1 /*
  2     Copyright 2008-2023
  3         Matthias Ehmann,
  4         Carsten Miller,
  5         Andreas Walter,
  6         Alfred Wassermann
  7 
  8     This file is part of JSXGraph.
  9 
 10     JSXGraph is free software dual licensed under the GNU LGPL or MIT License.
 11 
 12     You can redistribute it and/or modify it under the terms of the
 13 
 14       * GNU Lesser General Public License as published by
 15         the Free Software Foundation, either version 3 of the License, or
 16         (at your option) any later version
 17       OR
 18       * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT
 19 
 20     JSXGraph is distributed in the hope that it will be useful,
 21     but WITHOUT ANY WARRANTY; without even the implied warranty of
 22     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 23     GNU Lesser General Public License for more details.
 24 
 25     You should have received a copy of the GNU Lesser General Public License and
 26     the MIT License along with JSXGraph. If not, see <https://www.gnu.org/licenses/>
 27     and <https://opensource.org/licenses/MIT/>.
 28  */
 29 /*global JXG:true, define: true*/
 30 
 31 import JXG from "../jxg";
 32 import Const from "../base/constants";
 33 import Type from "../utils/type";
 34 import Mat from "../math/math";
 35 
 36 /**
 37  * Constructor for 3D curves.
 38  * @class Creates a new 3D curve object. Do not use this constructor to create a 3D curve. Use {@link JXG.View3D#create} with type {@link Curve3D} instead.
 39  *
 40  * @augments JXG.GeometryElement3D
 41  * @augments JXG.GeometryElement
 42  * @param {View3D} view
 43  * @param {Function} F
 44  * @param {Function} X
 45  * @param {Function} Y
 46  * @param {Function} Z
 47  * @param {Array} range
 48  * @param {Object} attributes
 49  * @see JXG.Board#generateName
 50  */
 51 JXG.Curve3D = function (view, F, X, Y, Z, range, attributes) {
 52     this.constructor(view.board, attributes, Const.OBJECT_TYPE_CURVE3D, Const.OBJECT_CLASS_3D);
 53     this.constructor3D(view, "curve3d");
 54 
 55     this.board.finalizeAdding(this);
 56 
 57     /**
 58      * @function
 59      * @ignore
 60      */
 61     this.F = F;
 62 
 63     /**
 64      * Function which maps u to x; i.e. it defines the x-coordinate of the curve
 65      * @function
 66      * @returns Number
 67      */
 68     this.X = X;
 69 
 70     /**
 71      * Function which maps u to y; i.e. it defines the y-coordinate of the curve
 72      * @function
 73      * @returns Number
 74      */
 75     this.Y = Y;
 76 
 77     /**
 78      * Function which maps u to z; i.e. it defines the x-coordinate of the curve
 79      * @function
 80      * @returns Number
 81      */
 82     this.Z = Z;
 83 
 84     this.dataX = null;
 85     this.dataY = null;
 86     this.dataZ = null;
 87 
 88     if (this.F !== null) {
 89         this.X = function (u) {
 90             return this.F(u)[0];
 91         };
 92         this.Y = function (u) {
 93             return this.F(u)[1];
 94         };
 95         this.Z = function (u) {
 96             return this.F(u)[2];
 97         };
 98     }
 99 
100     this.range = range;
101 
102     this.methodMap = Type.deepCopy(this.methodMap, {
103         // TODO
104     });
105 };
106 JXG.Curve3D.prototype = new JXG.GeometryElement();
107 Type.copyPrototypeMethods(JXG.Curve3D, JXG.GeometryElement3D, "constructor3D");
108 
109 JXG.extend(
110     JXG.Curve3D.prototype,
111     /** @lends JXG.Curve3D.prototype */ {
112         updateDataArray2D: function () {
113             var steps = Type.evaluate(this.visProp.numberpointshigh),
114                 r, s, e, delta, c2d, u, dataX, dataY,
115                 i,
116                 p = [0, 0, 0];
117 
118             dataX = [];
119             dataY = [];
120             if (Type.exists(this.dataX)) {
121                 steps = this.dataX.length;
122                 for (u = 0; u < steps; u++) {
123                     p = [this.dataX[u], this.dataY[u], this.dataZ[u]];
124                     c2d = this.view.project3DTo2D(p);
125                     dataX.push(c2d[1]);
126                     dataY.push(c2d[2]);
127                 }
128             } else if (Type.isArray(this.X)) {
129                 steps = this.X.length;
130                 for (u = 0; u < steps; u++) {
131                     p = [this.X[u], this.Y[u], this.Z[u]];
132                     c2d = this.view.project3DTo2D(p);
133                     dataX.push(c2d[1]);
134                     dataY.push(c2d[2]);
135                 }
136             } else {
137                 r = Type.evaluate(this.range);
138                 s = Type.evaluate(r[0]);
139                 e = Type.evaluate(r[1]);
140                 delta = (e - s) / (steps - 1);
141                 for (i = 0, u = s; i < steps && u <= e; i++, u += delta) {
142                     if (this.F !== null) {
143                         p = this.F(u);
144                     } else {
145                         p = [this.X(u), this.Y(u), this.Z(u)];
146                     }
147                     c2d = this.view.project3DTo2D(p);
148                     dataX.push(c2d[1]);
149                     dataY.push(c2d[2]);
150                 }
151             }
152             return { X: dataX, Y: dataY };
153         },
154 
155         updateDataArray: function() {
156         },
157 
158         update: function () {
159             // if (this.needsUpdate) {
160                 this.updateDataArray();
161             // }
162             return this;
163         },
164 
165         updateRenderer: function () {
166             this.needsUpdate = false;
167             return this;
168         }
169     }
170 );
171 
172 /**
173  * @class This element creates a 3D parametric curves.
