1 /*
  2     Copyright 2008-2024
  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 <https://www.gnu.org/licenses/>
 29     and <https://opensource.org/licenses/MIT/>.
 30  */
 31 
 32 /*global JXG: true, define: true*/
 33 /*jslint nomen: true, plusplus: true*/
 34 
 35 /**
 36  * @fileoverview In this file the geometry object Ticks is defined. Ticks provides
 37  * methods for creation and management of ticks on an axis.
 38  * @author graphjs
 39  * @version 0.1
 40  */
 41 
 42 import JXG from "../jxg.js";
 43 import Mat from "../math/math.js";
 44 import Geometry from "../math/geometry.js";
 45 import Numerics from "../math/numerics.js";
 46 import Const from "./constants.js";
 47 import GeometryElement from "./element.js";
 48 import Coords from "./coords.js";
 49 import Type from "../utils/type.js";
 50 
 51 /**
 52  * Creates ticks for an axis.
 53  * @class Ticks provides methods for creation and management
 54  * of ticks on an axis.
 55  * @param {JXG.Line} line Reference to the axis the ticks are drawn on.
 56  * @param {Number|Array} ticks Number defining the distance between two major ticks or an array defining static ticks.
 57  * @param {Object} attributes Properties
 58  * @see JXG.Line#addTicks
 59  * @constructor
 60  * @augments JXG.GeometryElement
 61  */
 62 JXG.Ticks = function (line, ticks, attributes) {
 63     this.constructor(line.board, attributes, Const.OBJECT_TYPE_TICKS, Const.OBJECT_CLASS_OTHER);
 64 
 65     /**
 66      * The line the ticks belong to.
 67      * @type JXG.Line
 68      * @private
 69      */
 70     this.line = line;
 71 
 72     /**
 73      * The board the ticks line is drawn on.
 74      * @type JXG.Board
 75      * @private
 76      */
 77     this.board = this.line.board;
 78 
 79     // /**
 80     //  * A function calculating ticks delta depending on the ticks number.
 81     //  * @type Function
 82     //  */
 83     // // this.ticksFunction = null;
 84 
 85     /**
 86      * Array of fixed ticks.
 87      * @type Array
 88      * @private
 89      */
 90     this.fixedTicks = null;
 91 
 92     /**
 93      * Flag if the ticks are equidistant. If true, their distance is defined by ticksFunction.
 94      * @type Boolean
 95      * @private
 96      */
 97     this.equidistant = false;
 98 
 99     /**
100      * A list of labels which have to be displayed in updateRenderer.
101      * @type Array
102      * @private
103      */
104     this.labelsData = [];
105 
106     if (Type.isFunction(ticks)) {
107         this.ticksFunction = ticks;
108         throw new Error("Function arguments are no longer supported.");
109     }
110 
111     if (Type.isArray(ticks)) {
112         this.fixedTicks = ticks;
113     } else {
114         // Obsolete:
115         // if (Math.abs(ticks) < Mat.eps || ticks < 0) {
116         //     ticks = attributes.defaultdistance;
117         // }
118         this.equidistant = true;
119     }
120 
121     // /**
122     //  * Least distance between two ticks, measured in pixels.
123     //  * @type int
124     //  */
125     // // this.minTicksDistance = attributes.minticksdistance;
126 
127     /**
128      * Stores the ticks coordinates
129      * @type Array
130      * @private
131      */
132     this.ticks = [];
133 
134     // /**
135     //  * Distance between two major ticks in user coordinates
136     //  * @type Number
137     //  */
138     // this.ticksDelta = 1;
139 
140     /**
141      * Array where the labels are saved. There is an array element for every tick,
142      * even for minor ticks which don't have labels. In this case the array element
143      * contains just <tt>null</tt>.
144      * @type Array
145      * @private
146      */
147     this.labels = [];
148 
149     /**
150      * Used to ensure the uniqueness of label ids this counter is used.
151      * @type number
152      * @private
153      */
154     this.labelCounter = 0;
155 
156     this.id = this.line.addTicks(this);
157     this.elType = "ticks";
158     this.inherits.push(this.labels);
159     this.board.setId(this, "Ti");
160 };
161 
162 JXG.Ticks.prototype = new GeometryElement();
163 
164 JXG.extend(
165     JXG.Ticks.prototype,
166     /** @lends JXG.Ticks.prototype */ {
167         // /**
168         //  * Ticks function:
169         //  * determines the distance (in user units) of two major ticks.
170         //  * See above in constructor and in @see JXG.GeometryElement#setAttribute
171         //  *
172         //  * @private
173         //  * @param {Number} ticks Distance between two major ticks
174         //  * @returns {Function} returns method ticksFunction
175         //  */
176         // // makeTicksFunction: function (ticks) {
177         //     // return function () {
178         //         ticksFunction: function () {
179         //                     var delta, b, dist,
180         //                     number_major_tick_intervals = 5;
181 
182         //                 if (this.evalVisProp('insertticks')) {
183         //                     b = this.getLowerAndUpperBounds(this.getZeroCoordinates(), 'ticksdistance');
184         //                     dist = b.upper - b.lower;
185 
186         //                     // delta: Proposed distance in user units between two major ticks
187         //                     delta = Math.pow(10, Math.floor(Math.log(dist / number_major_tick_intervals) / Math.LN10));
188         // console.log("delta", delta,  b.upper, b.lower, dist, dist / number_major_tick_intervals * 1.1)
189         //                     if (5 * delta < dist / number_major_tick_intervals * 1.1) {
190         //                         return 5 * delta;
191         //                     }
192         //                     if (2 * delta < dist / number_major_tick_intervals * 1.1) {
193         //                         return 2 * delta;
194         //                     }
195 
196         //                     // < v1.6.0:
197         //                     // delta = Math.pow(10, Math.floor(Math.log(0.6 * dist) / Math.LN10));
198         //                     if (false && dist <= 6 * delta) {
199         //                         delta *= 0.5;
200         //                     }
201         //                     return delta;
202         //                 }
203 
204         //                 // In case of insertTicks==false
205         //                 return this.evalVisProp('ticksdistance');
206         //                 // return ticks;
207         //             // };
208         //         },
209 
210         /**
211          * Checks whether (x,y) is near the line.
212          * Only available for line elements,  not for ticks on curves.
213          * @param {Number} x Coordinate in x direction, screen coordinates.
214          * @param {Number} y Coordinate in y direction, screen coordinates.
215          * @returns {Boolean} True if (x,y) is near the line, False otherwise.
216          */
217         hasPoint: function (x, y) {
218             var i, t, r, type,
219                 len = (this.ticks && this.ticks.length) || 0;
220 
221             if (Type.isObject(this.evalVisProp('precision'))) {
222                 type = this.board._inputDevice;
223                 r = this.evalVisProp('precision.' + type);
224             } else {
225                 // 'inherit'
226                 r = this.board.options.precision.hasPoint;
227             }
228             r += this.evalVisProp('strokewidth') * 0.5;
229             if (
230                 !this.line.evalVisProp('scalable') ||
231                 this.line.elementClass === Const.OBJECT_CLASS_CURVE
232             ) {
233                 return false;
234             }
235 
236             // Ignore non-axes and axes that are not horizontal or vertical
237             if (
238                 this.line.stdform[1] !== 0 &&
239                 this.line.stdform[2] !== 0 &&
240                 this.line.type !== Const.OBJECT_TYPE_AXIS
241             ) {
242                 return false;
243             }
244 
245             for (i = 0; i < len; i++) {
246                 t = this.ticks[i];
247 
248                 // Skip minor ticks
249                 if (t[2]) {
250                     // Ignore ticks at zero
251                     if (
252                         !(
253                             (this.line.stdform[1] === 0 &&
254                                 Math.abs(t[0][0] - this.line.point1.coords.scrCoords[1]) <
255                                 Mat.eps) ||
256                             (this.line.stdform[2] === 0 &&
257                                 Math.abs(t[1][0] - this.line.point1.coords.scrCoords[2]) <
258                                 Mat.eps)
259                         )
260                     ) {
261                         // tick length is not zero, ie. at least one pixel
262                         if (
263                             Math.abs(t[0][0] - t[0][1]) >= 1 ||
264                             Math.abs(t[1][0] - t[1][1]) >= 1
265                         ) {
266                             if (this.line.stdform[1] === 0) {
267                                 // Allow dragging near axes only.
268                                 if (
269                                     Math.abs(y - this.line.point1.coords.scrCoords[2]) < 2 * r &&
270                                     t[0][0] - r < x && x < t[0][1] + r
271                                 ) {
272                                     return true;
273                                 }
274                             } else if (this.line.stdform[2] === 0) {
275                                 if (
276                                     Math.abs(x - this.line.point1.coords.scrCoords[1]) < 2 * r &&
277                                     t[1][0] - r < y && y < t[1][1] + r
278                                 ) {
279                                     return true;
280                                 }
281                             }
282                         }
283                     }
284                 }
285             }
286 
287             return false;
288         },
289 
290         /**
291          * Sets x and y coordinate of the tick.
292          * @param {number} method The type of coordinates used here. Possible values are {@link JXG.COORDS_BY_USER} and {@link JXG.COORDS_BY_SCREEN}.
