates)\n",
- "\n",
- "plt.plot(linear_spacing_foil.xup_coordinates, linear_spacing_foil.yup_coordinates, label='upper profile (linear)')\n",
- "plt.plot(linear_spacing_foil.xdown_coordinates, linear_spacing_foil.ydown_coordinates, label='lower profile (linear)')\n",
- "\n",
- "plt.plot(cosine_spacing_foil.xup_coordinates, cosine_spacing_foil.yup_coordinates, label='upper profile (cosine)')\n",
- "plt.plot(cosine_spacing_foil.xdown_coordinates, cosine_spacing_foil.ydown_coordinates, label='lower profile (cosine)')\n",
- "\n",
- "plt.grid(linestyle='dotted')\n",
- "plt.axis('equal')\n",
- "plt.legend()\n",
- "plt.show()\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Now we proceed by computing some of the foil geometric features. We start by computing the chord line as well as plotting it."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 5,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "naca_6409.compute_chord_line(n_interpolated_points=None)\n",
- "naca_6409.plot(profile=True, chord_line=True, camber_line=False, ref_point=False, outfile=None)\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Now we compute and plot the camber line. Suppose we need to compute the camber coordinates but with 480 not just the default 240 points, then we can perform interpolation by specifying an integer to the argument `n_interpolated_points` in the method."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 6,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "naca_6409.compute_camber_line(n_interpolated_points=480)\n",
- "naca_6409.plot(profile=True, chord_line=False, camber_line=True, ref_point=False, outfile=None)\n"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "To plot the reference point, which is the mid point of the chord line, we change the truth value of the corresponding argument in the plot method."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 7,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "naca_6409.plot(profile=True, chord_line=False, camber_line=False, ref_point=True, outfile=None)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "Finally we print the values of the chord length, the maximum thickness, the maximum camber, and the leading and trailing edge coordinates, through the following script."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 8,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "NACA 6409 max thickness: 0.09028078486024707\n",
- "NACA 6409 max camber: 0.06000007200019134\n",
- "NACA 6409 chord length: 1.0\n",
- "NACA 6409 leading edge: [0. 0.]\n",
- "NACA 6409 trailing edge: [1. 0.]\n"
- ]
- }
- ],
- "source": [
- "print('NACA 6409 max thickness: ', naca_6409.max_thickness(n_interpolated_points=None))\n",
- "print('NACA 6409 max camber: ', naca_6409.max_camber(n_interpolated_points=None))\n",
- "print('NACA 6409 chord length: ', naca_6409.chord_length)\n",
- "print('NACA 6409 leading edge: ', naca_6409.leading_edge)\n",
- "print('NACA 6409 trailing edge: ', naca_6409.trailing_edge)"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "### 1.2 NACA-5 series and custom profiles"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "The profile generation using NACA-5 series or using custom data are both explained below, provided that all the previous demosntrations still apply to the following two classes.\n",
- "\n",
- "The NACA 24112 is generated through the object **naca_24112**"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 9,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "naca_24112 = NacaProfile(digits='24112', n_points=1000, cosine_spacing=True)\n",
- "naca_24112.plot()"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "For generating a custom profile, we need to know the coordinates in advance. \n",
- "\n",
- "By knowing the coordinates of the Boeing 707 airfoil (which are stored in 'data/boeing_707.csv' file), then we can instantiate the abject **boeing_707** of the class `CustomProfile`, and we pass the coordinates to the arguments `xup`, `yup`, `xdown`, `ydown` as follows"
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 10,
- "metadata": {},
- "outputs": [
- {
- "data": {
- "image/png": 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\n",
- "text/plain": [
- ""
- ]
- },
- "metadata": {},
- "output_type": "display_data"
- }
- ],
- "source": [
- "# Read the data file and then assign to the coordinates variables\n",
- "xup = np.zeros(61)\n",
- "yup = np.zeros(61)\n",
- "xdown = np.zeros(61)\n",
- "ydown = np.zeros(61)\n",
- "\n",
- "with open(\"data/boeing_707.csv\", \"r\") as f:\n",
- " lines = f.readlines()\n",
- "\n",
- "for i, line in enumerate(lines[1:62]):\n",
- " xup[i] = float(line)\n",
- "\n",
- "for i, line in enumerate(lines[64:125]):\n",
