      1 /*
      2     Copyright 2008-2023
      3         Matthias Ehmann,
      4         Carsten Miller,
      5         Alfred Wassermann
      6
      7     This file is part of JSXGraph.
      8
      9     JSXGraph is free software dual licensed under the GNU LGPL or MIT License.
     10
     11     You can redistribute it and/or modify it under the terms of the
     12
     13       * 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       OR
     17       * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT
     18
     19     JSXGraph is distributed in the hope that it will be useful,
     20     but WITHOUT ANY WARRANTY; without even the implied warranty of
     21     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
     22     GNU Lesser General Public License for more details.
     23
     24     You should have received a copy of the GNU Lesser General Public License and
     25     the MIT License along with JSXGraph. If not, see <https://www.gnu.org/licenses/>
     26     and <https://opensource.org/licenses/MIT/>.
     27  */
     28
     29 /*global JXG: true, define: true*/
     30 /*jslint nomen: true, plusplus: true*/
     31
     32 /**
     33  * @fileoverview Implementation of vector fields and slope fields.
     34  */
     35
     36 import JXG from "../jxg";
     37 import Type from "../utils/type";
     38
     39 /**
     40  * @class Vector field.
     41  * <p>
     42  * Plot a vector field either given by two functions f1(x, y) and f2(x,y) or by a function f(x, y) returning an array of size 2.
     43  *
     44  * @pseudo
     45  * @name Vectorfield
     46  * @augments JXG.Curve
     47  * @constructor
     48  * @type JXG.Curve
     49  * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
     50  * Parameter options:
     51  * @param {Array|Function|String} F Either an array containing two functions f1(x, y) and f2(x, y) or function f(x, y) returning an array of length 2.
     52  * @param {Array} xData Array of length 3 containing start value for x, number of steps, end value of x. The vector field will contain
     53  * (number of steps) + 1 vectors in direction of x.
     54  * @param {Array} yData Array of length 3 containing start value for y, number of steps, end value of y. The vector field will contain
     55  * (number of steps) + 1 vectors in direction of y.
     56  *
     57  * @example
     58  * // Defining functions
     59  * var fx = (x, y) => Math.sin(y);
     60  * var fy = (x, y) => Math.cos(x);
     61  *
     62  * var field = board.create('vectorfield', [
     63  *         [fx, fy],    // Defining function
     64  *         [-6, 25, 6], // Horizontal mesh
     65  *         [-5, 20, 5], // Vertical mesh
     66  *     ]);
     67  *
     68  * </pre><div id="JXGa2040e30-48ea-47d4-9840-bd24cd49150b" class="jxgbox" style="width: 500px; height: 500px;"></div>
     69  * <script type="text/javascript">
     70  *     (function() {
     71  *         var board = JXG.JSXGraph.initBoard('JXGa2040e30-48ea-47d4-9840-bd24cd49150b',
     72  *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
     73  *     // Defining functions
     74  *     var fx = (x, y) => Math.sin(y);
     75  *     var fy = (x, y) => Math.cos(x);
     76  *
     77  *     var field = board.create('vectorfield', [
     78  *             [fx, fy],    // Defining function
     79  *             [-6, 25, 6], // Horizontal mesh
     80  *             [-5, 20, 5], // Vertical mesh
     81  *         ]);
     82  *
     83  *     })();
     84  *
     85  * </script><pre>
     86  *
     87  * @example
     88  * // Slider to control length of vectors
     89  * var s = board.create('slider', [[-3, 7], [3, 7], [0, 0.33, 1]], {name: 'length'});
     90  * // Slider to control number of steps
     91  * var stepsize = board.create('slider', [[-3, 6], [3, 6], [1, 20, 100]], {name: 'steps', snapWidth: 1});
