1 /*
  2     Copyright 2008-2013
  3         Matthias Ehmann,
  4         Michael Gerhaeuser,
  5         Carsten Miller,
  6         Bianca Valentin,
  7         Alfred Wassermann,
  8         Peter Wilfahrt
  9 
 10     This file is part of JSXGraph.
 11 
 12     JSXGraph is free software dual licensed under the GNU LGPL or MIT License.
 13     
 14     You can redistribute it and/or modify it under the terms of the
 15     
 16       * GNU Lesser General Public License as published by
 17         the Free Software Foundation, either version 3 of the License, or
 18         (at your option) any later version
 19       OR
 20       * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT
 21     
 22     JSXGraph is distributed in the hope that it will be useful,
 23     but WITHOUT ANY WARRANTY; without even the implied warranty of
 24     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 25     GNU Lesser General Public License for more details.
 26     
 27     You should have received a copy of the GNU Lesser General Public License and
 28     the MIT License along with JSXGraph. If not, see <http://www.gnu.org/licenses/>
 29     and <http://opensource.org/licenses/MIT/>.
 30  */
 31 
 32 
 33 /*global JXG: true, define: true*/
 34 /*jslint nomen: true, plusplus: true*/
 35 
 36 /* depends:
 37  jxg
 38  base/constants
 39  base/coords
 40  math/math
 41  math/geometry
 42  server/server
 43  utils/type
 44  */
 45 
 46 /**
 47  * @fileoverview In this file the namespace Math.Symbolic is defined, which holds methods
 48  * and algorithms for symbolic computations.
 49  * @author graphjs
 50  */
 51 
 52 define([
 53     'jxg', 'base/constants', 'base/coords', 'math/math', 'math/geometry', 'server/server', 'utils/type'
 54 ], function (JXG, Const, Coords, Mat, Geometry, Server, Type) {
 55 
 56     "use strict";
 57 
 58     var undef;
 59 
 60     /**
 61      * The JXG.Math.Symbolic namespace holds algorithms for symbolic computations.
 62      * @name JXG.Math.Symbolic
 63      * @namespace
 64      */
 65     Mat.Symbolic = {
 66         /**
 67          * Generates symbolic coordinates for the part of a construction including all the elements from that
 68          * a specific element depends of. These coordinates will be stored in GeometryElement.symbolic.
 69          * @param {JXG.Board} board The board that's element get some symbolic coordinates.
 70          * @param {JXG.GeometryElement} element All ancestor of this element get symbolic coordinates.
 71          * @param {String} variable Name for the coordinates, e.g. x or u.
 72          * @param {String} append Method for how to append the number of the coordinates. Possible values are
 73          *                        'underscore' (e.g. x_2), 'none' (e.g. x2), 'brace' (e.g. x[2]).
 74          * @returns {Number} Number of coordinates given.
 75          * @memberof JXG.Math.Symbolic
 76          */
 77         generateSymbolicCoordinatesPartial: function (board, element, variable, append) {
 78             var t_num, t, k,
 79                 list = element.ancestors,
 80                 count = 0,
 81                 makeCoords = function (num) {
 82                     var r;
 83 
 84                     if (append === 'underscore') {
 85                         r = variable + '_{' + num + '}';
 86                     } else if (append === 'brace') {
 87                         r = variable + '[' + num + ']';
 88                     } else {
 89                         r = variable + num;
 90                     }
 91 
 92                     return r;
 93                 };
 94 
 95             board.listOfFreePoints = [];
 96             board.listOfDependantPoints = [];
 97 
 98             for (t in list) {
 99                 if (list.hasOwnProperty(t)) {
100                     t_num = 0;
101 
102                     if (Type.isPoint(list[t])) {
103                         for (k in list[t].ancestors) {
104                             if (list[t].ancestors.hasOwnProperty(k)) {
105                                 t_num++;
106                             }
107                         }
108 
109                         if (t_num === 0) {
110                             list[t].symbolic.x = list[t].coords.usrCoords[1];
111                             list[t].symbolic.y = list[t].coords.usrCoords[2];
112                             board.listOfFreePoints.push(list[t]);
113                         } else {
114                             count += 1;
115                             list[t].symbolic.x = makeCoords(count);
116                             count += 1;
117                             list[t].symbolic.y = makeCoords(count);
118                             board.listOfDependantPoints.push(list[t]);
119                         }
120 
121                     }
122                 }
123             }
124 
125             if (Type.isPoint(element)) {
126                 element.symbolic.x = 'x';
127                 element.symbolic.y = 'y';
128             }
129 
130             return count;
131         },
132 
133         /**
134          * Clears all .symbolic.x and .symbolic.y members on every point of a given board.
135          * @param {JXG.Board} board The board that's points get cleared their symbolic coordinates.
