1 /*
  2     Copyright 2008,2009
  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: you can redistribute it and/or modify
 13     it under the terms of the GNU Lesser General Public License as published by
 14     the Free Software Foundation, either version 3 of the License, or
 15     (at your option) any later version.
 16 
 17     JSXGraph is distributed in the hope that it will be useful,
 18     but WITHOUT ANY WARRANTY; without even the implied warranty of
 19     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 20     GNU Lesser General Public License for more details.
 21 
 22     You should have received a copy of the GNU Lesser General Public License
 23     along with JSXGraph. If not, see <http://www.gnu.org/licenses/>.
 24 */
 25 
 26 /**
 27  * @fileoverview In this file the namespace Math.Symbolic is defined, which holds methods
 28  * and algorithms for symbolic computations.
 29  * @author graphjs
 30  */
 31 
 32 /**
 33  * The JXG.Math.Symbolic namespace holds algorithms for symbolic computations.
 34  * @namespace
 35  */
 36 JXG.Math.Symbolic = function(JXG, undefined) {
 37 
 38     /** @lends JXG.Math.Symbolic */
 39     return {
 40         /**
 41          * Generates symbolic coordinates for the part of a construction including all the elements from that
 42          * a specific element depends of. These coordinates will be stored in GeometryElement.symbolic.
 43          * @param {JXG.Board} board The board that's element get some symbolic coordinates.
 44          * @param {JXG.GeometryElement} element All ancestor of this element get symbolic coordinates.
 45          * @param {String} variable Name for the coordinates, e.g. x or u.
 46          * @param {String} append Method for how to append the number of the coordinates. Possible values are
 47          *                        'underscore' (e.g. x_2), 'none' (e.g. x2), 'brace' (e.g. x[2]).
 48          * @returns {Number} Number of coordinates given.
 49          */
 50         generateSymbolicCoordinatesPartial: function(board, element, variable, append) {
 51             var makeCoords = function(num) {
 52                     var r;
 53                     if (append === 'underscore')
 54                         r = '' + variable + '_{' + num + '}';
 55                     else if (append == 'brace')
 56                         r = '' + variable + '[' + num + ']';
 57                     else
 58                         r = '' + variable + '' + num;
 59 
 60                     return r;
 61                 },
 62                 list = element.ancestors,
 63                 count = 0, t_num, t, k;
 64 
 65             board.listOfFreePoints = [];
 66             board.listOfDependantPoints = [];
 67 
 68             for (t in list) {
 69                 t_num = 0;
 70                 if (JXG.isPoint(list[t])) {
 71                     for (k in list[t].ancestors) {
 72                         t_num++;
 73                     }
 74                     if (t_num === 0) {
 75                         list[t].symbolic.x = list[t].coords.usrCoords[1];
 76                         list[t].symbolic.y = list[t].coords.usrCoords[2];
 77                         board.listOfFreePoints.push(list[t]);
 78 
 79                     } else {
 80                         count++;
 81                         list[t].symbolic.x = makeCoords(count);
 82                         count++;
 83                         list[t].symbolic.y = makeCoords(count);
 84                         board.listOfDependantPoints.push(list[t]);
 85                     }
 86 
 87                 }
 88             }
 89 
 90             if (JXG.isPoint(element)) {
 91                 element.symbolic.x = 'x';
 92                 element.symbolic.y = 'y';
 93             }
 94 
 95             return count;
 96         },
 97 
 98         /**
 99          * Clears all .symbolic.x and .symbolic.y members on every point of a given board.
100          * @param {JXG.Board} board The board that's points get cleared their symbolic coordinates.
101          */
102         clearSymbolicCoordinates: function(board) {
103             var clear = function(list) {
104                     var t, l = (list && list.length) || 0;
105 
106                     for (t = 0; t < l; t++) {
107                         if (JXG.isPoint(list[t])) {
108                             list[t].symbolic.x = '';
109                             list[t].symbolic.y = '';
110                         }
111                     }
112                 };
113 
114             clear(board.listOfFreePoints);
115             clear(board.listOfDependantPoints);
116 
117             delete (board.listOfFreePoints);
118             delete (board.listOfDependantPoints);
119         },
120 
121         /**
122          * Generates polynomials for a part of the construction including all the points from that
123          * a specific element depends of.
