      1 /*
      2     Copyright 2008-2017
      3         Matthias Ehmann,
      4         Michael Gerhaeuser,
      5         Carsten Miller,
      6         Bianca Valentin,
      7         Alfred Wassermann,
      8         Peter Wilfahrt
      9
     10     This file is part of JSXGraph.
     11
     12     JSXGraph is free software dual licensed under the GNU LGPL or MIT License.
     13
     14     You can redistribute it and/or modify it under the terms of the
     15
     16       * GNU Lesser General Public License as published by
     17         the Free Software Foundation, either version 3 of the License, or
     18         (at your option) any later version
     19       OR
     20       * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT
     21
     22     JSXGraph is distributed in the hope that it will be useful,
     23     but WITHOUT ANY WARRANTY; without even the implied warranty of
     24     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
     25     GNU Lesser General Public License for more details.
     26
     27     You should have received a copy of the GNU Lesser General Public License and
     28     the MIT License along with JSXGraph. If not, see <http://www.gnu.org/licenses/>
     29     and <http://opensource.org/licenses/MIT/>.
     30  */
     31
     32
     33 /*global JXG: true, define: true*/
     34 /*jslint nomen: true, plusplus: true*/
     35
     36 /* depends:
     37  jxg
     38  math/math
     39  math/geometry
     40  base/constants
     41  base/element
     42  base/coords
     43  utils/type
     44   elements:
     45    text
     46  */
     47
     48 /**
     49  * @fileoverview In this file the geometry object Ticks is defined. Ticks provides
     50  * methods for creation and management of ticks on an axis.
     51  * @author graphjs
     52  * @version 0.1
     53  */
     54
     55 define([
     56     'jxg', 'math/math', 'math/geometry', 'base/constants', 'base/element', 'base/coords', 'utils/type', 'base/text'
     57 ], function (JXG, Mat, Geometry, Const, GeometryElement, Coords, Type, Text) {
     58
     59     "use strict";
     60
     61     /**
     62      * Creates ticks for an axis.
     63      * @class Ticks provides methods for creation and management
     64      * of ticks on an axis.
     65      * @param {JXG.Line} line Reference to the axis the ticks are drawn on.
     66      * @param {Number|Array} ticks Number defining the distance between two major ticks or an array defining static ticks.
     67      * @param {Object} attributes Properties
     68      * @see JXG.Line#addTicks
     69      * @constructor
     70      * @extends JXG.GeometryElement
     71      */
     72     JXG.Ticks = function (line, ticks, attributes) {
     73         this.constructor(line.board, attributes, Const.OBJECT_TYPE_TICKS, Const.OBJECT_CLASS_OTHER);
     74
     75         /**
     76          * The line the ticks belong to.
     77          * @type JXG.Line
     78          */
     79         this.line = line;
     80
     81         /**
     82          * The board the ticks line is drawn on.
     83          * @type JXG.Board
     84          */
     85         this.board = this.line.board;
     86
     87         /**
     88          * A function calculating ticks delta depending on the ticks number.
     89          * @type Function
     90          */
     91         this.ticksFunction = null;
     92
     93         /**
     94          * Array of fixed ticks.
     95          * @type Array
     96          */
     97         this.fixedTicks = null;
     98
     99         /**
    100          * Equidistant ticks. Distance is defined by ticksFunction
    101          * @type Boolean
    102          */
    103         this.equidistant = false;
    104
    105         if (Type.isFunction(ticks)) {
    106             this.ticksFunction = ticks;
    107             throw new Error("Function arguments are no longer supported.");
    108         }
    109
    110         if (Type.isArray(ticks)) {
    111             this.fixedTicks = ticks;
    112         } else {
    113             if (Math.abs(ticks) < Mat.eps || ticks < 0) {
    114                 ticks = attributes.defaultdistance;
    115             }
    116
    117             /*
    118              * Ticks function:
    119              * determines the distance (in user units) of two major ticks
    120              */
    121             this.ticksFunction = this.makeTicksFunction(ticks);
    122
    123             this.equidistant = true;
    124         }
    125
    126         /**
    127          * Least distance between two ticks, measured in pixels.