293          * @param {Array} coords coordinates in screen/user units
294          * @param {Array} oldcoords previous coordinates in screen/user units
295          * @returns {JXG.Ticks} this element
296          */
297         setPositionDirectly: function (method, coords, oldcoords) {
298             var dx, dy,
299                 c = new Coords(method, coords, this.board),
300                 oldc = new Coords(method, oldcoords, this.board),
301                 bb = this.board.getBoundingBox();
302 
303             if (
304                 this.line.type !== Const.OBJECT_TYPE_AXIS ||
305                 !this.line.evalVisProp('scalable')
306             ) {
307                 return this;
308             }
309 
310             if (
311                 Math.abs(this.line.stdform[1]) < Mat.eps &&
312                 Math.abs(c.usrCoords[1] * oldc.usrCoords[1]) > Mat.eps
313             ) {
314                 // Horizontal line
315                 dx = oldc.usrCoords[1] / c.usrCoords[1];
316                 bb[0] *= dx;
317                 bb[2] *= dx;
318                 this.board.setBoundingBox(bb, this.board.keepaspectratio, "update");
319             } else if (
320                 Math.abs(this.line.stdform[2]) < Mat.eps &&
321                 Math.abs(c.usrCoords[2] * oldc.usrCoords[2]) > Mat.eps
322             ) {
323                 // Vertical line
324                 dy = oldc.usrCoords[2] / c.usrCoords[2];
325                 bb[3] *= dy;
326                 bb[1] *= dy;
327                 this.board.setBoundingBox(bb, this.board.keepaspectratio, "update");
328             }
329 
330             return this;
331         },
332 
333         /**
334          * (Re-)calculates the ticks coordinates.
335          * @private
336          */
337         calculateTicksCoordinates: function () {
338             var coordsZero, b, r_max, bb;
339 
340             if (this.line.elementClass === Const.OBJECT_CLASS_LINE) {
341                 // Calculate Ticks width and height in Screen and User Coordinates
342                 this.setTicksSizeVariables();
343 
344                 // If the parent line is not finite, we can stop here.
345                 if (Math.abs(this.dx) < Mat.eps && Math.abs(this.dy) < Mat.eps) {
346                     return;
347                 }
348             }
349 
350             // Get Zero (coords element for lines, number for curves)
351             coordsZero = this.getZeroCoordinates();
352 
353             // Calculate lower bound and upper bound limits based on distance
354             // between p1 and center and p2 and center
355             if (this.line.elementClass === Const.OBJECT_CLASS_LINE) {
356                 b = this.getLowerAndUpperBounds(coordsZero, 'ticksdistance');
357             } else {
358                 b = {
359                     lower: this.line.minX(),
360                     upper: this.line.maxX(),
361                     a1: 0,
362                     a2: 0,
363                     m1: 0,
364                     m2: 0
365                 };
366             }
367 
368             if (this.evalVisProp('type') === "polar") {
369                 bb = this.board.getBoundingBox();
370                 r_max = Math.max(
371                     Mat.hypot(bb[0], bb[1]),
372                     Mat.hypot(bb[2], bb[3])
373                 );
374                 b.upper = r_max;
375             }
376 
377             // Clean up
378             this.ticks = [];
379             this.labelsData = [];
380             // Create Ticks Coordinates and Labels
381             if (this.equidistant) {
382                 this.generateEquidistantTicks(coordsZero, b);
383             } else {
384                 this.generateFixedTicks(coordsZero, b);
385             }
386 
387             return this;
388         },
389 
390         /**
391          * Sets the variables used to set the height and slope of each tick.
392          *
393          * @private
394          */
395         setTicksSizeVariables: function (pos) {
396             var d,
397                 mi,
398                 ma,
399                 len,
400                 distMaj = this.evalVisProp('majorheight') * 0.5,
401                 distMin = this.evalVisProp('minorheight') * 0.5;
402 
403             // For curves:
404             if (Type.exists(pos)) {
405                 mi = this.line.minX();
406                 ma = this.line.maxX();
407                 len = this.line.points.length;
408                 if (len < 2) {
409                     this.dxMaj = 0;
410                     this.dyMaj = 0;
411                 } else if (Mat.relDif(pos, mi) < Mat.eps) {
412                     this.dxMaj =
413                         this.line.points[0].usrCoords[2] - this.line.points[1].usrCoords[2];
414                     this.dyMaj =
415                         this.line.points[1].usrCoords[1] - this.line.points[0].usrCoords[1];
416                 } else if (Mat.relDif(pos, ma) < Mat.eps) {
417                     this.dxMaj =
418                         this.line.points[len - 2].usrCoords[2] -
419                         this.line.points[len - 1].usrCoords[2];
420                     this.dyMaj =
421                         this.line.points[len - 1].usrCoords[1] -
422                         this.line.points[len - 2].usrCoords[1];
423                 } else {
424                     this.dxMaj = -Numerics.D(this.line.Y)(pos);
425                     this.dyMaj = Numerics.D(this.line.X)(pos);
426                 }
427             } else {
428                 // ticks width and height in screen units
429                 this.dxMaj = this.line.stdform[1];
430                 this.dyMaj = this.line.stdform[2];
431             }
432             this.dxMin = this.dxMaj;
433             this.dyMin = this.dyMaj;
434 
435             // ticks width and height in user units
436             this.dx = this.dxMaj;
437             this.dy = this.dyMaj;
438 
439             // After this, the length of the vector (dxMaj, dyMaj) in screen coordinates is equal to distMaj pixel.
440             d = Mat.hypot(this.dxMaj * this.board.unitX, this.dyMaj * this.board.unitY);
441             this.dxMaj *= (distMaj / d) * this.board.unitX;
442             this.dyMaj *= (distMaj / d) * this.board.unitY;
443             this.dxMin *= (distMin / d) * this.board.unitX;
444             this.dyMin *= (distMin / d) * this.board.unitY;
445 
446             // Grid-like ticks?
447             this.minStyle = this.evalVisProp('minorheight') < 0 ? "infinite" : "finite";
448             this.majStyle = this.evalVisProp('majorheight') < 0 ? "infinite" : "finite";
449         },
450 
451         /**
452          * Returns the coordinates of the point zero of the line.
453          *
454          * If the line is an {@link Axis}, the coordinates of the projection of the board's zero point is returned
455          *
456          * Otherwise, the coordinates of the point that acts as zero are
457          * established depending on the value of {@link JXG.Ticks#anchor}
458          *
459          * @returns {JXG.Coords} Coords object for the zero point on the line
460          * @private
461          */
462         getZeroCoordinates: function () {
463             var c1x, c1y, c1z, c2x, c2y, c2z,
464                 t, mi, ma,
465                 ev_a = this.evalVisProp('anchor');
466 
467             if (this.line.elementClass === Const.OBJECT_CLASS_LINE) {
468                 if (this.line.type === Const.OBJECT_TYPE_AXIS) {
469                     return Geometry.projectPointToLine(
470                         {
471                             coords: {
472                                 usrCoords: [1, 0, 0]
473                             }
474                         },
475                         this.line,
476                         this.board
477                     );
478                 }
479                 c1z = this.line.point1.coords.usrCoords[0];
480                 c1x = this.line.point1.coords.usrCoords[1];
481                 c1y = this.line.point1.coords.usrCoords[2];
482                 c2z = this.line.point2.coords.usrCoords[0];
483                 c2x = this.line.point2.coords.usrCoords[1];
484                 c2y = this.line.point2.coords.usrCoords[2];
485 
486                 if (ev_a === "right") {
487                     return this.line.point2.coords;
488                 }
489                 if (ev_a === "middle") {
490                     return new Coords(
491                         Const.COORDS_BY_USER,
492                         [(c1z + c2z) * 0.5, (c1x + c2x) * 0.5, (c1y + c2y) * 0.5],
493                         this.board
494                     );
495                 }
496                 if (Type.isNumber(ev_a)) {
497                     return new Coords(
498                         Const.COORDS_BY_USER,
499                         [
500                             c1z + (c2z - c1z) * ev_a,
501                             c1x + (c2x - c1x) * ev_a,
502                             c1y + (c2y - c1y) * ev_a
503                         ],
504                         this.board
505                     );
506                 }
507                 return this.line.point1.coords;
508             }
509             mi = this.line.minX();
510             ma = this.line.maxX();
511             if (ev_a === "right") {
512                 t = ma;
513             } else if (ev_a === "middle") {
514                 t = (mi + ma) * 0.5;
515             } else if (Type.isNumber(ev_a)) {
516                 t = mi * (1 - ev_a) + ma * ev_a;
517                 // t = ev_a;
518             } else {
519                 t = mi;
520             }
521             return t;
522         },
523 
524         /**
525          * Calculate the lower and upper bounds for tick rendering.
526          * If {@link JXG.Ticks#includeBoundaries} is false, the boundaries will exclude point1 and point2.
527          *
528          * @param  {JXG.Coords} coordsZero
529          * @returns {String} [type] If type=='ticksdistance', the bounds are
530          *                         the intersection of the line with the bounding box of the board, respecting
531          *                         the value of the line attribute 'margin' and the width of arrow heads.
532          *                         Otherwise, it is the projection of the corners of the bounding box
533          *                         to the line - without the attribute 'margin' and width of arrow heads.
534          *  <br>
535          *                         The first case is needed to determine which ticks are displayed, i.e. where to stop.
536          *                         The second case is to determine the distance between ticks in case of 'insertTicks:true'.
537          * @returns {Object}     {lower: Number, upper: Number } containing the lower and upper bounds in user units.