124          * @param {JXG.Board} board The board that's points polynomials will be generated.
125          * @param {JXG.GeometryElement} element All points in the set of ancestors of this element are used to generate the set of polynomials.
126          * @returns {Array} An array of polynomials as strings.
127          */
128         generatePolynomials: function(board, element, generateCoords) {
129             var list = element.ancestors,
130                 number_of_ancestors,
131                 pgs = [],
132                 result = [],
133                 t, k, i;
134 
135             if (generateCoords)
136                 this.generateSymbolicCoordinatesPartial(board, element, 'u', 'brace');
137 
138             list[element.id] = element;
139 
140             for (t in list) {
141                 number_of_ancestors = 0;
142                 pgs = [];
143                 if (JXG.isPoint(list[t])) {
144                     for (k in list[t].ancestors) {
145                         number_of_ancestors++;
146                     }
147                     if (number_of_ancestors > 0) {
148                         pgs = list[t].generatePolynomial();
149                         for (i = 0; i < pgs.length; i++)
150                             result.push(pgs[i]);
151                     }
152                 }
153             }
154 
155             if (generateCoords)
156                 this.clearSymbolicCoordinates(board);
157 
158             return result;
159         },
160 
161         /**
162          * Calculate geometric locus of a point given on a board. Invokes python script on server.
163          * @param {JXG.Board} board The board on which the point lies.
164          * @param {JXG.Point} point The point that will be traced.
165          * @returns {Array} An array of points.
166          */
167         geometricLocusByGroebnerBase: function(board, point) {
168             var numDependent = this.generateSymbolicCoordinatesPartial(board, point, 'u', 'brace'),
169                 poly, polyStr, result, oldRadius = {},
170                 xsye = new JXG.Coords(JXG.COORDS_BY_USR, [0,0], board),
171                 xeys = new JXG.Coords(JXG.COORDS_BY_USR, [board.canvasWidth, board.canvasHeight], board),
172                 P1, P2, i, sf = 1, transx = 0, transy = 0, rot = 0, c, s, tx,
173                 xs, xe, ys, ye,
174 
175                 isIn = function(item, array) {
176                     var i;
177                     for (i = 0; i < array.length; i++) {
178                         if (array[i].id === item) {
179                             return true;
180                         }
181                     }
182                     return false;
183                 },
184                 bol = board.options.locus;
185 
186 
187             if (JXG.Server.modules.geoloci === undefined)
188                 JXG.Server.loadModule('geoloci');
189 
190             if (JXG.Server.modules.geoloci === undefined)
191                 throw new Error("JSXGraph: Unable to load JXG.Server module 'geoloci.py'.");
192 
193             xs = xsye.usrCoords[1];
194             xe = xeys.usrCoords[1];
195             ys = xeys.usrCoords[2];
196             ye = xsye.usrCoords[2];
197 
198             // Optimizations - but only if the user wants to
199             //   Step 1: Translate all related points, such that one point P1 (board.options.locus.toOrigin if set
200             //     or a random point otherwise) is moved to (0, 0)
201             //   Step 2: Rotate the construction around the new P1, such that another point P2 (board.options.locus.to10 if set
202             //     or a random point \neq P1 otherwise) is moved onto the positive x-axis
203             //  Step 3: Dilate the construction, such that P2 is moved to (1, 0)
204             //  Step 4: Give the scale factor (sf), the rotation (rot) and the translation vector (transx, transy) to
205             //    the server, which retransforms the plot (if any).