    128          * @type int
    129          */
    130         this.minTicksDistance = attributes.minticksdistance;
    131
    132         /**
    133          * Stores the ticks coordinates
    134          * @type {Array}
    135          */
    136         this.ticks = [];
    137
    138         /**
    139          * Distance between two major ticks in user coordinates
    140          * @type {Number}
    141          */
    142         this.ticksDelta = 1;
    143
    144         /**
    145          * Array where the labels are saved. There is an array element for every tick,
    146          * even for minor ticks which don't have labels. In this case the array element
    147          * contains just <tt>null</tt>.
    148          * @type Array
    149          */
    150         this.labels = [];
    151
    152         /**
    153          * A list of labels which have to be displayed in updateRenderer.
    154          * @type {Array}
    155          */
    156         this.labelData = [];
    157
    158         /**
    159          * To ensure the uniqueness of label ids this counter is used.
    160          * @type {number}
    161          */
    162         this.labelCounter = 0;
    163
    164         this.id = this.line.addTicks(this);
    165         this.elType = 'ticks';
    166         this.inherits.push(this.labels);
    167         this.board.setId(this, 'Ti');
    168     };
    169
    170     JXG.Ticks.prototype = new GeometryElement();
    171
    172     JXG.extend(JXG.Ticks.prototype, /** @lends JXG.Ticks.prototype */ {
    173
    174         /**
    175          * Ticks function:
    176          * determines the distance (in user units) of two major ticks.
    177          * See above in constructor and in @see JXG.GeometryElement#setAttribute
    178          *
    179          * @private
    180          * @param {Number} ticks Distance between two major ticks
    181          * @returns {Function} returns method ticksFunction
    182          */
    183         makeTicksFunction: function (ticks) {
    184             return function () {
    185                 var delta, b, dist;
    186
    187                 if (Type.evaluate(this.visProp.insertticks)) {
    188                     b = this.getLowerAndUpperBounds(this.getZeroCoordinates(), 'ticksdistance');
    189                     dist = b.upper - b.lower;
    190                     delta = Math.pow(10, Math.floor(Math.log(0.6 * dist) / Math.LN10));
    191                     if (dist <= 6 * delta) {
    192                         delta *= 0.5;
    193                     }
    194                     return delta;
    195                 }
    196
    197                 // upto 0.99.1:
    198                 return ticks;
    199             };
    200         },
    201
    202         /**
    203          * Checks whether (x,y) is near the line.
    204          * @param {Number} x Coordinate in x direction, screen coordinates.
    205          * @param {Number} y Coordinate in y direction, screen coordinates.
    206          * @returns {Boolean} True if (x,y) is near the line, False otherwise.
    207          */
    208         hasPoint: function (x, y) {
    209             var i, t,
    210                 len = (this.ticks && this.ticks.length) || 0,
    211                 r = this.board.options.precision.hasPoint +
    212                         Type.evaluate(this.visProp.strokewidth) * 0.5;
    213
    214             if (!Type.evaluate(this.line.visProp.scalable)) {
    215                 return false;
    216             }
    217
    218             // Ignore non-axes and axes that are not horizontal or vertical
    219             if (this.line.stdform[1] !== 0 && this.line.stdform[2] !== 0 && this.line.type !== Const.OBJECT_TYPE_AXIS) {
    220                 return false;
    221             }
    222
    223             for (i = 0; i < len; i++) {
    224                 t = this.ticks[i];
    225
    226                 // Skip minor ticks
    227                 if (t[2]) {
    228                     // Ignore ticks at zero
    229                     if (!((this.line.stdform[1] === 0 && Math.abs(t[0][0] - this.line.point1.coords.scrCoords[1]) < Mat.eps) ||
    230                             (this.line.stdform[2] === 0 && Math.abs(t[1][0] - this.line.point1.coords.scrCoords[2]) < Mat.eps))) {
    231                         // tick length is not zero, ie. at least one pixel
    232                         if (Math.abs(t[0][0] - t[0][1]) >= 1 || Math.abs(t[1][0] - t[1][1]) >= 1) {
    233                             if (this.line.stdform[1] === 0) {
    234                                 // Allow dragging near axes only.