538          *
539          * @private
540          */
541         getLowerAndUpperBounds: function (coordsZero, type) {
542             var lowerBound, upperBound,
543                 fA, lA,
544                 point1, point2,
545                 isPoint1inBoard, isPoint2inBoard,
546                 // We use the distance from zero to P1 and P2 to establish lower and higher points
547                 dZeroPoint1, dZeroPoint2,
548                 arrowData,
549                 // angle,
550                 a1, a2, m1, m2,
551                 eps = Mat.eps * 10,
552                 ev_sf = this.line.evalVisProp('straightfirst'),
553                 ev_sl = this.line.evalVisProp('straightlast'),
554                 ev_i = this.evalVisProp('includeboundaries');
555 
556             // The line's defining points that will be adjusted to be within the board limits
557             if (this.line.elementClass === Const.OBJECT_CLASS_CURVE) {
558                 return {
559                     lower: this.line.minX(),
560                     upper: this.line.maxX()
561                 };
562             }
563 
564             point1 = new Coords(Const.COORDS_BY_USER, this.line.point1.coords.usrCoords, this.board);
565             point2 = new Coords(Const.COORDS_BY_USER, this.line.point2.coords.usrCoords, this.board);
566 
567             // Are the original defining points within the board?
568             isPoint1inBoard =
569                 Math.abs(point1.usrCoords[0]) >= Mat.eps &&
570                 point1.scrCoords[1] >= 0.0 &&
571                 point1.scrCoords[1] <= this.board.canvasWidth &&
572                 point1.scrCoords[2] >= 0.0 &&
573                 point1.scrCoords[2] <= this.board.canvasHeight;
574             isPoint2inBoard =
575                 Math.abs(point2.usrCoords[0]) >= Mat.eps &&
576                 point2.scrCoords[1] >= 0.0 &&
577                 point2.scrCoords[1] <= this.board.canvasWidth &&
578                 point2.scrCoords[2] >= 0.0 &&
579                 point2.scrCoords[2] <= this.board.canvasHeight;
580 
581             // Adjust line limit points to be within the board
582             if (Type.exists(type) && type === 'ticksdistance') {
583                 // The good old calcStraight is needed for determining the distance between major ticks.
584                 // Here, only the visual area is of importance
585                 Geometry.calcStraight(this.line, point1, point2, 0);
586                 m1 = this.getDistanceFromZero(coordsZero, point1);
587                 m2 = this.getDistanceFromZero(coordsZero, point2);
588                 Geometry.calcStraight(this.line, point1, point2, this.line.evalVisProp('margin'));
589                 m1 = this.getDistanceFromZero(coordsZero, point1) - m1;
590                 m2 = this.getDistanceFromZero(coordsZero, point2).m2;
591             } else {
592                 // This function projects the corners of the board to the line.
593                 // This is important for diagonal lines with infinite tick lines.
594                 Geometry.calcLineDelimitingPoints(this.line, point1, point2);
595             }
596 
597             // Shorten ticks bounds such that ticks are not through arrow heads
598             fA = this.line.evalVisProp('firstarrow');
599             lA = this.line.evalVisProp('lastarrow');
600 
601             a1 = this.getDistanceFromZero(coordsZero, point1);
602             a2 = this.getDistanceFromZero(coordsZero, point2);
603             if (fA || lA) {
604                 // Do not display ticks at through arrow heads.
605                 // In arrowData we ignore the highlighting status.
606                 // Ticks would appear to be too nervous.
607                 arrowData = this.board.renderer.getArrowHeadData(
608                     this.line,
609                     this.line.evalVisProp('strokewidth'),
610                     ''
611                 );
612 
613                 this.board.renderer.getPositionArrowHead(
614                     this.line,
615                     point1,
616                     point2,
617                     arrowData
618                 );
619             }
620             // Calculate (signed) distance from Zero to P1 and to P2
621             dZeroPoint1 = this.getDistanceFromZero(coordsZero, point1);
622             dZeroPoint2 = this.getDistanceFromZero(coordsZero, point2);
623 
624             // Recompute lengths of arrow heads
625             a1 = dZeroPoint1 - a1;
626             a2 = dZeroPoint1 - a2;
627 
628             // We have to establish if the direction is P1->P2 or P2->P1 to set the lower and upper
629             // bounds appropriately. As the distances contain also a sign to indicate direction,
630             // we can compare dZeroPoint1 and dZeroPoint2 to establish the line direction
631             if (dZeroPoint1 < dZeroPoint2) {
632                 // Line goes P1->P2
633                 lowerBound = dZeroPoint1;
634                 upperBound = dZeroPoint2;
635 
636                 if (!ev_sf && isPoint1inBoard && !ev_i) {
637                     lowerBound += eps;
638                 }
639                 if (!ev_sl && isPoint2inBoard && !ev_i) {
640                     upperBound -= eps;
641                 }
642             } else if (dZeroPoint2 < dZeroPoint1) {
643                 // Line goes P2->P1
644                 // Does this happen at all?
645                 lowerBound = dZeroPoint2;
646                 upperBound = dZeroPoint1;
647 
648                 if (!ev_sl && isPoint2inBoard && !ev_i) {
649                     lowerBound += eps;
650                 }
651                 if (!ev_sf && isPoint1inBoard && !ev_i) {
652                     upperBound -= eps;
653                 }
654             } else {
655                 // P1 = P2 = Zero, we can't do a thing
656                 lowerBound = 0;
657                 upperBound = 0;
658             }
659 
660             return {
661                 lower: lowerBound,
662                 upper: upperBound,
663                 a1: a1,
664                 a2: a2,
665                 m1: m1,
666                 m2: m2
667             };
668         },
669 
670         /**
671          * Calculates the signed distance in user coordinates from zero to a given point.
672          * Sign is positive, if the direction from zero to point is the same as the direction
673          * zero to point2 of the line.
674          *
675          * @param  {JXG.Coords} zero  coordinates of the point considered zero
676          * @param  {JXG.Coords} point coordinates of the point to find out the distance
677          * @returns {Number}           distance between zero and point, including its sign
678          * @private
679          */
680         getDistanceFromZero: function (zero, point) {
681             var p1, p2, dirLine, dirPoint, distance;
682 
683             p1 = this.line.point1.coords;
684             p2 = this.line.point2.coords;
685             distance = zero.distance(Const.COORDS_BY_USER, point);
686 
687             // Establish sign
688             dirLine = [
689                 p2.usrCoords[0] - p1.usrCoords[0],
690                 p2.usrCoords[1] - p1.usrCoords[1],
691                 p2.usrCoords[2] - p1.usrCoords[2]
692             ];
693             dirPoint = [
694                 point.usrCoords[0] - zero.usrCoords[0],
695                 point.usrCoords[1] - zero.usrCoords[1],
696                 point.usrCoords[2] - zero.usrCoords[2]
697             ];
698             if (Mat.innerProduct(dirLine, dirPoint, 3) < 0) {
699                 distance *= -1;
700             }
701 
702             return distance;
703         },
704 
705         /**
706          * Creates ticks coordinates and labels automatically.
707          * The frequency of ticks is affected by the values of {@link JXG.Ticks#insertTicks}, {@link JXG.Ticks#minTicksDistance},
708          * and {@link JXG.Ticks#ticksDistance}
709          *
710          * @param  {JXG.Coords} coordsZero coordinates of the point considered zero
711          * @param  {Object}     bounds     contains the lower and upper bounds for ticks placement
712          * @private
713          */
714         generateEquidistantTicks: function (coordsZero, bounds) {
715             var tickPosition,
716                 eps = Mat.eps,
717                 deltas, ticksDelta,
718                 // ev_mia = this.evalVisProp('minorticksinarrow'),
719                 // ev_maa = this.evalVisProp('minorticksinarrow'),
720                 // ev_mla = this.evalVisProp('minorticksinarrow'),
721                 ev_mt = this.evalVisProp('minorticks');
722 
723             // Determine a proposed distance between major ticks in user units
724             ticksDelta = this.getDistanceMajorTicks();
725 
726             // Obsolete, since this.equidistant is always true at this point
727             // ticksDelta = this.equidistant ? this.ticksFunction(1) : this.ticksDelta;
728 
729             if (this.line.elementClass === Const.OBJECT_CLASS_LINE) {
730                 // Calculate x and y distances between two points on the line which are 1 unit apart
731                 // In essence, these are cosine and sine.
732                 deltas = this.getXandYdeltas();
733             }
734 
735             ticksDelta *= this.evalVisProp('scale');
736 
737             // In case of insertTicks, adjust ticks distance to satisfy the minTicksDistance restriction.
738             // if (ev_it) { // } && this.minTicksDistance > Mat.eps) {
739             //     ticksDelta = this.adjustTickDistance(ticksDelta, coordsZero, deltas);
740             // }
741 
742             // Convert ticksdelta to the distance between two minor ticks
743             ticksDelta /= (ev_mt + 1);
744             this.ticksDelta = ticksDelta;
745 
746             if (ticksDelta < Mat.eps) {
747                 return;
748             }
749 
750             // Position ticks from zero to the positive side while not reaching the upper boundary
751             tickPosition = 0;
752             if (!this.evalVisProp('drawzero')) {
753                 tickPosition = ticksDelta;
754             }
755             while (tickPosition <= bounds.upper + eps) {
756                 // Only draw ticks when we are within bounds, ignore case where tickPosition < lower < upper
757                 if (tickPosition >= bounds.lower - eps) {
758                     this.processTickPosition(coordsZero, tickPosition, ticksDelta, deltas);
759                 }
760                 tickPosition += ticksDelta;
761 
762                 // Emergency out
763                 if (bounds.upper - tickPosition > ticksDelta * 10000) {
764                     break;
765                 }
766             }
767 
768             // Position ticks from zero (not inclusive) to the negative side while not reaching the lower boundary
769             tickPosition = -ticksDelta;
770             while (tickPosition >= bounds.lower - eps) {
771                 // Only draw ticks when we are within bounds, ignore case where lower < upper < tickPosition
772                 if (tickPosition <= bounds.upper + eps) {
773                     this.processTickPosition(coordsZero, tickPosition, ticksDelta, deltas);
774                 }
775                 tickPosition -= ticksDelta;
776 
777                 // Emergency out
778                 if (tickPosition - bounds.lower > ticksDelta * 10000) {
779                     break;
780                 }
781             }
782         },
783 
784         /**
785          * Calculates the distance between two major ticks in user units.