136          * @memberof JXG.Math.Symbolic
137          */
138         clearSymbolicCoordinates: function (board) {
139             var clear = function (list) {
140                     var t, l = (list && list.length) || 0;
141 
142                     for (t = 0; t < l; t++) {
143                         if (Type.isPoint(list[t])) {
144                             list[t].symbolic.x = '';
145                             list[t].symbolic.y = '';
146                         }
147                     }
148                 };
149 
150             clear(board.listOfFreePoints);
151             clear(board.listOfDependantPoints);
152 
153             delete (board.listOfFreePoints);
154             delete (board.listOfDependantPoints);
155         },
156 
157         /**
158          * Generates polynomials for a part of the construction including all the points from that
159          * a specific element depends of.
160          * @param {JXG.Board} board The board that's points polynomials will be generated.
161          * @param {JXG.GeometryElement} element All points in the set of ancestors of this element are used to generate the set of polynomials.
162          * @param {Boolean} generateCoords
163          * @returns {Array} An array of polynomials as strings.
164          * @memberof JXG.Math.Symbolic
165          */
166         generatePolynomials: function (board, element, generateCoords) {
167             var t, k, i,
168                 list = element.ancestors,
169                 number_of_ancestors,
170                 pgs = [],
171                 result = [];
172 
173             if (generateCoords) {
174                 this.generateSymbolicCoordinatesPartial(board, element, 'u', 'brace');
175             }
176 
177             list[element.id] = element;
178 
179             for (t in list) {
180                 if (list.hasOwnProperty(t)) {
181                     number_of_ancestors = 0;
182                     pgs = [];
183 
184                     if (Type.isPoint(list[t])) {
185                         for (k in list[t].ancestors) {
186                             if (list[t].ancestors.hasOwnProperty(k)) {
187                                 number_of_ancestors++;
188                             }
189                         }
190                         if (number_of_ancestors > 0) {
191                             pgs = list[t].generatePolynomial();
192 
193                             for (i = 0; i < pgs.length; i++) {
194                                 result.push(pgs[i]);
195                             }
196                         }
197                     }
198                 }
199             }
200 
201             if (generateCoords) {
202                 this.clearSymbolicCoordinates(board);
203             }
204 
205             return result;
206         },
207 
208         /**
209          * Calculate geometric locus of a point given on a board. Invokes python script on server.
210          * @param {JXG.Board} board The board on which the point lies.
211          * @param {JXG.Point} point The point that will be traced.
212          * @returns {Array} An array of points.
213          * @memberof JXG.Math.Symbolic
214          */
215         geometricLocusByGroebnerBase: function (board, point) {
216             var poly, polyStr, result,
217                 P1, P2, i,
218                 xs, xe, ys, ye,
219                 c, s, tx,
220                 bol = board.options.locus,
221                 oldRadius = {},
222                 numDependent = this.generateSymbolicCoordinatesPartial(board, point, 'u', 'brace'),
223                 xsye = new Coords(Const.COORDS_BY_USR, [0, 0], board),
224                 xeys = new Coords(Const.COORDS_BY_USR, [board.canvasWidth, board.canvasHeight], board),
225                 sf = 1, transx = 0, transy = 0, rot = 0;
226 
227             if (Server.modules.geoloci === undef) {
228                 Server.loadModule('geoloci');
229             }
230 
231             if (Server.modules.geoloci === undef) {
232                 throw new Error("JSXGraph: Unable to load JXG.Server module 'geoloci.py'.");
233             }
234 
235             xs = xsye.usrCoords[1];
236             xe = xeys.usrCoords[1];
237             ys = xeys.usrCoords[2];
238             ye = xsye.usrCoords[2];
239 
240             // Optimizations - but only if the user wants to
241             //   Step 1: Translate all related points, such that one point P1 (board.options.locus.toOrigin if set
242             //     or a random point otherwise) is moved to (0, 0)
243             //   Step 2: Rotate the construction around the new P1, such that another point P2 (board.options.locus.to10 if set
244             //     or a random point \neq P1 otherwise) is moved onto the positive x-axis
245             //  Step 3: Dilate the construction, such that P2 is moved to (1, 0)
246             //  Step 4: Give the scale factor (sf), the rotation (rot) and the translation vector (transx, transy) to
247             //    the server, which retransforms the plot (if any).