    235                                 if (Math.abs(y - (t[1][0] + t[1][1]) * 0.5) < 2 * r && t[0][0] - r < x && x < t[0][1] + r) {
    236                                     return true;
    237                                 }
    238                             } else if (this.line.stdform[2] === 0) {
    239                                 if (Math.abs(x - (t[0][0] + t[0][1]) * 0.5) < 2 * r && t[1][0] - r < y && y < t[1][1] + r) {
    240                                     return true;
    241                                 }
    242                             }
    243                         }
    244                     }
    245                 }
    246             }
    247
    248             return false;
    249         },
    250
    251         /**
    252          * Sets x and y coordinate of the tick.
    253          * @param {number} method The type of coordinates used here. Possible values are {@link JXG.COORDS_BY_USER} and {@link JXG.COORDS_BY_SCREEN}.
    254          * @param {Array} coords coordinates in screen/user units
    255          * @param {Array} oldcoords previous coordinates in screen/user units
    256          * @returns {JXG.Ticks} this element
    257          */
    258         setPositionDirectly: function (method, coords, oldcoords) {
    259             var dx, dy,
    260                 c = new Coords(method, coords, this.board),
    261                 oldc = new Coords(method, oldcoords, this.board),
    262                 bb = this.board.getBoundingBox();
    263
    264             if (!Type.evaluate(this.line.visProp.scalable)) {
    265                 return this;
    266             }
    267
    268             // horizontal line
    269             if (Math.abs(this.line.stdform[1]) < Mat.eps && Math.abs(c.usrCoords[1] * oldc.usrCoords[1]) > Mat.eps) {
    270                 dx = oldc.usrCoords[1] / c.usrCoords[1];
    271                 bb[0] *= dx;
    272                 bb[2] *= dx;
    273                 this.board.setBoundingBox(bb, false);
    274             // vertical line
    275             } else if (Math.abs(this.line.stdform[2]) < Mat.eps && Math.abs(c.usrCoords[2] * oldc.usrCoords[2]) > Mat.eps) {
    276                 dy = oldc.usrCoords[2] / c.usrCoords[2];
    277                 bb[3] *= dy;
    278                 bb[1] *= dy;
    279                 this.board.setBoundingBox(bb, false);
    280             }
    281
    282             return this;
    283         },
    284
    285         /**
    286          * (Re-)calculates the ticks coordinates.
    287          * @private
    288          */
    289         calculateTicksCoordinates: function () {
    290             var coordsZero, bounds;
    291
    292             // Calculate Ticks width and height in Screen and User Coordinates
    293             this.setTicksSizeVariables();
    294             // If the parent line is not finite, we can stop here.
    295             if (Math.abs(this.dx) < Mat.eps &&
    296                 Math.abs(this.dy) < Mat.eps) {
    297                 return;
    298             }
    299
    300             // Get Zero
    301             coordsZero = this.getZeroCoordinates();
    302
    303             // Calculate lower bound and upper bound limits based on distance between p1 and centre and p2 and centre
    304             bounds = this.getLowerAndUpperBounds(coordsZero);
    305
    306             // Clean up
    307             this.ticks = [];
    308             this.labelsData = [];
    309             // Create Ticks Coordinates and Labels
    310             if (this.equidistant) {
    311                 this.generateEquidistantTicks(coordsZero, bounds);
    312             } else {
    313                 this.generateFixedTicks(coordsZero, bounds);
    314             }
    315
    316             return this;
    317         },
    318
    319         /**
    320          * Sets the variables used to set the height and slope of each tick.
    321          *
    322          * @private
    323          */
    324         setTicksSizeVariables: function () {
    325             var d,
    326                 distMaj = Type.evaluate(this.visProp.majorheight) * 0.5,
    327                 distMin = Type.evaluate(this.visProp.minorheight) * 0.5;
    328
    329             // ticks width and height in screen units
    330             this.dxMaj = this.line.stdform[1];
    331             this.dyMaj = this.line.stdform[2];
    332             this.dxMin = this.dxMaj;
    333             this.dyMin = this.dyMaj;
    334
    335             // ticks width and height in user units
    336             this.dx = this.dxMaj;
    337             this.dy = this.dyMaj;
    338
    339             // After this, the length of the vector (dxMaj, dyMaj) in screen coordinates is equal to distMaj pixel.