174  * @pseudo
175  * @description A 3D parametric curve is defined by a function
176  *    <i>F: R<sup>1</sup> → R<sup>3</sup></i>.
177  *
178  * @name Curve3D
179  * @augments Curve
180  * @constructor
181  * @type Object
182  * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.
183  * @param {Function_Function_Function_Array,Function} F<sub>X</sub>,F<sub>Y</sub>,F<sub>Z</sub>,range
184  * F<sub>X</sub>(u), F<sub>Y</sub>(u), F<sub>Z</sub>(u) are functions returning a number, range is the array containing
185  * lower and upper bound for the range of the parameter u. range may also be a function returning an array of length two.
186  * @param {Function_Array,Function} F,range Alternatively: F<sub>[X,Y,Z]</sub>(u) a function returning an array [x,y,z] of
187  * numbers, range as above.
188  * @param {Array_Array_Array} X,Y,Z Three arrays containing the coordinate points which define the curve.
189  */
190 JXG.createCurve3D = function (board, parents, attributes) {
191     var view = parents[0],
192         F, X, Y, Z, range, attr, el;
193 
194     if (parents.length === 3) {
195         F = parents[1];
196         range = parents[2];
197         X = null;
198         Y = null;
199         Z = null;
200     } else {
201         X = parents[1];
202         Y = parents[2];
203         Z = parents[3];
204         range = parents[4];
205         F = null;
206     }
207     // TODO Throw error
208 
209     attr = Type.copyAttributes(attributes, board.options, "curve3d");
210     el = new JXG.Curve3D(view, F, X, Y, Z, range, attr);
211 
212     attr = el.setAttr2D(attr);
213     el.element2D = view.create("curve", [[], []], attr);
214     /**
215      * @class
216      * @ignore
217      */
218     el.element2D.updateDataArray = function () {
219         var ret = el.updateDataArray2D();
220         this.dataX = ret.X;
221         this.dataY = ret.Y;
222     };
223     el.addChild(el.element2D);
224     el.inherits.push(el.element2D);
225     el.element2D.setParents(el);
226 
227     el.element2D.prepareUpdate().update();
228     if (!board.isSuspendedUpdate) {
229         el.element2D.updateVisibility().updateRenderer();
230     }
231 
232     return el;
233 };
234 
235 JXG.registerElement("curve3d", JXG.createCurve3D);
236 
237 /**
238  * @class 3D vector field.
239  * <p>
240  * Plot a vector field either given by three functions
241  * f1(x, y, z), f2(x, y, z), and f3(x, y, z) or by a function f(x, y, z)
242  * returning an array of size 3.
243  *
244  * @pseudo
245  * @name Vectorfield3D
246  * @augments JXG.Curve3D
247  * @constructor
248  * @type JXG.Curve3D
249  * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown.
250  * Parameter options:
251  * @param {Array|Function|String} F Either an array containing three functions f1(x, y, z), f2(x, y, z),
252  * and f3(x, y) or function f(x, y, z) returning an array of length 3.
253  * @param {Array} xData Array of length 3 containing start value for x, number of steps,
254  * end value of x. The vector field will contain (number of steps) + 1 vectors in direction of x.
255  * @param {Array} yData Array of length 3 containing start value for y, number of steps,
256  * end value of y. The vector field will contain (number of steps) + 1 vectors in direction of y.
257  * @param {Array} zData Array of length 3 containing start value for z, number of steps,
258  * end value of z. The vector field will contain (number of steps) + 1 vectors in direction of z.
259  */
260 JXG.createVectorfield3D = function (board, parents, attributes) {
261     var view = parents[0],
262         el, attr;
263 
264     if (!(parents.length >= 5 &&
265         (Type.isArray(parents[1]) || Type.isFunction(parents[0]) || Type.isString(parents[0])) &&
266         (Type.isArray(parents[2]) && parents[1].length === 3) &&
267         (Type.isArray(parents[3]) && parents[2].length === 3) &&
268         (Type.isArray(parents[4]) && parents[3].length === 3)
269     )) {
270         throw new Error(
271             "JSXGraph: Can't create vector field 3D with parent types " +
272             "'" + typeof parents[0] + "', " +
273             "'" + typeof parents[1] + "', " +
274             "'" + typeof parents[2] + "'."  +
275             "'" + typeof parents[1] + "', "
276         );
277     }
278 
279     attr = Type.copyAttributes(attributes, board.options, 'vectorfield3d');
280     el = view.create('curve3d', [[], [], []], attr);
281 
282     /**
283      * Set the defining functions of 3D vector field.