248 
249             // Step 1
250             if (bol.translateToOrigin && (board.listOfFreePoints.length > 0)) {
251                 if ((bol.toOrigin !== undef) && (bol.toOrigin !== null) && Type.isInArray(board.listOfFreePoints, bol.toOrigin.id)) {
252                     P1 = bol.toOrigin;
253                 } else {
254                     P1 = board.listOfFreePoints[0];
255                 }
256 
257                 transx = P1.symbolic.x;
258                 transy = P1.symbolic.y;
259                 // translate the whole construction
260                 for (i = 0; i < board.listOfFreePoints.length; i++) {
261                     board.listOfFreePoints[i].symbolic.x -= transx;
262                     board.listOfFreePoints[i].symbolic.y -= transy;
263                 }
264 
265                 xs -= transx;
266                 xe -= transx;
267                 ys -= transy;
268                 ye -= transy;
269 
270                 // Step 2
271                 if (bol.translateTo10 && (board.listOfFreePoints.length > 1)) {
272                     if ((bol.to10 !== undef) && (bol.to10 !== null) && (bol.to10.id !== bol.toOrigin.id) && Type.isInArray(board.listOfFreePoints, bol.to10.id)) {
273                         P2 = bol.to10;
274                     } else {
275                         if (board.listOfFreePoints[0].id === P1.id) {
276                             P2 = board.listOfFreePoints[1];
277                         } else {
278                             P2 = board.listOfFreePoints[0];
279                         }
280                     }
281 
282                     rot = Geometry.rad([1, 0], [0, 0], [P2.symbolic.x, P2.symbolic.y]);
283                     c = Math.cos(-rot);
284                     s = Math.sin(-rot);
285 
286 
287                     for (i = 0; i < board.listOfFreePoints.length; i++) {
288                         tx = board.listOfFreePoints[i].symbolic.x;
289                         board.listOfFreePoints[i].symbolic.x = c * board.listOfFreePoints[i].symbolic.x - s * board.listOfFreePoints[i].symbolic.y;
290                         board.listOfFreePoints[i].symbolic.y = s * tx + c * board.listOfFreePoints[i].symbolic.y;
291                     }
292 
293                     // thanks to the rotation this is zero
294                     P2.symbolic.y = 0;
295 
296                     tx = xs;
297                     xs = c * xs - s * ys;
298                     ys = s * tx + c * ys;
299                     tx = xe;
300                     xe = c * xe - s * ye;
301                     ye = s * tx + c * ye;
302 
303                     // Step 3
304                     if (bol.stretch && (Math.abs(P2.symbolic.x) > Mat.eps)) {
305                         sf = P2.symbolic.x;
306 
307                         for (i = 0; i < board.listOfFreePoints.length; i++) {
308                             board.listOfFreePoints[i].symbolic.x /= sf;
309                             board.listOfFreePoints[i].symbolic.y /= sf;
310                         }
311 
312                         for (i = 0; i < board.objectsList.length; i++) {
313                             if ((board.objectsList[i].elementClass === Const.OBJECT_CLASS_CIRCLE) && (board.objectsList[i].method === 'pointRadius')) {
314                                 oldRadius[i] = board.objectsList[i].radius;
315                                 board.objectsList[i].radius /= sf;
316                             }
317                         }
318 
319                         xs /= sf;
320                         xe /= sf;
321                         ys /= sf;
322                         ye /= sf;
323 
324                         // this is now 1
325                         P2.symbolic.x = 1;
326                     }
327                 }
328 
329                 // make the coordinates "as rational as possible"
330                 for (i = 0; i < board.listOfFreePoints.length; i++) {
331                     tx = board.listOfFreePoints[i].symbolic.x;
332 
333                     if (Math.abs(tx) < Mat.eps) {
334                         board.listOfFreePoints[i].symbolic.x = 0;
335                     }
336 
337                     if (Math.abs(tx - Math.round(tx)) < Mat.eps) {
338                         board.listOfFreePoints[i].symbolic.x = Math.round(tx);
339                     }
340 
341                     tx = board.listOfFreePoints[i].symbolic.y;
342 
343                     if (Math.abs(tx) < Mat.eps) {
344                         board.listOfFreePoints[i].symbolic.y = 0;
345                     }
346 
347                     if (Math.abs(tx - Math.round(tx)) < Mat.eps) {
348                         board.listOfFreePoints[i].symbolic.y = Math.round(tx);
349                     }
350                 }
351             }
352 
353             // end of optimizations
354 
355             poly = this.generatePolynomials(board, point);
356             polyStr = poly.join(',');
357 
358             this.cbp = function (data) {
359                 result = data;
360             };
361 
362             this.cb = Type.bind(this.cbp, this);
363 
364             Server.modules.geoloci.lociCoCoA(xs, xe, ys, ye, numDependent, polyStr, sf, rot, transx, transy, this.cb, true);
365 
366             this.clearSymbolicCoordinates(board);
367 
368             for (i in oldRadius) {
369                 if (oldRadius.hasOwnProperty(i)) {
370                     board.objects[i].radius = oldRadius[i];
371                 }
372             }
373 
374 
375             return result;
376         }
377     };
378 
379     return Mat.Symbolic;
380 });
381