    340             d = Math.sqrt(
    341                 this.dxMaj * this.dxMaj * this.board.unitX * this.board.unitX +
    342                     this.dyMaj * this.dyMaj * this.board.unitY * this.board.unitY
    343             );
    344             this.dxMaj *= distMaj / d * this.board.unitX;
    345             this.dyMaj *= distMaj / d * this.board.unitY;
    346             this.dxMin *= distMin / d * this.board.unitX;
    347             this.dyMin *= distMin / d * this.board.unitY;
    348
    349             // Grid-like ticks?
    350             this.minStyle= (Type.evaluate(this.visProp.minorheight) < 0) ? 'infinite' : 'finite';
    351             this.majStyle= (Type.evaluate(this.visProp.majorheight) < 0) ? 'infinite' : 'finite';
    352         },
    353
    354         /**
    355          * Returns the coordinates of the point zero of the line.
    356          *
    357          * If the line is an {@link Axis}, the coordinates of the projection of the board's zero point is returned
    358          *
    359          * Otherwise, the coordinates of the point that acts as zero are established depending on the value of {@link JXG.Ticks#anchor}
    360          *
    361          * @returns {JXG.Coords} Coords object for the Zero point on the line
    362          * @private
    363          */
    364         getZeroCoordinates: function () {
    365             var c1x, c1y, c1z, c2x, c2y, c2z,
    366                 ev_a = Type.evaluate(this.visProp.anchor);
    367
    368             if (this.line.type === Const.OBJECT_TYPE_AXIS) {
    369                 return Geometry.projectPointToLine({
    370                     coords: {
    371                         usrCoords: [1, 0, 0]
    372                     }
    373                 }, this.line, this.board);
    374             }
    375
    376             c1z = this.line.point1.coords.usrCoords[0];
    377             c1x = this.line.point1.coords.usrCoords[1];
    378             c1y = this.line.point1.coords.usrCoords[2];
    379             c2z = this.line.point2.coords.usrCoords[0];
    380             c2x = this.line.point2.coords.usrCoords[1];
    381             c2y = this.line.point2.coords.usrCoords[2];
    382
    383             if (ev_a === 'right') {
    384                 return this.line.point2.coords;
    385             } else if (ev_a === 'middle') {
    386                 return new Coords(Const.COORDS_BY_USER, [
    387                     (c1z + c2z) * 0.5,
    388                     (c1x + c2x) * 0.5,
    389                     (c1y + c2y) * 0.5
    390                 ], this.board);
    391             } else if (Type.isNumber(ev_a)) {
    392                 return new Coords(Const.COORDS_BY_USER, [
    393                     c1z + (c2z - c1z) * ev_a,
    394                     c1x + (c2x - c1x) * ev_a,
    395                     c1y + (c2y - c1y) * ev_a
    396                 ], this.board);
    397             }
    398
    399             return this.line.point1.coords;
    400         },
    401
    402         /**
    403          * Calculate the lower and upper bounds for tick rendering
    404          * If {@link JXG.Ticks#includeBoundaries} is false, the boundaries will exclude point1 and point2
    405          *
    406          * @param  {JXG.Coords} coordsZero
    407          * @returns {String} type  (Optional) If type=='ticksdistance' the bounds are
    408          *                         the intersection of the line with the bounding box of the board.
    409          *                         Otherwise it is the projection of the corners of the bounding box
    410          *                         to the line. The first case i s needed to automatically
    411          *                         generate ticks. The second case is for drawing of the ticks.
    412          * @returns {Object}     contains the lower and upper bounds
    413          *
    414          * @private
    415          */
    416         getLowerAndUpperBounds: function (coordsZero, type) {
    417             var lowerBound, upperBound,
    418                 // The line's defining points that will be adjusted to be within the board limits
    419                 point1 = new Coords(Const.COORDS_BY_USER, this.line.point1.coords.usrCoords, this.board),
    420                 point2 = new Coords(Const.COORDS_BY_USER, this.line.point2.coords.usrCoords, this.board),
    421                 // Are the original defining points within the board?
