      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