786          * <ul>
787          * <li> If the attribute "insertTicks" is false, the value of the attribute
788          * "ticksDistance" is returned. The attribute "minTicksDistance" is ignored in this case.
789          * <li> If the attribute "insertTicks" is true, the attribute "ticksDistance" is ignored.
790          * The distance between two major ticks is computed
791          * as <i>a 10<sup>i</sup></i>, where <i>a</i> is one of <i>{1, 2, 5}</i> and
792          * the number <i>a 10<sup>i</sup></i> is maximized such that there are approximately
793          * 6 major ticks and there are at least "minTicksDistance" pixel between minor ticks.
794          * The latter restriction has priority over the number of major ticks.
795          * </ul>
796          * @returns Number
797          * @private
798          */
799         getDistanceMajorTicks: function () {
800             var delta, delta2,
801                 b, d, dist,
802                 scale,
803                 numberMajorTicks = 5,
804                 maxDist, minDist, ev_minti;
805 
806             if (this.evalVisProp('insertticks')) {
807                 // Case of insertTicks==true:
808                 // Here, we ignore the attribute 'margin'
809                 b = this.getLowerAndUpperBounds(this.getZeroCoordinates(), '');
810 
811                 dist = (b.upper - b.lower);
812                 scale = this.evalVisProp('scale');
813 
814                 maxDist = dist / (numberMajorTicks + 1) / scale;
815                 minDist = this.evalVisProp('minticksdistance') / scale;
816                 ev_minti = this.evalVisProp('minorticks');
817 
818                 d = this.getXandYdeltas();
819                 d.x *= this.board.unitX;
820                 d.y *= this.board.unitY;
821                 minDist /= Mat.hypot(d.x, d.y);
822                 minDist *= (ev_minti + 1);
823 
824                 // Determine minimal delta to fulfill the minTicksDistance constraint
825                 delta = Math.pow(10, Math.floor(Math.log(minDist) / Math.LN10));
826                 if (2 * delta >= minDist) {
827                     delta *= 2;
828                 } else if (5 * delta >= minDist) {
829                     delta *= 5;
830                 }
831 
832                 // Determine maximal delta to fulfill the constraint to have approx. "numberMajorTicks" majorTicks
833                 delta2 = Math.pow(10, Math.floor(Math.log(maxDist) / Math.LN10));
834                 if (5 * delta2 < maxDist) {
835                     delta2 *= 5;
836                 } else if (2 * delta2 < maxDist) {
837                     delta2 *= 2;
838                 }
839                 // Take the larger value of the two delta's, that is
840                 // minTicksDistance has priority over numberMajorTicks
841                 delta = Math.max(delta, delta2);
842 
843                 // < v1.6.0:
844                 // delta = Math.pow(10, Math.floor(Math.log(0.6 * dist) / Math.LN10));
845                 // if (false && dist <= 6 * delta) {
846                 //     delta *= 0.5;
847                 // }
848                 return delta;
849             }
850 
851             // Case of insertTicks==false
852             return this.evalVisProp('ticksdistance');
853         },
854 
855         //         /**
856         //          * Auxiliary method used by {@link JXG.Ticks#generateEquidistantTicks} to adjust the
857         //          * distance between two ticks depending on {@link JXG.Ticks#minTicksDistance} value
858         //          *
859         //          * @param  {Number}     ticksDelta  distance between two major ticks in user coordinates
860         //          * @param  {JXG.Coords} coordsZero  coordinates of the point considered zero
861         //          * @param  {Object}     deltas      x and y distance in pixel between two user units
862         //          * @param  {Object}     bounds      upper and lower bound of the tick positions in user units.
863         //          * @private
864         //          */
865         //         adjustTickDistance: function (ticksDelta, coordsZero, deltas) {
866         //             var nx,
867         //                 ny,
868         //                 // bounds,
869         //                 distScr,
870         //                 sgn = 1,
871         //                 ev_mintd = this.evalVisProp('minticksdistance'),
872         //                 ev_minti = this.evalVisProp('minorticks');
873 
874         //             if (this.line.elementClass === Const.OBJECT_CLASS_CURVE) {
875         //                 return ticksDelta;
876         //             }
877         //             // Seems to be ignored:
878         //             // bounds = this.getLowerAndUpperBounds(coordsZero, "ticksdistance");
879 
880         //             // distScr is the distance between two major Ticks in pixel
881         //             nx = coordsZero.usrCoords[1] + deltas.x * ticksDelta;
882         //             ny = coordsZero.usrCoords[2] + deltas.y * ticksDelta;
883         //             distScr = coordsZero.distance(
884         //                 Const.COORDS_BY_SCREEN,
885         //                 new Coords(Const.COORDS_BY_USER, [nx, ny], this.board)
886         //             );
887         // // console.log(deltas, distScr, this.board.unitX, this.board.unitY, "ticksDelta:", ticksDelta);
888 
889         //             if (ticksDelta === 0.0) {
890         //                 return 0.0;
891         //             }
892 
893         // // console.log(":", distScr, ev_minti + 1, distScr / (ev_minti + 1), ev_mintd)
894         //             while (false && distScr / (ev_minti + 1) < ev_mintd) {
895         //                 if (sgn === 1) {
896         //                     ticksDelta *= 2;
897         //                 } else {
898         //                     ticksDelta *= 5;
899         //                 }
900         //                 sgn *= -1;
901 
902         //                 nx = coordsZero.usrCoords[1] + deltas.x * ticksDelta;
903         //                 ny = coordsZero.usrCoords[2] + deltas.y * ticksDelta;
904         //                 distScr = coordsZero.distance(
905         //                     Const.COORDS_BY_SCREEN,
906         //                     new Coords(Const.COORDS_BY_USER, [nx, ny], this.board)
907         //                 );
908         //             }
909 
910         //             return ticksDelta;
911         //         },
912 
913         /**
914          * Auxiliary method used by {@link JXG.Ticks#generateEquidistantTicks} to create a tick
915          * in the line at the given tickPosition.
916          *
917          * @param  {JXG.Coords} coordsZero    coordinates of the point considered zero
918          * @param  {Number}     tickPosition  current tick position relative to zero
919          * @param  {Number}     ticksDelta    distance between two major ticks in user coordinates
920          * @param  {Object}     deltas      x and y distance between two major ticks
921          * @private
922          */
923         processTickPosition: function (coordsZero, tickPosition, ticksDelta, deltas) {
924             var x,
925                 y,
926                 tickCoords,
927                 ti,
928                 isLabelPosition,
929                 ticksPerLabel = this.evalVisProp('ticksperlabel'),
930                 labelVal = null;
931 
932             // Calculates tick coordinates
933             if (this.line.elementClass === Const.OBJECT_CLASS_LINE) {
934                 x = coordsZero.usrCoords[1] + tickPosition * deltas.x;
935                 y = coordsZero.usrCoords[2] + tickPosition * deltas.y;
936             } else {
937                 x = this.line.X(coordsZero + tickPosition);
938                 y = this.line.Y(coordsZero + tickPosition);
939             }
940             tickCoords = new Coords(Const.COORDS_BY_USER, [x, y], this.board);
941             if (this.line.elementClass === Const.OBJECT_CLASS_CURVE) {
942                 labelVal = coordsZero + tickPosition;
943                 this.setTicksSizeVariables(labelVal);
944             }
945 
946             // Test if tick is a major tick.
947             // This is the case if tickPosition/ticksDelta is
948             // a multiple of the number of minorticks+1
949             tickCoords.major =
950                 Math.round(tickPosition / ticksDelta) %
951                 (this.evalVisProp('minorticks') + 1) ===
952                 0;
953 
954             if (!ticksPerLabel) {
955                 // In case of null, 0 or false, majorTicks are labelled
956                 ticksPerLabel = this.evalVisProp('minorticks') + 1;
957             }
958             isLabelPosition = Math.round(tickPosition / ticksDelta) % ticksPerLabel === 0;
959 
960             // Compute the start position and the end position of a tick.
961             // If both positions are out of the canvas, ti is empty.
962             ti = this.createTickPath(tickCoords, tickCoords.major);
963             if (ti.length === 3) {
964                 this.ticks.push(ti);
965                 if (isLabelPosition && this.evalVisProp('drawlabels')) {
966                     // Create a label at this position
967                     this.labelsData.push(
968                         this.generateLabelData(
969                             this.generateLabelText(tickCoords, coordsZero, labelVal),
970                             tickCoords,
971                             this.ticks.length
972                         )
973                     );
974                 } else {
975                     // minor ticks have no labels
976                     this.labelsData.push(null);
977                 }
978             }
979         },
980 
981         /**
982          * Creates ticks coordinates and labels based on {@link JXG.Ticks#fixedTicks} and {@link JXG.Ticks#labels}.