    422                 isPoint1inBoard = (Math.abs(point1.usrCoords[0]) >= Mat.eps &&
    423                     point1.scrCoords[1] >= 0.0 && point1.scrCoords[1] <= this.board.canvasWidth &&
    424                     point1.scrCoords[2] >= 0.0 && point1.scrCoords[2] <= this.board.canvasHeight),
    425                 isPoint2inBoard = (Math.abs(point2.usrCoords[0]) >= Mat.eps &&
    426                     point2.scrCoords[1] >= 0.0 && point2.scrCoords[1] <= this.board.canvasWidth &&
    427                     point2.scrCoords[2] >= 0.0 && point2.scrCoords[2] <= this.board.canvasHeight),
    428                 // We use the distance from zero to P1 and P2 to establish lower and higher points
    429                 dZeroPoint1, dZeroPoint2,
    430                 ev_sf = Type.evaluate(this.line.visProp.straightfirst),
    431                 ev_sl = Type.evaluate(this.line.visProp.straightlast),
    432                 ev_i = Type.evaluate(this.visProp.includeboundaries),
    433                 obj;
    434
    435             // Adjust line limit points to be within the board
    436             if (Type.exists(type) || type === 'tickdistance') {
    437                 // The good old calcStraight is needed for determining the distance between major ticks.
    438                 // Here, only the visual area is of importance
    439                 Geometry.calcStraight(this.line, point1, point2, Type.evaluate(this.line.visProp.margin));
    440             } else {
    441                 // This function projects the corners of the board to the line.
    442                 // This is important for diagonal lines with infinite tick lines.
    443                 Geometry.calcLineDelimitingPoints(this.line, point1, point2);
    444             }
    445             // Shorten ticks bounds such that ticks are not through arrow heads
    446             obj = this.board.renderer.getPositionArrowHead(this.line, point1, point2,
    447                         Type.evaluate(this.line.visProp.strokewidth));
    448             point1.setCoordinates(Const.COORDS_BY_SCREEN, [
    449                     point1.scrCoords[1] - obj.d1x,
    450                     point1.scrCoords[2] - obj.d1y,
    451                 ]);
    452             point2.setCoordinates(Const.COORDS_BY_SCREEN, [
    453                     point2.scrCoords[1] - obj.d2x,
    454                     point2.scrCoords[2] - obj.d2y,
    455                 ]);
    456
    457             // Calculate distance from Zero to P1 and to P2
    458             dZeroPoint1 = this.getDistanceFromZero(coordsZero, point1);
    459             dZeroPoint2 = this.getDistanceFromZero(coordsZero, point2);
    460
    461             // We have to establish if the direction is P1->P2 or P2->P1 to set the lower and upper
    462             // boundaries appropriately. As the distances contain also a sign to indicate direction,
    463             // we can compare dZeroPoint1 and dZeroPoint2 to establish the line direction
    464             if (dZeroPoint1 < dZeroPoint2) { // Line goes P1->P2
    465                 lowerBound = dZeroPoint1;
    466                 if (!ev_sf && isPoint1inBoard && !ev_i) {
    467                     lowerBound += Mat.eps;
    468                 }
    469                 upperBound = dZeroPoint2;
    470                 if (!ev_sl && isPoint2inBoard && !ev_i) {
    471                     upperBound -= Mat.eps;
    472                 }
    473             } else if (dZeroPoint2 < dZeroPoint1) { // Line goes P2->P1
    474                 lowerBound = dZeroPoint2;
    475                 if (!ev_sl && isPoint2inBoard && !ev_i) {
    476                     lowerBound += Mat.eps;
    477                 }
    478                 upperBound = dZeroPoint1;
    479                 if (!ev_sf && isPoint1inBoard && !ev_i) {
    480                     upperBound -= Mat.eps;
    481                 }
    482             } else { // P1 = P2 = Zero, we can't do a thing
    483                 lowerBound = 0;
    484                 upperBound = 0;
    485             }
    486
    487             return {
    488                 lower: lowerBound,
    489                 upper: upperBound
    490             };
    491         },
    492
    493         /**
    494          * Calculates the distance in user coordinates from zero to a given point including its sign
    495          *
    496          * @param  {JXG.Coords} zero  coordinates of the point considered zero
    497          * @param  {JXG.Coords} point coordinates of the point to find out the distance
    498          * @returns {Number}           distance between zero and point, including its sign
    499          * @private
    500          */
    501         getDistanceFromZero: function (zero, point) {