284      * @memberOf Vectorfield3D
285      * @name setF
286      * @function
287      * @param {Array|Function} func Either an array containing three functions f1(x, y, z),
288      * f2(x, y, z), and f3(x, y, z) or function f(x, y, z) returning an array of length 3.
289      * @returns {Object} Reference to the 3D vector field object.
290      *
291      * @example
292      * field.setF([(x, y, z) => Math.sin(y), (x, y, z) => Math.cos(x), (x, y, z) => z]);
293      * board.update();
294      *
295      */
296     el.setF = function (func, varnames) {
297         var f0, f1, f2;
298         if (Type.isArray(func)) {
299             f0 = Type.createFunction(func[0], this.board, varnames);
300             f1 = Type.createFunction(func[1], this.board, varnames);
301             f2 = Type.createFunction(func[2], this.board, varnames);
302             /**
303              * @ignore
304              */
305             this.F = function (x, y, z) {
306                 return [f0(x, y, z), f1(x, y, z), f2(x, y, z)];
307             };
308         } else {
309             this.F = Type.createFunction(func, el.board, varnames);
310         }
311         return this;
312     };
313 
314     el.setF(parents[1], 'x, y, z');
315     el.xData = parents[2];
316     el.yData = parents[3];
317     el.zData = parents[4];
318 
319     el.updateDataArray = function () {
320         var k, i, j,
321             v, nrm,
322             x, y, z,
323             scale = Type.evaluate(this.visProp.scale),
324             start = [
325                 Type.evaluate(this.xData[0]),
326                 Type.evaluate(this.yData[0]),
327                 Type.evaluate(this.zData[0])
328             ],
329             steps = [
330                 Type.evaluate(this.xData[1]),
331                 Type.evaluate(this.yData[1]),
332                 Type.evaluate(this.zData[1])
333             ],
334             end = [
335                 Type.evaluate(this.xData[2]),
336                 Type.evaluate(this.yData[2]),
337                 Type.evaluate(this.zData[2])
338             ],
339             delta = [
340                 (end[0] - start[0]) / steps[0],
341                 (end[1] - start[1]) / steps[1],
342                 (end[2] - start[2]) / steps[2]
343             ],
344             phi, theta1, theta2, theta,
345             showArrow = Type.evaluate(this.visProp.arrowhead.enabled),
346             leg, leg_x, leg_y, leg_z, alpha;
347 
348         if (showArrow) {
349             // Arrow head style
350             // leg = 8;
351             // alpha = Math.PI * 0.125;
352             leg = Type.evaluate(this.visProp.arrowhead.size);
353             alpha = Type.evaluate(this.visProp.arrowhead.angle);
354             leg_x = leg / board.unitX;
355             leg_y = leg / board.unitY;
356             leg_z = leg / Math.sqrt(board.unitX * board.unitY);
357         }
358 
359         this.dataX = [];
360         this.dataY = [];
361         this.dataZ = [];
362         for (i = 0, x = start[0]; i <= steps[0]; x += delta[0], i++) {
363             for (j = 0, y = start[1]; j <= steps[1]; y += delta[1], j++) {
364                 for (k = 0, z = start[2]; k <= steps[2]; z += delta[2], k++) {
365                     v = this.F(x, y, z);
366                     nrm = Mat.norm(v);
367                     if (nrm < Number.EPSILON) {
368                         continue;
369                     }
370 
371                     v[0] *= scale;
372                     v[1] *= scale;
373                     v[2] *= scale;
374                     this.dataX = this.dataX.concat([x, x + v[0], NaN]);
375                     this.dataY = this.dataY.concat([y, y + v[1], NaN]);
376                     this.dataZ = this.dataZ.concat([z, z + v[2], NaN]);
377 
378                     if (showArrow) {
379                         // Arrow head
380                         nrm *= scale;
381                         phi = Math.atan2(v[1], v[0]);
382                         theta = Math.asin(v[2] / nrm);
383                         theta1 = theta - alpha;
384                         theta2 = theta + alpha;
385                         this.dataX = this.dataX.concat([
386                             x + v[0] - leg_x * Math.cos(phi) * Math.cos(theta1),
387                             x + v[0],
388                             x + v[0] - leg_x * Math.cos(phi) * Math.cos(theta2),
389                             NaN]);
390                         this.dataY = this.dataY.concat([
391                             y + v[1] - leg_y * Math.sin(phi) * Math.cos(theta1),
392                             y + v[1],
393                             y + v[1] - leg_y * Math.sin(phi) * Math.cos(theta2),
394                             NaN]);
395                         this.dataZ = this.dataZ.concat([
396                             z + v[2] - leg_z * Math.sin(theta2),
397                             z + v[2],
398                             z + v[2] - leg_z * Math.sin(theta1),
399                             NaN]);
400                     }
401                 }
402             }
403         }
404     };
405 
406     el.methodMap = Type.deepCopy(el.methodMap, {
407         setF: "setF"
408     });
409 
410     return el;
411 };
412 
413 JXG.registerElement("vectorfield3D", JXG.createVectorfield3D);
414