206 
207             // Step 1
208             if (bol.translateToOrigin && (board.listOfFreePoints.length > 0)) {
209                 if ((bol.toOrigin !== undefined) && (bol.toOrigin != null) && isIn(bol.toOrigin.id, board.listOfFreePoints)) {
210                     P1 = bol.toOrigin;
211                 } else {
212                     P1 = board.listOfFreePoints[0];
213                 }
214 
215                 transx = P1.symbolic.x;
216                 transy = P1.symbolic.y;
217                 // translate the whole construction
218                 for (i = 0; i < board.listOfFreePoints.length; i++) {
219                     board.listOfFreePoints[i].symbolic.x -= transx;
220                     board.listOfFreePoints[i].symbolic.y -= transy;
221                 }
222 
223                 xs -= transx;
224                 xe -= transx;
225                 ys -= transy;
226                 ye -= transy;
227 
228                 // Step 2
229                 if (bol.translateTo10 && (board.listOfFreePoints.length > 1)) {
230                     if ((bol.to10 !== undefined) && (bol.to10 != null) && (bol.to10.id != bol.toOrigin.id) && isIn(bol.to10.id, board.listOfFreePoints)) {
231                         P2 = bol.to10;
232                     } else {
233                         if (board.listOfFreePoints[0].id == P1.id)
234                             P2 = board.listOfFreePoints[1];
235                         else
236                             P2 = board.listOfFreePoints[0];
237                     }
238 
239                     rot = JXG.Math.Geometry.rad([1, 0], [0, 0], [P2.symbolic.x, P2.symbolic.y]);
240                     c = Math.cos(-rot);
241                     s = Math.sin(-rot);
242 
243 
244                     for (i = 0; i < board.listOfFreePoints.length; i++) {
245                         tx = board.listOfFreePoints[i].symbolic.x;
246                         board.listOfFreePoints[i].symbolic.x = c * board.listOfFreePoints[i].symbolic.x - s * board.listOfFreePoints[i].symbolic.y;
247                         board.listOfFreePoints[i].symbolic.y = s * tx + c * board.listOfFreePoints[i].symbolic.y;
248                     }
249 
250                     // thanks to the rotation this is zero
251                     P2.symbolic.y = 0;
252 
253                     tx = xs;
254                     xs = c * xs - s * ys;
255                     ys = s * tx + c * ys;
256                     tx = xe;
257                     xe = c * xe - s * ye;
258                     ye = s * tx + c * ye;
259 
260                     // Step 3
261                     if (bol.stretch && (Math.abs(P2.symbolic.x) > JXG.Math.eps)) {
262                         sf = P2.symbolic.x;
263 
264                         for (i = 0; i < board.listOfFreePoints.length; i++) {
265                             board.listOfFreePoints[i].symbolic.x /= sf;
266                             board.listOfFreePoints[i].symbolic.y /= sf;
267                         }
268 
269                         for (i in board.objects) {
270                             if ((board.objects[i].elementClass == JXG.OBJECT_CLASS_CIRCLE) && (board.objects[i].method == 'pointRadius')) {
271                                 oldRadius[i] = board.objects[i].radius;
272                                 board.objects[i].radius /= sf;
273                             }
274                         }
275 
276                         xs /= sf;
277                         xe /= sf;
278                         ys /= sf;
279                         ye /= sf;
280 
281                         // this is now 1
282                         P2.symbolic.x = 1;
283                     }
284                 }
285 
286                 // make the coordinates "as rational as possible"
287                 for (i = 0; i < board.listOfFreePoints.length; i++) {
288                     tx = board.listOfFreePoints[i].symbolic.x;
289                     if (Math.abs(tx) < JXG.Math.eps)
290                         board.listOfFreePoints[i].symbolic.x = 0;
291                     if (Math.abs(tx - Math.round(tx)) < JXG.Math.eps)
292                         board.listOfFreePoints[i].symbolic.x = Math.round(tx);
293 
294                     tx = board.listOfFreePoints[i].symbolic.y;
295                     if (Math.abs(tx) < JXG.Math.eps)
296                         board.listOfFreePoints[i].symbolic.y = 0;
297                     if (Math.abs(tx - Math.round(tx)) < JXG.Math.eps)
298                         board.listOfFreePoints[i].symbolic.y = Math.round(tx);
299                 }
300             }
301 
302             // end of optimizations
303 
304             poly = this.generatePolynomials(board, point);
305             polyStr = poly.join(',');
306 
307             this.cbp = function(data) {
308                 //alert(data.exectime);
309                 //callback(data.datax, data.datay, data.polynomial);
310                 result = data;
311             };
312 
313             this.cb = JXG.bind(this.cbp, this);
314 
315             JXG.Server.modules.geoloci.lociCoCoA(xs, xe, ys, ye, numDependent, polyStr, sf, rot, transx, transy, this.cb, true);
316 
317             this.clearSymbolicCoordinates(board);
318 
319             for (i in oldRadius) {
320                 board.objects[i].radius = oldRadius[i];
321             }
322 
323 
324             return result;
325         }
326 
327 
328     }
329 }(JXG);
330 
331