983          *
984          * @param  {JXG.Coords} coordsZero Coordinates of the point considered zero
985          * @param  {Object}     bounds     contains the lower and upper bounds for ticks placement
986          * @private
987          */
988         generateFixedTicks: function (coordsZero, bounds) {
989             var tickCoords,
990                 labelText,
991                 i,
992                 ti,
993                 x,
994                 y,
995                 eps2 = Mat.eps,
996                 fixedTick,
997                 hasLabelOverrides = Type.isArray(this.visProp.labels),
998                 deltas,
999                 ev_dl = this.evalVisProp('drawlabels');
1000 
1001             if (this.line.elementClass === Const.OBJECT_CLASS_LINE) {
1002                 // Calculate x and y distances between two points on the line which are 1 unit apart
1003                 // In essence, these are cosine and sine.
1004                 deltas = this.getXandYdeltas();
1005             }
1006             for (i = 0; i < this.fixedTicks.length; i++) {
1007                 if (this.line.elementClass === Const.OBJECT_CLASS_LINE) {
1008                     fixedTick = this.fixedTicks[i];
1009                     x = coordsZero.usrCoords[1] + fixedTick * deltas.x;
1010                     y = coordsZero.usrCoords[2] + fixedTick * deltas.y;
1011                 } else {
1012                     fixedTick = coordsZero + this.fixedTicks[i];
1013                     x = this.line.X(fixedTick);
1014                     y = this.line.Y(fixedTick);
1015                 }
1016                 tickCoords = new Coords(Const.COORDS_BY_USER, [x, y], this.board);
1017 
1018                 if (this.line.elementClass === Const.OBJECT_CLASS_CURVE) {
1019                     this.setTicksSizeVariables(fixedTick);
1020                 }
1021 
1022                 // Compute the start position and the end position of a tick.
1023                 // If tick is out of the canvas, ti is empty.
1024                 ti = this.createTickPath(tickCoords, true);
1025                 if (
1026                     ti.length === 3 &&
1027                     fixedTick >= bounds.lower - eps2 &&
1028                     fixedTick <= bounds.upper + eps2
1029                 ) {
1030                     this.ticks.push(ti);
1031 
1032                     if (ev_dl && (hasLabelOverrides || Type.exists(this.visProp.labels[i]))) {
1033                         labelText = hasLabelOverrides
1034                             ? this.evalVisProp('labels.' + i)
1035                             : fixedTick;
1036                         this.labelsData.push(
1037                             this.generateLabelData(
1038                                 this.generateLabelText(tickCoords, coordsZero, labelText),
1039                                 tickCoords,
1040                                 i
1041                             )
1042                         );
1043                     } else {
1044                         this.labelsData.push(null);
1045                     }
1046                 }
1047             }
1048         },
1049 
1050         /**
1051          * Calculates the x and y distances in user coordinates between two units in user space.
1052          * In essence, these are cosine and sine. The only work to be done is to determine
1053          * the direction of the line.
1054          *
1055          * @returns {Object}
1056          * @private
1057          */
1058         getXandYdeltas: function () {
1059             var // Auxiliary points to store the start and end of the line according to its direction
1060                 point1UsrCoords,
1061                 point2UsrCoords,
1062                 distP1P2 = this.line.point1.Dist(this.line.point2);
1063 
1064             // if (this.line.type === Const.OBJECT_TYPE_AXIS) {
1065             //     // When line is an Axis, direction depends on board coordinates system
1066             //     // Assume line.point1 and line.point2 are in correct order
1067             //     point1UsrCoords = this.line.point1.coords.usrCoords;
1068             //     point2UsrCoords = this.line.point2.coords.usrCoords;
1069             //     // Check if direction is incorrect, then swap
1070             //     if (
1071             //         point1UsrCoords[1] > point2UsrCoords[1] ||
1072             //         (Math.abs(point1UsrCoords[1] - point2UsrCoords[1]) < Mat.eps &&
1073             //             point1UsrCoords[2] > point2UsrCoords[2])
1074             //     ) {
1075             //         point1UsrCoords = this.line.point2.coords.usrCoords;
1076             //         point2UsrCoords = this.line.point1.coords.usrCoords;
1077             //     }
1078             // } /* if (this.line.elementClass === Const.OBJECT_CLASS_LINE)*/ else {
1079                 // Line direction is always from P1 to P2 for non axis types
1080                 point1UsrCoords = this.line.point1.coords.usrCoords;
1081                 point2UsrCoords = this.line.point2.coords.usrCoords;
1082             // }
1083             return {
1084                 x: (point2UsrCoords[1] - point1UsrCoords[1]) / distP1P2,
1085                 y: (point2UsrCoords[2] - point1UsrCoords[2]) / distP1P2
1086             };
1087         },
1088 
1089         /**
1090          * Check if (parts of) the tick is inside the canvas. The tick intersects the boundary
1091          * at two positions: [x[0], y[0]] and [x[1], y[1]] in screen coordinates.
1092          * @param  {Array}  x Array of length two
1093          * @param  {Array}  y Array of length two
1094          * @return {Boolean}   true if parts of the tick are inside of the canvas or on the boundary.
1095          */
1096         _isInsideCanvas: function (x, y, m) {
1097             var cw = this.board.canvasWidth,
1098                 ch = this.board.canvasHeight;
1099 
1100             if (m === undefined) {
1101                 m = 0;
1102             }
1103             return (
1104                 (x[0] >= m && x[0] <= cw - m && y[0] >= m && y[0] <= ch - m) ||
1105                 (x[1] >= m && x[1] <= cw - m && y[1] >= m && y[1] <= ch - m)
1106             );
1107         },
1108 
1109         /**
1110          * @param {JXG.Coords} coords Coordinates of the tick on the line.
1111          * @param {Boolean} major True if tick is major tick.
1112          * @returns {Array} Array of length 3 containing path coordinates in screen coordinates
1113          *                 of the tick (arrays of length 2). 3rd entry is true if major tick otherwise false.
1114          *                 If the tick is outside of the canvas, the return array is empty.
1115          * @private
1116          */
1117         createTickPath: function (coords, major) {
1118             var c,
1119                 lineStdForm,
1120                 intersection,
1121                 dxs,
1122                 dys,
1123                 dxr,
1124                 dyr,
1125                 alpha,
1126                 style,
1127                 x = [-2000000, -2000000],
1128                 y = [-2000000, -2000000],
1129                 i, r, r_max, bb, full, delta,
1130                 // Used for infinite ticks
1131                 te0, te1, // Tick ending visProps
1132                 dists; // 'signed' distances of intersections to the parent line
1133 
1134             c = coords.scrCoords;
1135             if (major) {
1136                 dxs = this.dxMaj;
1137                 dys = this.dyMaj;
1138                 style = this.majStyle;
1139                 te0 = this.evalVisProp('majortickendings.0') > 0;
1140                 te1 = this.evalVisProp('majortickendings.1') > 0;
1141             } else {
1142                 dxs = this.dxMin;
1143                 dys = this.dyMin;
1144                 style = this.minStyle;
1145                 te0 = this.evalVisProp('tickendings.0') > 0;
1146                 te1 = this.evalVisProp('tickendings.1') > 0;
1147             }
1148             lineStdForm = [-dys * c[1] - dxs * c[2], dys, dxs];
1149 
1150             // For all ticks regardless if of finite or infinite
1151             // tick length the intersection with the canvas border is
1152             // computed.
1153             if (major && this.evalVisProp('type') === "polar") {
1154                 // polar style
1155                 bb = this.board.getBoundingBox();
1156                 full = 2.0 * Math.PI;
1157                 delta = full / 180;
1158                 //ratio = this.board.unitY / this.board.X;
1159 
1160                 // usrCoords: Test if 'circle' is inside of the canvas
1161                 c = coords.usrCoords;
1162                 r = Mat.hypot(c[1], c[2]);
1163                 r_max = Math.max(
1164                     Mat.hypot(bb[0], bb[1]),
1165                     Mat.hypot(bb[2], bb[3])
1166                 );
1167 
1168                 if (r < r_max) {
1169                     // Now, switch to screen coords
1170                     x = [];
1171                     y = [];
1172                     for (i = 0; i <= full; i += delta) {
1173                         x.push(
1174                             this.board.origin.scrCoords[1] + r * Math.cos(i) * this.board.unitX
1175                         );
1176                         y.push(
1177                             this.board.origin.scrCoords[2] + r * Math.sin(i) * this.board.unitY
1178                         );
1179                     }
1180                     return [x, y, major];
1181                 }
1182             } else {
1183                 // line style
1184                 if (style === 'infinite') {
1185                     // Problematic are infinite ticks which have set tickendings:[0,1].
1186                     // For example, this is the default setting for minor ticks
1187                     if (this.evalVisProp('ignoreinfinitetickendings')) {
1188                         te0 = te1 = true;
1189                     }
1190                     intersection = Geometry.meetLineBoard(lineStdForm, this.board);
1191 
1192                     if (te0 && te1) {
1193                         x[0] = intersection[0].scrCoords[1];
1194                         x[1] = intersection[1].scrCoords[1];
1195                         y[0] = intersection[0].scrCoords[2];
1196                         y[1] = intersection[1].scrCoords[2];
1197                     } else {
1198                         // Assuming the usrCoords of both intersections are normalized, a 'signed distance'
1199                         // with respect to the parent line is computed for the intersections. The sign is
1200                         // used to conclude whether the point is either at the left or right side of the
1201                         // line. The magnitude can be used to compare the points and determine which point
1202                         // is closest to the line.