     92  *
     93  * // Defining functions
     94  * var fx = (x, y) => 0.2 * y;
     95  * var fy = (x, y) => 0.2 * (Math.cos(x) - 2) * Math.sin(x);
     96  *
     97  * var field = board.create('vectorfield', [
     98  *         [fx, fy],        // Defining function
     99  *         [-6, () => stepsize.Value(), 6], // Horizontal mesh
    100  *         [-5, () => stepsize.Value(), 5], // Vertical mesh
    101  *     ], {
    102  *         highlightStrokeColor: JXG.palette.blue, // Make highlighting invisible
    103  *
    104  *         scale: () => s.Value(), // Scaling of vectors
    105  *
    106  *         arrowHead: {
    107  *             enabled: true,
    108  *             size: 8,  // Pixel length of arrow head
    109  *             angle: Math.PI / 16
    110  *         }
    111  * });
    112  *
    113  * </pre><div id="JXG9196337e-66f0-4d09-8065-11d88c4ff140" class="jxgbox" style="width: 500px; height: 500px;"></div>
    114  * <script type="text/javascript">
    115  *     (function() {
    116  *         var board = JXG.JSXGraph.initBoard('JXG9196337e-66f0-4d09-8065-11d88c4ff140',
    117  *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
    118  *     // Slider to control length of vectors
    119  *     var s = board.create('slider', [[-3, 7], [3, 7], [0, 0.33, 1]], {name: 'length'});
    120  *     // Slider to control number of steps
    121  *     var stepsize = board.create('slider', [[-3, 6], [3, 6], [1, 20, 100]], {name: 'steps', snapWidth: 1});
    122  *
    123  *     // Defining functions
    124  *     var fx = (x, y) => 0.2 * y;
    125  *     var fy = (x, y) => 0.2 * (Math.cos(x) - 2) * Math.sin(x);
    126  *
    127  *     var field = board.create('vectorfield', [
    128  *             [fx, fy],        // Defining function
    129  *             [-6, () => stepsize.Value(), 6], // Horizontal mesh
    130  *             [-5, () => stepsize.Value(), 5], // Vertical mesh
    131  *         ], {
    132  *             highlightStrokeColor: JXG.palette.blue, // Make highlighting invisible
    133  *
    134  *             scale: () => s.Value(), // Scaling of vectors
    135  *
    136  *             arrowHead: {
    137  *                 enabled: true,
    138  *                 size: 8,  // Pixel length of arrow head
    139  *                 angle: Math.PI / 16
    140  *             }
    141  *     });
    142  *
    143  *     })();
    144  *
    145  * </script><pre>
    146  *
    147  */
    148 JXG.createVectorField = function (board, parents, attributes) {
    149     var el, attr;
    150
    151     if (!(parents.length >= 3 &&
    152         (Type.isArray(parents[0]) || Type.isFunction(parents[0]) || Type.isString(parents[0])) &&
    153         (Type.isArray(parents[1]) && parents[1].length === 3) &&
    154         (Type.isArray(parents[2]) && parents[2].length === 3)
    155     )) {
    156         throw new Error(
    157             "JSXGraph: Can't create vector field with parent types " +
    158             "'" + typeof parents[0] + "', " +
    159             "'" + typeof parents[1] + "', " +
    160             "'" + typeof parents[2] + "'."
    161         );
    162     }
    163
    164     attr = Type.copyAttributes(attributes, board.options, 'vectorfield');
    165
    166     /**
    167      * @type {JXG.Curve}
    168      * @ignore
    169      */
    170     el = board.create('curve', [[], []], attr);
    171     el.elType = 'vectorfield';
    172
    173     /**
    174      * Set the defining functions of vector field.
    175      * @memberOf Vectorfield
    176      * @name setF
    177      * @function
    178      * @param {Array|Function} func Either an array containing two functions f1(x, y) and f2(x, y) or function f(x, y) returning an array of length 2.
    179      * @returns {Object} Reference to the vector field object.