    502             var eps = Mat.eps,
    503                 distance = zero.distance(Const.COORDS_BY_USER, point);
    504
    505             // Establish sign
    506             if (this.line.type === Const.OBJECT_TYPE_AXIS) {
    507                 if ((Mat.relDif(zero.usrCoords[1], point.usrCoords[1]) > eps &&
    508                         zero.usrCoords[1] - point.usrCoords[1] > eps) ||
    509                     (Mat.relDif(zero.usrCoords[2], point.usrCoords[2]) > eps &&
    510                         zero.usrCoords[2] - point.usrCoords[2] > eps)) {
    511
    512                     distance *= -1;
    513                 }
    514             } else if (Type.evaluate(this.visProp.anchor) === 'right') {
    515                 if (Geometry.isSameDirection(zero, this.line.point1.coords, point)) {
    516                     distance *= -1;
    517                 }
    518             } else {
    519                 if (!Geometry.isSameDirection(zero, this.line.point2.coords, point)) {
    520                     distance *= -1;
    521                 }
    522             }
    523             return distance;
    524         },
    525
    526         /**
    527          * Creates ticks coordinates and labels automatically.
    528          * The frequency of ticks is affected by the values of {@link JXG.Ticks#insertTicks} and {@link JXG.Ticks#ticksDistance}
    529          *
    530          * @param  {JXG.Coords} coordsZero coordinates of the point considered zero
    531          * @param  {Object}     bounds     contains the lower and upper boundaries for ticks placement
    532          * @private
    533          */
    534         generateEquidistantTicks: function (coordsZero, bounds) {
    535             var tickPosition,
    536                 // Calculate X and Y distance between two major ticks
    537                 deltas = this.getXandYdeltas(),
    538                 // Distance between two major ticks in user coordinates
    539                 ticksDelta = (this.equidistant ? this.ticksFunction(1) : this.ticksDelta),
    540                 ev_it = Type.evaluate(this.visProp.insertticks),
    541                 ev_mt = Type.evaluate(this.visProp.minorticks);
    542
    543             // adjust ticks distance
    544             ticksDelta *= Type.evaluate(this.visProp.scale);
    545             if (ev_it && this.minTicksDistance > Mat.eps) {
    546                 ticksDelta = this.adjustTickDistance(ticksDelta, coordsZero, deltas);
    547                 ticksDelta /= (ev_mt + 1);
    548             } else if (!ev_it) {
    549                 ticksDelta /= (ev_mt + 1);
    550             }
    551             this.ticksDelta = ticksDelta;
    552
    553             if (ticksDelta < Mat.eps) {
    554                 return;
    555             }
    556
    557             // Position ticks from zero to the positive side while not reaching the upper boundary
    558             tickPosition = 0;
    559             if (!Type.evaluate(this.visProp.drawzero)) {
    560                 tickPosition = ticksDelta;
    561             }
    562             while (tickPosition <= bounds.upper) {
    563                 // Only draw ticks when we are within bounds, ignore case where  tickPosition < lower < upper
    564                 if (tickPosition >= bounds.lower) {
    565                     this.processTickPosition(coordsZero, tickPosition, ticksDelta, deltas);
    566                 }
    567                 tickPosition += ticksDelta;
    568             }
    569
    570             // Position ticks from zero (not inclusive) to the negative side while not reaching the lower boundary
    571             tickPosition = -ticksDelta;
    572             while (tickPosition >= bounds.lower) {
    573                 // Only draw ticks when we are within bounds, ignore case where lower < upper < tickPosition
    574                 if (tickPosition <= bounds.upper) {
    575                     this.processTickPosition(coordsZero, tickPosition, ticksDelta, deltas);
    576                 }
    577                 tickPosition -= ticksDelta;
    578             }
    579         },
    580
    581         /**
    582          * Auxiliary method used by {@link JXG.Ticks#generateEquidistantTicks} to adjust the
    583          * distance between two ticks depending on {@link JXG.Ticks#minTicksDistance} value
    584          *
    585          * @param  {Number}     ticksDelta  distance between two major ticks in user coordinates
    586          * @param  {JXG.Coords} coordsZero  coordinates of the point considered zero
    587          * @param  {Object}     deltas      x and y distance in pixel between two user units
    588          * @param  {Object}     bounds      upper and lower bound of the tick positions in user units.