1203                         dists = [
1204                             Mat.innerProduct(
1205                                 intersection[0].usrCoords.slice(1, 3),
1206                                 this.line.stdform.slice(1, 3)
1207                             ) + this.line.stdform[0],
1208                             Mat.innerProduct(
1209                                 intersection[1].usrCoords.slice(1, 3),
1210                                 this.line.stdform.slice(1, 3)
1211                             ) + this.line.stdform[0]
1212                         ];
1213 
1214                         // Reverse intersection array order if first intersection is not the leftmost one.
1215                         if (dists[0] < dists[1]) {
1216                             intersection.reverse();
1217                             dists.reverse();
1218                         }
1219 
1220                         if (te0) { // Left-infinite tick
1221                             if (dists[0] < 0) { // intersections at the wrong side of line
1222                                 return [];
1223                             } else if (dists[1] < 0) { // 'default' case, tick drawn from line to board bounds
1224                                 x[0] = intersection[0].scrCoords[1];
1225                                 y[0] = intersection[0].scrCoords[2];
1226                                 x[1] = c[1];
1227                                 y[1] = c[2];
1228                             } else { // tick visible, but coords of tick on line are outside the visible area
1229                                 x[0] = intersection[0].scrCoords[1];
1230                                 y[0] = intersection[0].scrCoords[2];
1231                                 x[1] = intersection[1].scrCoords[1];
1232                                 y[1] = intersection[1].scrCoords[2];
1233                             }
1234                         } else if (te1) { // Right-infinite tick
1235                             if (dists[1] > 0) { // intersections at the wrong side of line
1236                                 return [];
1237                             } else if (dists[0] > 0) { // 'default' case, tick drawn from line to board bounds
1238                                 x[0] = c[1];
1239                                 y[0] = c[2];
1240                                 x[1] = intersection[1].scrCoords[1];
1241                                 y[1] = intersection[1].scrCoords[2];
1242                             } else { // tick visible, but coords of tick on line are outside the visible area
1243                                 x[0] = intersection[0].scrCoords[1];
1244                                 y[0] = intersection[0].scrCoords[2];
1245                                 x[1] = intersection[1].scrCoords[1];
1246                                 y[1] = intersection[1].scrCoords[2];
1247                             }
1248                         }
1249                     }
1250                 } else {
1251                     if (this.evalVisProp('face') === ">") {
1252                         alpha = Math.PI / 4;
1253                     } else if (this.evalVisProp('face') === "<") {
1254                         alpha = -Math.PI / 4;
1255                     } else {
1256                         alpha = 0;
1257                     }
1258                     dxr = Math.cos(alpha) * dxs - Math.sin(alpha) * dys;
1259                     dyr = Math.sin(alpha) * dxs + Math.cos(alpha) * dys;
1260 
1261                     x[0] = c[1] + dxr * te0;
1262                     y[0] = c[2] - dyr * te0;
1263                     x[1] = c[1];
1264                     y[1] = c[2];
1265 
1266                     alpha = -alpha;
1267                     dxr = Math.cos(alpha) * dxs - Math.sin(alpha) * dys;
1268                     dyr = Math.sin(alpha) * dxs + Math.cos(alpha) * dys;
1269 
1270                     x[2] = c[1] - dxr * te1;
1271                     y[2] = c[2] + dyr * te1;
1272                 }
1273 
1274                 // Check if (parts of) the tick is inside the canvas.
1275                 if (this._isInsideCanvas(x, y)) {
1276                     return [x, y, major];
1277                 }
1278             }
1279 
1280             return [];
1281         },
1282 
1283         /**
1284          * Format label texts. Show the desired number of digits
1285          * and use utf-8 minus sign.
1286          * @param  {Number} value Number to be displayed
1287          * @return {String}       The value converted into a string.
1288          * @private
1289          */
1290         formatLabelText: function (value) {
1291             var labelText,
1292                 digits,
1293                 ev_um = this.evalVisProp('label.usemathjax'),
1294                 ev_uk = this.evalVisProp('label.usekatex'),
1295                 ev_s = this.evalVisProp('scalesymbol');
1296 
1297             if (Type.isNumber(value)) {
1298                 if (this.evalVisProp('label.tofraction')) {
1299                     if (ev_um) {
1300                         labelText = '\\(' + Type.toFraction(value, true) + '\\)';
1301                     } else {
1302                         labelText = Type.toFraction(value, ev_uk);
1303                     }
1304                 } else {
1305                     digits = this.evalVisProp('digits');
1306                     if (this.useLocale()) {
1307                         labelText = this.formatNumberLocale(value, digits);
1308                     } else {
1309                         labelText = (Math.round(value * 1e11) / 1e11).toString();
1310 
1311                         if (
1312                             labelText.length > this.evalVisProp('maxlabellength') ||
1313                             labelText.indexOf("e") !== -1
1314                         ) {
1315                             if (this.evalVisProp('precision') !== 3 && digits === 3) {
1316                                 // Use the deprecated attribute "precision"
1317                                 digits = this.evalVisProp('precision');
1318                             }
1319 
1320                             //labelText = value.toPrecision(digits).toString();
1321                             labelText = value.toExponential(digits).toString();
1322                         }
1323                     }
1324                 }
1325 
1326                 if (this.evalVisProp('beautifulscientificticklabels')) {
1327                     labelText = this.beautifyScientificNotationLabel(labelText);
1328                 }
1329 
1330                 if (labelText.indexOf(".") > -1 && labelText.indexOf("e") === -1) {
1331                     // trim trailing zeros
1332                     labelText = labelText.replace(/0+$/, "");
1333                     // trim trailing .
1334                     labelText = labelText.replace(/\.$/, "");
1335                 }
1336             } else {
1337                 labelText = value.toString();
1338             }
1339 
1340             if (ev_s.length > 0) {
1341                 if (labelText === "1") {
1342                     labelText = ev_s;
1343                 } else if (labelText === "-1") {
1344                     labelText = "-" + ev_s;
1345                 } else if (labelText !== "0") {
1346                     labelText = labelText + ev_s;
1347                 }
1348             }
1349 
1350             if (this.evalVisProp('useunicodeminus')) {
1351                 labelText = labelText.replace(/-/g, "\u2212");
1352             }
1353             return labelText;
1354         },
1355 
1356         /**
1357          * Formats label texts to make labels displayed in scientific notation look beautiful.
1358          * For example, label 5.00e+6 will become 5•10⁶, label -1.00e-7 will become into -1•10⁻⁷
1359          * @param {String} labelText - The label that we want to convert
1360          * @returns {String} If labelText was not in scientific notation, return labelText without modifications.
1361          * Otherwise returns beautified labelText with proper superscript notation.
1362          */
1363         beautifyScientificNotationLabel: function (labelText) {
1364             var returnString;
1365 
1366             if (labelText.indexOf("e") === -1) {
1367                 return labelText;
1368             }
1369 
1370             // Clean up trailing 0's, so numbers like 5.00e+6.0 for example become into 5e+6
1371             returnString =
1372                 parseFloat(labelText.substring(0, labelText.indexOf("e"))) +
1373                 labelText.substring(labelText.indexOf("e"));
1374 
1375             // Replace symbols like -,0,1,2,3,4,5,6,7,8,9 with their superscript version.
1376             // Gets rid of + symbol since there is no need for it anymore.
1377             returnString = returnString.replace(/e(.*)$/g, function (match, $1) {
1378                 var temp = "\u2022" + "10";
1379                 // Note: Since board ticks do not support HTTP elements like <sub>, we need to replace
1380                 // all the numbers with superscript Unicode characters.
1381                 temp += $1
1382                     .replace(/-/g, "\u207B")
1383                     .replace(/\+/g, "")
1384                     .replace(/0/g, "\u2070")
1385                     .replace(/1/g, "\u00B9")
1386                     .replace(/2/g, "\u00B2")
1387                     .replace(/3/g, "\u00B3")
1388                     .replace(/4/g, "\u2074")
1389                     .replace(/5/g, "\u2075")
1390                     .replace(/6/g, "\u2076")
1391                     .replace(/7/g, "\u2077")
1392                     .replace(/8/g, "\u2078")
1393                     .replace(/9/g, "\u2079");
1394 
1395                 return temp;
1396             });
1397 
1398             return returnString;
1399         },
1400 
1401         /**
1402          * Creates the label text for a given tick. A value for the text can be provided as a number or string
1403          *
1404          * @param  {JXG.Coords}    tick  The Coords-object of the tick to create a label for
1405          * @param  {JXG.Coords}    zero  The Coords-object of line's zero
1406          * @param  {Number|String} value A predefined value for this tick
1407          * @returns {String}
1408          * @private
1409          */
1410         generateLabelText: function (tick, zero, value) {
1411             var labelText, distance;
1412 
1413             // No value provided, equidistant, so assign distance as value
1414             if (!Type.exists(value)) {
1415                 // could be null or undefined
1416                 distance = this.getDistanceFromZero(zero, tick);
1417                 if (Math.abs(distance) < Mat.eps) {
1418                     // Point is zero
1419                     return "0";
1420                 }
1421                 value = distance / this.evalVisProp('scale');
1422             }
1423             labelText = this.formatLabelText(value);
1424 
1425             return labelText;
1426         },
1427 
1428         /**
1429          * Create a tick label data, i.e. text and coordinates
1430          * @param  {String}     labelText
1431          * @param  {JXG.Coords} tick
1432          * @param  {Number}     tickNumber
1433          * @returns {Object} with properties 'x', 'y', 't' (text), 'i' (tick number) or null in case of o label
1434          * @private
1435          */
1436         generateLabelData: function (labelText, tick, tickNumber) {
1437             var xa, ya, m, fs;
1438 
1439             // Test if large portions of the label are inside of the canvas
1440             // This is the last chance to abandon the creation of the label if it is mostly
1441             // outside of the canvas.