    180      *
    181      * @example
    182      * field.setF([(x, y) => Math.sin(y), (x, y) => Math.cos(x)]);
    183      * board.update();
    184      *
    185      */
    186     el.setF = function (func, varnames) {
    187         var f0, f1;
    188         if (Type.isArray(func)) {
    189             f0 = Type.createFunction(func[0], this.board, varnames);
    190             f1 = Type.createFunction(func[1], this.board, varnames);
    191             /**
    192              * @ignore
    193              */
    194             this.F = function (x, y) { return [f0(x, y), f1(x, y)]; };
    195         } else {
    196             this.F = Type.createFunction(func, el.board, varnames);
    197         }
    198         return this;
    199     };
    200
    201     el.setF(parents[0], 'x, y');
    202     el.xData = parents[1];
    203     el.yData = parents[2];
    204
    205     el.updateDataArray = function () {
    206         var x, y, i, j,
    207             scale = Type.evaluate(this.visProp.scale),
    208             start_x = Type.evaluate(this.xData[0]),
    209             steps_x = Type.evaluate(this.xData[1]),
    210             end_x = Type.evaluate(this.xData[2]),
    211             delta_x = (end_x - start_x) / steps_x,
    212
    213             start_y = Type.evaluate(this.yData[0]),
    214             steps_y = Type.evaluate(this.yData[1]),
    215             end_y = Type.evaluate(this.yData[2]),
    216             delta_y = (end_y - start_y) / steps_y,
    217             v, theta, phi1, phi2,
    218
    219             showArrow = Type.evaluate(this.visProp.arrowhead.enabled),
    220             leg, leg_x, leg_y, alpha;
    221
    222
    223         if (showArrow) {
    224             // Arrow head style
    225             leg = Type.evaluate(this.visProp.arrowhead.size);
    226             leg_x = leg / board.unitX;
    227             leg_y = leg / board.unitY;
    228             alpha = Type.evaluate(this.visProp.arrowhead.angle);
    229         }
    230
    231         this.dataX = [];
    232         this.dataY = [];
    233
    234         for (i = 0, x = start_x; i <= steps_x; x += delta_x, i++) {
    235             for (j = 0, y = start_y; j <= steps_y; y += delta_y, j++) {
    236                 v = this.F(x, y);
    237                 v[0] *= scale;
    238                 v[1] *= scale;
    239
    240                 this.dataX = this.dataX.concat([x, x + v[0], NaN]);
    241                 this.dataY = this.dataY.concat([y, y + v[1], NaN]);
    242
    243                 if (showArrow && Math.abs(v[0]) + Math.abs(v[1]) > 0.0) {
    244                     // Arrow head
    245                     theta = Math.atan2(v[1], v[0]);
    246                     phi1 = theta + alpha;
    247                     phi2 = theta - alpha;
    248                     this.dataX = this.dataX.concat([x + v[0] - Math.cos(phi1) * leg_x, x + v[0], x + v[0] - Math.cos(phi2) * leg_x, NaN]);
    249                     this.dataY = this.dataY.concat([y + v[1] - Math.sin(phi1) * leg_y, y + v[1], y + v[1] - Math.sin(phi2) * leg_y, NaN]);
    250                 }
    251             }
    252         }
    253     };
    254
    255     el.methodMap = Type.deepCopy(el.methodMap, {
    256         setF: "setF"
    257     });
    258
    259     return el;
    260 };
    261
    262 JXG.registerElement("vectorfield", JXG.createVectorField);
    263
    264 /**
    265  * @class Slope field.
    266  * <p>
    267  * Plot a slope field given by a function f(x, y) returning a number.
    268  *
    269  * @pseudo
    270  * @name Slopefield
    271  * @augments Vectorfield
    272  * @constructor
    273  * @type JXG.Curve
    274  * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
    275  * Parameter options:
    276  * @param {Function|String} F Function f(x, y) returning a number.
    277  * @param {Array} xData Array of length 3 containing start value for x, number of steps, end value of x. The slope field will contain
    278  * (number of steps) + 1 vectors in direction of x.
    279  * @param {Array} yData Array of length 3 containing start value for y, number of steps, end value of y. The slope field will contain
    280  * (number of steps) + 1 vectors in direction of y.