    589          * @private
    590          */
    591         adjustTickDistance: function (ticksDelta, coordsZero, deltas) {
    592             var nx, ny, bounds,
    593                 distScr,
    594                 sgn = 1;
    595
    596             bounds = this.getLowerAndUpperBounds(coordsZero, 'ticksdistance');
    597             nx = coordsZero.usrCoords[1] + deltas.x * ticksDelta;
    598             ny = coordsZero.usrCoords[2] + deltas.y * ticksDelta;
    599             distScr = coordsZero.distance(Const.COORDS_BY_SCREEN, new Coords(Const.COORDS_BY_USER, [nx, ny], this.board));
    600             while (distScr / (Type.evaluate(this.visProp.minorticks) + 1) < this.minTicksDistance) {
    601                 if (sgn === 1) {
    602                     ticksDelta *= 2;
    603                 } else {
    604                     ticksDelta *= 5;
    605                 }
    606                 sgn *= -1;
    607
    608                 nx = coordsZero.usrCoords[1] + deltas.x * ticksDelta;
    609                 ny = coordsZero.usrCoords[2] + deltas.y * ticksDelta;
    610                 distScr = coordsZero.distance(Const.COORDS_BY_SCREEN, new Coords(Const.COORDS_BY_USER, [nx, ny], this.board));
    611             }
    612             return ticksDelta;
    613         },
    614
    615         /**
    616          * Auxiliary method used by {@link JXG.Ticks#generateEquidistantTicks} to create a tick
    617          * in the line at the given tickPosition.
    618          *
    619          * @param  {JXG.Coords} coordsZero    coordinates of the point considered zero
    620          * @param  {Number}     tickPosition  current tick position relative to zero
    621          * @param  {Number}     ticksDelta    distance between two major ticks in user coordinates
    622          * @param  {Object}     deltas      x and y distance between two major ticks
    623          * @private
    624          */
    625         processTickPosition: function (coordsZero, tickPosition, ticksDelta, deltas) {
    626             var x, y, tickCoords, ti;
    627
    628             // Calculates tick coordinates
    629             x = coordsZero.usrCoords[1] + tickPosition * deltas.x;
    630             y = coordsZero.usrCoords[2] + tickPosition * deltas.y;
    631             tickCoords = new Coords(Const.COORDS_BY_USER, [x, y], this.board);
    632
    633             // Test if tick is a major tick.
    634             // This is the case if tickPosition/ticksDelta is
    635             // a multiple of the number of minorticks+1
    636             tickCoords.major = Math.round(tickPosition / ticksDelta) % (Type.evaluate(this.visProp.minorticks) + 1) === 0;
    637
    638             // Compute the start position and the end position of a tick.
    639             // If both positions are out of the canvas, ti is empty.
    640             ti = this.tickEndings(tickCoords, tickCoords.major);
    641             if (ti.length === 3) {
    642                 this.ticks.push(ti);
    643                 if (tickCoords.major && Type.evaluate(this.visProp.drawlabels)) {
    644                     this.labelsData.push(
    645                         this.generateLabelData(
    646                             this.generateLabelText(tickCoords, coordsZero),
    647                             tickCoords,
    648                             this.ticks.length
    649                         )
    650                     );
    651                 } else {
    652                     this.labelsData.push(null);
    653                 }
    654             }
    655         },
    656
    657         /**
    658          * Creates ticks coordinates and labels based on {@link JXG.Ticks#fixedTicks} and {@link JXG.Ticks#labels}.