1442             fs = this.evalVisProp('label.fontsize');
1443             xa = [tick.scrCoords[1], tick.scrCoords[1]];
1444             ya = [tick.scrCoords[2], tick.scrCoords[2]];
1445             m = fs === undefined ? 12 : fs;
1446             m *= 0.5;
1447             if (!this._isInsideCanvas(xa, ya, m)) {
1448                 return null;
1449             }
1450 
1451             xa = this.evalVisProp('label.offset')[0];
1452             ya = this.evalVisProp('label.offset')[1];
1453 
1454             return {
1455                 x: tick.usrCoords[1] + xa / this.board.unitX,
1456                 y: tick.usrCoords[2] + ya / this.board.unitY,
1457                 t: labelText,
1458                 i: tickNumber
1459             };
1460         },
1461 
1462         /**
1463          * Recalculate the tick positions and the labels.
1464          * @returns {JXG.Ticks}
1465          */
1466         update: function () {
1467             if (this.needsUpdate) {
1468                 //this.visPropCalc.visible = this.evalVisProp('visible');
1469                 // A canvas with no width or height will create an endless loop, so ignore it
1470                 if (this.board.canvasWidth !== 0 && this.board.canvasHeight !== 0) {
1471                     this.calculateTicksCoordinates();
1472                 }
1473                 // this.updateVisibility(this.line.visPropCalc.visible);
1474                 //
1475                 // for (var i = 0; i < this.labels.length; i++) {
1476                 //     if (this.labels[i] !== null) {
1477                 //         this.labels[i].prepareUpdate()
1478                 //             .updateVisibility(this.line.visPropCalc.visible)
1479                 //             .updateRenderer();
1480                 //     }
1481                 // }
1482             }
1483 
1484             return this;
1485         },
1486 
1487         /**
1488          * Uses the boards renderer to update the arc.
1489          * @returns {JXG.Ticks} Reference to the object.
1490          */
1491         updateRenderer: function () {
1492             if (!this.needsUpdate) {
1493                 return this;
1494             }
1495 
1496             if (this.visPropCalc.visible) {
1497                 this.board.renderer.updateTicks(this);
1498             }
1499             this.updateRendererLabels();
1500 
1501             this.setDisplayRendNode();
1502             // if (this.visPropCalc.visible != this.visPropOld.visible) {
1503             //     this.board.renderer.display(this, this.visPropCalc.visible);
1504             //     this.visPropOld.visible = this.visPropCalc.visible;
1505             // }
1506 
1507             this.needsUpdate = false;
1508             return this;
1509         },
1510 
1511         /**
1512          * Updates the label elements of the major ticks.
1513          *
1514          * @private
1515          * @returns {JXG.Ticks} Reference to the object.
1516          */
1517         updateRendererLabels: function () {
1518             var i, j, lenData, lenLabels, attr, label, ld, visible;
1519 
1520             // The number of labels needed
1521             lenData = this.labelsData.length;
1522             // The number of labels which already exist
1523             // The existing labels are stored in this.labels[]
1524             // The new label positions and label values are stored in this.labelsData[]
1525             lenLabels = this.labels.length;
1526 
1527             for (i = 0, j = 0; i < lenData; i++) {
1528                 if (this.labelsData[i] === null) {
1529                     // This is a tick without label
1530                     continue;
1531                 }
1532 
1533                 ld = this.labelsData[i];
1534                 if (j < lenLabels) {
1535                     // Take an already existing text element
1536                     label = this.labels[j];
1537                     label.setText(ld.t);
1538                     label.setCoords(ld.x, ld.y);
1539                     j++;
1540                 } else {
1541                     // A new text element is needed
1542                     this.labelCounter += 1;
1543 
1544                     attr = {
1545                         isLabel: true,
1546                         layer: this.board.options.layer.line,
1547                         highlightStrokeColor: this.board.options.text.strokeColor,
1548                         highlightStrokeWidth: this.board.options.text.strokeWidth,
1549                         highlightStrokeOpacity: this.board.options.text.strokeOpacity,
1550                         priv: this.visProp.priv
1551                     };
1552                     attr = Type.deepCopy(attr, this.visProp.label);
1553                     attr.id = this.id + ld.i + "Label" + this.labelCounter;
1554 
1555                     label = JXG.createText(this.board, [ld.x, ld.y, ld.t], attr);
1556                     this.addChild(label);
1557                     label.setParents(this);
1558                     label.isDraggable = false;
1559                     label.dump = false;
1560                     this.labels.push(label);
1561                 }
1562 
1563                 // Look-ahead if the label inherits visibility.
1564                 // If yes, update label.
1565                 visible = this.evalVisProp('label.visible');
1566                 if (visible === 'inherit') {
1567                     visible = this.visPropCalc.visible;
1568                 }
1569 
1570                 label.prepareUpdate().updateVisibility(visible).updateRenderer();
1571 
1572                 label.distanceX = this.evalVisProp('label.offset')[0];
1573                 label.distanceY = this.evalVisProp('label.offset')[1];
1574             }
1575 
1576             // Hide unused labels
1577             lenData = j;
1578             for (j = lenData; j < lenLabels; j++) {
1579                 this.board.renderer.display(this.labels[j], false);
1580                 // Tick labels have the attribute "visible: 'inherit'"
1581                 // This must explicitly set to false, otherwise
1582                 // this labels would be set to visible in the upcoming
1583                 // update of the labels.
1584                 this.labels[j].visProp.visible = this.labels[j].visPropCalc.visible = false;
1585             }
1586 
1587             return this;
1588         },
1589 
1590         hideElement: function () {
1591             var i;
1592 
1593             JXG.deprecated("Element.hideElement()", "Element.setDisplayRendNode()");
1594 
1595             this.visPropCalc.visible = false;
1596             this.board.renderer.display(this, false);
1597             for (i = 0; i < this.labels.length; i++) {
1598                 if (Type.exists(this.labels[i])) {
1599                     this.labels[i].hideElement();
1600                 }
1601             }
1602 
1603             return this;
1604         },
1605 
1606         showElement: function () {
1607             var i;
1608 
1609             JXG.deprecated("Element.showElement()", "Element.setDisplayRendNode()");
1610 
1611             this.visPropCalc.visible = true;
1612             this.board.renderer.display(this, false);
1613 
1614             for (i = 0; i < this.labels.length; i++) {
1615                 if (Type.exists(this.labels[i])) {
1616                     this.labels[i].showElement();
1617                 }
1618             }
1619 
1620             return this;
1621         }
1622     }
1623 );
1624 
1625 /**
1626  * @class Ticks are used as distance markers on a line or curve.
1627  * They are mainly used for axis elements and slider elements. Ticks may stretch infinitely
1628  * or finitely, which can be set with {@link Ticks#majorHeight} and {@link Ticks#minorHeight}.
1629  * <p>
1630  * There are the following ways to position the tick lines:
1631  * <ol>
1632  *  <li> If an array is given as optional second parameter for the constructor
1633  * like e.g. <tt>board.create('ticks', [line, [1, 4, 5]])</tt>, then there will be (fixed) ticks at position
1634  * 1, 4 and 5 of the line.
1635  *  <li> If there is only one parameter given, like e.g. <tt>board.create('ticks', [line])</tt>, the ticks will be set
1636  * equidistant across the line element. There are two variants:
1637  *    <ol type="i">
1638  *      <li> Setting the attribute <tt>insertTicks:false</tt>: in this case the distance between two major ticks
1639  *          is determined by the attribute <tt>ticksDistance</tt>. This distance is given in user units.
1640  *      <li> Setting the attribute <tt>insertTicks:true</tt>: in this case the distance between two major ticks
1641  *          is set automatically, depending on
1642  *          <ul>
1643  *              <li> the size of the board,
1644  *              <li> the attribute <tt>minTicksDistance</tt>,  which is the minimum distance between two consecutive minor ticks (in pixel).
1645  *          </ul>
1646  * The distance between two major ticks is a value of the form
1647  * <i>a 10<sup>i</sup></i>, where <i>a</i> is one of <i>{1, 2, 5}</i> and
1648  * the number <i>a 10<sup>i</sup></i> is maximized such that there are approximately
1649  * 6 major ticks and there are at least "minTicksDistance" pixel between minor ticks.
1650  * </ol>
1651  * <p>
1652  * For arbitrary lines (and not axes) a "zero coordinate" is determined
1653  * which defines where the first tick is positioned. This zero coordinate
1654  * can be altered with the attribute <tt>anchor</tt>. Possible values are "left", "middle", "right" or a number.
1655  * The default value is "left".
1656  *
1657  * @pseudo
1658  * @name Ticks
1659  * @augments JXG.Ticks
1660  * @constructor
1661  * @type JXG.Ticks
1662  * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.
1663  * @param {JXG.Line|JXG.Curve} line The parents consist of the line or curve the ticks are going to be attached to.
1664  * @param {Array} [ticks] Optional array of numbers. If given, a fixed number of static ticks is created
1665  * at these user-supplied positions.
1666  * <p>
1667  * Deprecated: Alternatively, a number defining the distance between two major ticks
1668  * can be specified. However, this is meanwhile ignored. Use attribute <tt>ticksDistance</tt> instead.
1669  *
1670  * @example
1671  * // Add ticks to line 'l1' through 'p1' and 'p2'. The major ticks are
1672  * // two units apart and 40 px long.