    281  * @example
    282  * var field = board.create('slopefield', [
    283  *     (x, y) => x * x - x - 2,
    284  *     [-6, 25, 6], // Horizontal mesh
    285  *     [-5, 20, 5]  // Vertical mesh
    286  * ]);
    287  *
    288  * </pre><div id="JXG8a2ee562-eea1-4ce0-91ca-46b71fc7543d" class="jxgbox" style="width: 500px; height: 500px;"></div>
    289  * <script type="text/javascript">
    290  *     (function() {
    291  *         var board = JXG.JSXGraph.initBoard('JXG8a2ee562-eea1-4ce0-91ca-46b71fc7543d',
    292  *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
    293  *     var field = board.create('slopefield', [
    294  *         (x, y) => x * x - x - 2,
    295  *         [-6, 25, 6], [-5, 20, 5]
    296  *     ]);
    297  *
    298  *     })();
    299  *
    300  * </script><pre>
    301  *
    302  * @example
    303  * // Slider to control length of vectors
    304  * var s = board.create('slider', [[-3, 7], [3, 7], [0, 0.33, 1]], {name: 'length'});
    305  * // Slider to control number of steps
    306  * var stepsize = board.create('slider', [[-3, 6], [3, 6], [1, 20, 100]], {name: 'steps', snapWidth: 1});
    307  *
    308  * var field = board.create('slopefield', [
    309  *     (x, y) => x * x - y * y,
    310  *     [-6, () => stepsize.Value(), 6],
    311  *     [-5, () => stepsize.Value(), 5]],
    312  *     {
    313  *         strokeWidth: 1.5,
    314  *         highlightStrokeWidth: 0.5,
    315  *         highlightStrokeColor: JXG.palette.blue,
    316  *
    317  *         scale: () => s.Value(),
    318  *
    319  *         arrowHead: {
    320  *             enabled: false,
    321  *             size: 8,
    322  *             angle: Math.PI / 16
    323  *         }
    324  *     });
    325  *
    326  * </pre><div id="JXG1ec9e4d7-6094-4d2b-b72f-4efddd514f55" class="jxgbox" style="width: 500px; height: 500px;"></div>
    327  * <script type="text/javascript">
    328  *     (function() {
    329  *         var board = JXG.JSXGraph.initBoard('JXG1ec9e4d7-6094-4d2b-b72f-4efddd514f55',
    330  *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
    331  *     // Slider to control length of vectors
    332  *     var s = board.create('slider', [[-3, 7], [3, 7], [0, 0.33, 1]], {name: 'length'});
    333  *     // Slider to control number of steps
    334  *     var stepsize = board.create('slider', [[-3, 6], [3, 6], [1, 20, 100]], {name: 'steps', snapWidth: 1});
    335  *
    336  *     var field = board.create('slopefield', [
    337  *         (x, y) => x * x - y * y,
    338  *         [-6, () => stepsize.Value(), 6],
    339  *         [-5, () => stepsize.Value(), 5]],
    340  *         {
    341  *             strokeWidth: 1.5,
    342  *             highlightStrokeWidth: 0.5,
    343  *             highlightStrokeColor: JXG.palette.blue,
    344  *
    345  *             scale: () => s.Value(),
    346  *
    347  *             arrowHead: {
    348  *                 enabled: false,
    349  *                 size: 8,
    350  *                 angle: Math.PI / 16
    351  *             }
    352  *         });
    353  *
    354  *     })();
    355  *
    356  * </script><pre>
    357  *
    358  */
    359 JXG.createSlopeField = function (board, parents, attributes) {
    360     var el, f, attr;
    361
    362     if (!(parents.length >= 3 &&
    363         (Type.isFunction(parents[0]) || Type.isString(parents[0])) &&
    364         (Type.isArray(parents[1]) && parents[1].length === 3) &&
    365         (Type.isArray(parents[2]) && parents[2].length === 3)
    366     )) {
    367         throw new Error(
    368             "JSXGraph: Can't create slope field with parent types " +
    369             "'" + typeof parents[0] + "', " +
    370             "'" + typeof parents[1] + "', " +
    371             "'" + typeof parents[2] + "'."
    372         );
    373     }
    374
    375     f = Type.createFunction(parents[0], board, 'x, y');
    376     parents[0] = function (x, y) {
    377         var z = f(x, y),
    378             nrm = Math.sqrt(1 + z * z);
    379         return [1 / nrm, z / nrm];
    380     };
    381     attr = Type.copyAttributes(attributes, board.options, 'slopefield');
    382     /**
    383      * @type {JXG.Curve}
    384      * @ignore
    385      */
    386     el = board.create('vectorfield', parents, attr);
    387     el.elType = 'slopefield';
    388
    389     /**
    390      * Set the defining functions of slope field.
    391      * @name Slopefield#setF
    392      * @function
    393      * @param {Function} func Function f(x, y) returning a number.
    394      * @returns {Object} Reference to the slope field object.
    395      *
    396      * @example
    397      * field.setF((x, y) => x * x + y * y);
    398      * board.update();
    399      *
    400      */
    401     el.setF = function (func, varnames) {
    402         var f = Type.createFunction(func, el.board, varnames);
    403
    404         /**
    405          * @ignore
    406          */
    407         this.F = function (x, y) {
    408             var z = f(x, y),
    409                 nrm = Math.sqrt(1 + z * z);
    410             return [1 / nrm, z / nrm];
    411         };
    412     };
    413
    414     el.methodMap = Type.deepCopy(el.methodMap, {
    415         setF: "setF"
    416     });
    417
    418     return el;
    419 };
    420
    421 JXG.registerElement("slopefield", JXG.createSlopeField);
    422