- " yup[i] = float(line)\n",
- "\n",
- "for i, line in enumerate(lines[127:188]):\n",
- " xdown[i] = float(line)\n",
- "\n",
- "for i, line in enumerate(lines[190:251]):\n",
- " ydown[i] = float(line)\n",
- "\n",
- "# Instantiate the class object\n",
- "boeing_707 = CustomProfile(xup=xup, yup=yup, xdown=xdown, ydown=ydown)\n",
- "\n",
- "boeing_707.compute_camber_line()\n",
- "\n",
- "boeing_707.plot(profile=True, chord_line=False, camber_line=True, ref_point=False)\n"
- ]
- }
- ],
- "metadata": {
- "kernelspec": {
- "display_name": "Python 3",
- "language": "python",
- "name": "python3"
- },
- "language_info": {
- "codemirror_mode": {
- "name": "ipython",
- "version": 3
- },
- "file_extension": ".py",
- "mimetype": "text/x-python",
- "name": "python",
- "nbconvert_exporter": "python",
- "pygments_lexer": "ipython3",
- "version": "3.8.8"
- }
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
diff --git a/tutorials/tutorial-2-transform_foils.ipynb b/tutorials/tutorial-2-transform_foils.ipynb
deleted file mode 100644
index 0a32fa6..0000000
--- a/tutorials/tutorial-2-transform_foils.ipynb
+++ /dev/null
@@ -1,742 +0,0 @@
-{
- "cells": [
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "# BladeX"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "## Tutorial 2: Prepare a blade 2D sectional profile - Transform foils"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "In this tutorial we present the transformation operations that can be applied to the generated foils. More specifically we show how to rotate, translate, reflect, and scale the foils. Moreover, we show how to deform the camber line and hence deforming the whole foil."
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "First of all we import from BladeX the `NacaProfile` class for generating the NACA foils that we shall operate on.\n",
- "Finally we import `numpy` and we set `matplotlib` for the notebook."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 1,
- "metadata": {},
- "outputs": [],
- "source": [
- "import matplotlib.pyplot as plt\n",
- "import numpy as np\n",
- "from bladex import NacaProfile"
- ]
- },
- {
- "cell_type": "markdown",
- "metadata": {},
- "source": [
- "We instantiate the object **naca_0012** of the `NacaProfile` class, which correspond to the NACA-0012 foil. We plot the profile coordinates. In such plot the leading edge would lie at the origin while the trailing edge would be at the point `(1.0, 0.0)`. Now we translate the foil coordinates by a vector `(1.0, 0.0)`, thus we expect the foil to have updated leading edge and trailing edge at points `(1.0, 0.0)` and `(2.0, 0.0)`, respectively."
- ]
- },
- {
- "cell_type": "code",
- "execution_count": 2,
- "metadata": {},
- "outputs": [
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "DEBUG:matplotlib.font_manager:findfont: Matching sans\\-serif:style=normal:variant=normal:weight=normal:stretch=normal:size=10.0.\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 0.33499999999999996\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 1.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 1.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 0.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.25\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.24\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.24\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.535\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 1.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n"
- ]
- },
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.535\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.535\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.43\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.24\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.24\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n"
- ]
- },
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.25\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 1.535\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.25\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.24\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.25\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.24\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 0.24\n"
- ]
- },
- {
- "name": "stdout",
- "output_type": "stream",
- "text": [
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.335\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 11.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.05\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.24\n",
- "DEBUG:matplotlib.font_manager:findfont: score() = 10.145\n",
- "DEBUG:matplotlib.font_manager:findfont: score(
- 
- 
- 
- 
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