1673  *   var p1 = board.create('point', [0, 3]);
1674  *   var p2 = board.create('point', [1, 3]);
1675  *   var l1 = board.create('line', [p1, p2]);
1676  *   var t = board.create('ticks', [l1], {
1677  *      ticksDistance: 2,
1678  *      majorHeight: 40
1679  *   });
1680  * </pre><div class="jxgbox" id="JXGee7f2d68-75fc-4ec0-9931-c76918427e63" style="width: 300px; height: 300px;"></div>
1681  * <script type="text/javascript">
1682  * (function () {
1683  *   var board = JXG.JSXGraph.initBoard('JXGee7f2d68-75fc-4ec0-9931-c76918427e63', {
1684  *   boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: true});
1685  *   var p1 = board.create('point', [0, 3]);
1686  *   var p2 = board.create('point', [1, 3]);
1687  *   var l1 = board.create('line', [p1, p2]);
1688  *   var t = board.create('ticks', [l1, 2], {ticksDistance: 2, majorHeight: 40});
1689  * })();
1690  * </script><pre>
1691  * @example
1692  *  // Create ticks labels as fractions
1693  * board.create('axis', [[0,1], [1,1]], {
1694  *     ticks: {
1695  *         label: {
1696  *             toFraction: true,
1697  *             useMathjax: true,
1698  *             display: 'html',
1699  *             anchorX: 'middle',
1700  *             offset: [0, -10]
1701  *         }
1702  *     }
1703  * });
1704  *
1705  * </pre><div id="JXG4455acb2-6bf3-4801-8887-d7fcc1e4e1da" class="jxgbox" style="width: 300px; height: 300px;"></div>
1706  * <script src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js" id="MathJax-script"></script>
1707  * <script type="text/javascript">
1708  *     (function() {
1709  *         var board = JXG.JSXGraph.initBoard('JXG4455acb2-6bf3-4801-8887-d7fcc1e4e1da',
1710  *             {boundingbox: [-1.2, 2.3, 1.2, -2.3], axis: true, showcopyright: false, shownavigation: false});
1711  *             board.create('axis', [[0,1], [1,1]], {
1712  *                 ticks: {
1713  *                     label: {
1714  *                         toFraction: true,
1715  *             useMathjax: true,
1716  *             display: 'html',
1717  *             anchorX: 'middle',
1718  *             offset: [0, -10]
1719  *                     }
1720  *                 }
1721  *             });
1722  *
1723  *     })();
1724  *
1725  * </script><pre>
1726  *
1727  * @example
1728  */
1729 JXG.createTicks = function (board, parents, attributes) {
1730     var el,
1731         dist,
1732         attr = Type.copyAttributes(attributes, board.options, "ticks");
1733 
1734     if (parents.length < 2) {
1735         dist = attr.ticksdistance; // Will be ignored anyhow and attr.ticksDistance will be used instead
1736     } else {
1737         dist = parents[1];
1738     }
1739 
1740     if (
1741         parents[0].elementClass === Const.OBJECT_CLASS_LINE ||
1742         parents[0].elementClass === Const.OBJECT_CLASS_CURVE
1743     ) {
1744         el = new JXG.Ticks(parents[0], dist, attr);
1745     } else {
1746         throw new Error(
1747             "JSXGraph: Can't create Ticks with parent types '" + typeof parents[0] + "'."
1748         );
1749     }
1750 
1751     // deprecated
1752     if (Type.isFunction(attr.generatelabelvalue)) {
1753         el.generateLabelText = attr.generatelabelvalue;
1754     }
1755     if (Type.isFunction(attr.generatelabeltext)) {
1756         el.generateLabelText = attr.generatelabeltext;
1757     }
1758 
1759     el.setParents(parents[0]);
1760     el.isDraggable = true;
1761     el.fullUpdate(parents[0].visPropCalc.visible);
1762 
1763     return el;
1764 };
1765 
1766 /**
1767  * @class Hatches can be used to mark congruent lines or curves.
1768  * @pseudo
1769  * @name Hatch
1770  * @augments JXG.Ticks
1771  * @constructor
1772  * @type JXG.Ticks
1773  * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.
1774  * @param {JXG.Line|JXG.curve} line The line or curve the hatch marks are going to be attached to.
1775  * @param {Number} numberofhashes Number of dashes. The distance of the hashes can be controlled with the attribute ticksDistance.
1776  * @example
1777  * // Create an axis providing two coords pairs.
1778  *   var p1 = board.create('point', [0, 3]);
1779  *   var p2 = board.create('point', [1, 3]);
1780  *   var l1 = board.create('line', [p1, p2]);
1781  *   var t = board.create('hatch', [l1, 3]);
1782  * </pre><div class="jxgbox" id="JXG4a20af06-4395-451c-b7d1-002757cf01be" style="width: 300px; height: 300px;"></div>
1783  * <script type="text/javascript">
1784  * (function () {
1785  *   var board = JXG.JSXGraph.initBoard('JXG4a20af06-4395-451c-b7d1-002757cf01be', {boundingbox: [-1, 7, 7, -1], showcopyright: false, shownavigation: false});
1786  *   var p1 = board.create('point', [0, 3]);
1787  *   var p2 = board.create('point', [1, 3]);
1788  *   var l1 = board.create('line', [p1, p2]);
1789  *   var t = board.create('hatch', [l1, 3]);
1790  * })();
1791  * </script><pre>
1792  *
1793  * @example
1794  * // Alter the position of the hatch
1795  *
1796  * var p = board.create('point', [-5, 0]);
1797  * var q = board.create('point', [5, 0]);
1798  * var li = board.create('line', [p, q]);
1799  * var h = board.create('hatch', [li, 2], {anchor: 0.2, ticksDistance:0.4});
1800  *
1801  * </pre><div id="JXG05d720ee-99c9-11e6-a9c7-901b0e1b8723" class="jxgbox" style="width: 300px; height: 300px;"></div>
1802  * <script type="text/javascript">
1803  *     (function() {
1804  *         var board = JXG.JSXGraph.initBoard('JXG05d720ee-99c9-11e6-a9c7-901b0e1b8723',
1805  *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
1806  *
1807  *     var p = board.create('point', [-5, 0]);
1808  *     var q = board.create('point', [5, 0]);
1809  *     var li = board.create('line', [p, q]);
1810  *     var h = board.create('hatch', [li, 2], {anchor: 0.2, ticksDistance:0.4});
1811  *
1812  *     })();
1813  *
1814  * </script><pre>
1815  *
1816  * @example
1817  * // Alternative hatch faces
1818  *
1819  * var li = board.create('line', [[-6,0], [6,3]]);
1820  * var h1 = board.create('hatch', [li, 2], {tickEndings: [1,1], face:'|'});
1821  * var h2 = board.create('hatch', [li, 2], {tickEndings: [1,1], face:'>', anchor: 0.3});
1822  * var h3 = board.create('hatch', [li, 2], {tickEndings: [1,1], face:'<', anchor: 0.7});
1823  *
1824  * </pre><div id="JXG974f7e89-eac8-4187-9aa3-fb8068e8384b" class="jxgbox" style="width: 300px; height: 300px;"></div>
1825  * <script type="text/javascript">
1826  *     (function() {
1827  *         var board = JXG.JSXGraph.initBoard('JXG974f7e89-eac8-4187-9aa3-fb8068e8384b',
1828  *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
1829  *     // Alternative hatch faces
1830  *
1831  *     var li = board.create('line', [[-6,0], [6,3]]);
1832  *     var h1 = board.create('hatch', [li, 2], {tickEndings: [1,1], face:'|'});
1833  *     var h2 = board.create('hatch', [li, 2], {tickEndings: [1,1], face:'>', anchor: 0.3});
1834  *     var h3 = board.create('hatch', [li, 2], {tickEndings: [1,1], face:'<', anchor: 0.7});
1835  *
1836  *     })();
1837  *
1838  * </script><pre>
1839  *
1840  */
1841 JXG.createHatchmark = function (board, parents, attributes) {
1842     var num, i, base, width, totalwidth, el,
1843         pos = [],
1844         attr = Type.copyAttributes(attributes, board.options, 'hatch');
1845 
1846     if (
1847         (parents[0].elementClass !== Const.OBJECT_CLASS_LINE &&
1848             parents[0].elementClass !== Const.OBJECT_CLASS_CURVE) ||
1849         typeof parents[1] !== "number"
1850     ) {
1851         throw new Error(
1852             "JSXGraph: Can't create Hatch mark with parent types '" +
1853             typeof parents[0] +
1854             "' and '" +
1855             typeof parents[1] +
1856             " and ''" +
1857             typeof parents[2] +
1858             "'."
1859         );
1860     }
1861 
1862     num = parents[1];
1863     width = attr.ticksdistance;
1864     totalwidth = (num - 1) * width;
1865     base = -totalwidth * 0.5;
1866 
1867     for (i = 0; i < num; i++) {
1868         pos[i] = base + i * width;
1869     }
1870 
1871     el = board.create('ticks', [parents[0], pos], attr);
1872     el.elType = 'hatch';
1873     parents[0].inherits.push(el);
1874 
1875     return el;
1876 };
1877 
1878 JXG.registerElement("ticks", JXG.createTicks);
1879 JXG.registerElement("hash", JXG.createHatchmark);
1880 JXG.registerElement("hatch", JXG.createHatchmark);
1881 
1882 export default JXG.Ticks;
1883 // export default {
1884 //     Ticks: JXG.Ticks,
1885 //     createTicks: JXG.createTicks,
1886 //     createHashmark: JXG.createHatchmark,
1887 //     createHatchmark: JXG.createHatchmark
1888 // };
1889