    659          *
    660          * @param  {JXG.Coords} coordsZero Coordinates of the point considered zero
    661          * @param  {Object}     bounds     contains the lower and upper boundaries for ticks placement
    662          * @private
    663          */
    664         generateFixedTicks: function (coordsZero, bounds) {
    665             var tickCoords, labelText, i, ti,
    666                 x, y,
    667                 hasLabelOverrides = Type.isArray(this.visProp.labels),
    668                 // Calculate X and Y distance between two major points in the line
    669                 deltas = this.getXandYdeltas(),
    670                 ev_dl = Type.evaluate(this.visProp.drawlabels);
    671
    672             for (i = 0; i < this.fixedTicks.length; i++) {
    673                 x = coordsZero.usrCoords[1] + this.fixedTicks[i] * deltas.x;
    674                 y = coordsZero.usrCoords[2] + this.fixedTicks[i] * deltas.y;
    675                 tickCoords = new Coords(Const.COORDS_BY_USER, [x, y], this.board);
    676
    677                 // Compute the start position and the end position of a tick.
    678                 // If tick is out of the canvas, ti is empty.
    679                 ti = this.tickEndings(tickCoords, true);
    680                 if (ti.length === 3 && this.fixedTicks[i] >= bounds.lower &&
    681                     this.fixedTicks[i] <= bounds.upper) {
    682                     this.ticks.push(ti);
    683
    684                     if (ev_dl &&
    685                             (hasLabelOverrides || Type.exists(this.visProp.labels[i]))) {
    686                         labelText = hasLabelOverrides ?
    687                                         Type.evaluate(this.visProp.labels[i]) : this.fixedTicks[i];
    688                         this.labelsData.push(
    689                             this.generateLabelData(
    690                                 this.generateLabelText(tickCoords, coordsZero, labelText),
    691                                 tickCoords,
    692                                 i
    693                             )
    694                         );
    695                     } else {
    696                         this.labelsData.push(null);
    697                     }
    698                 }
    699             }
    700         },
    701
    702         /**
    703          * Calculates the x and y distance in pixel between two units in user space.
    704          *
    705          * @returns {Object}
    706          * @private
    707          */
    708         getXandYdeltas: function () {
    709             var
    710                 // Auxiliary points to store the start and end of the line according to its direction
    711                 point1UsrCoords, point2UsrCoords,
    712                 distP1P2 = this.line.point1.Dist(this.line.point2);
    713
    714             if (this.line.type === Const.OBJECT_TYPE_AXIS) {
    715                 // When line is an Axis, direction depends on Board Coordinates system
    716
    717                 // assume line.point1 and line.point2 are in correct order
    718                 point1UsrCoords = this.line.point1.coords.usrCoords;
    719                 point2UsrCoords = this.line.point2.coords.usrCoords;
    720
    721                 // Check if direction is incorrect, then swap
    722                 if (point1UsrCoords[1] > point2UsrCoords[1] ||
    723                         (Math.abs(point1UsrCoords[1] - point2UsrCoords[1]) < Mat.eps &&
    724                         point1UsrCoords[2] > point2UsrCoords[2])) {
    725                     point1UsrCoords = this.line.point2.coords.usrCoords;
    726                     point2UsrCoords = this.line.point1.coords.usrCoords;
    727                 }
    728             } else {
    729                 // line direction is always from P1 to P2 for non Axis types
    730                 point1UsrCoords = this.line.point1.coords.usrCoords;
    731                 point2UsrCoords = this.line.point2.coords.usrCoords;
    732             }
    733             return {
    734                 x: (point2UsrCoords[1] - point1UsrCoords[1]) / distP1P2,
    735                 y: (point2UsrCoords[2] - point1UsrCoords[2]) / distP1P2
    736             };
    737         },
    738
    739         /**
    740          * Check if (parts of) the tick is inside the canvas. The tick intersects the boundary
    741          * at two positions: [x[0], y[0]] and [x[1], y[1]] in screen coordinates.
    742          * @param  {Array}  x Array of length two
    743          * @param  {Array}  y Array of length two
    744          * @return {Boolean}   true if parts of the tick are inside of the canvas or on the boundary.
    745          */
    746         _isInsideCanvas: function(x, y, m) {
    747             var cw = this.board.canvasWidth,
    748                 ch = this.board.canvasHeight;
    749
    750             if (m === undefined) {
    751                 m = 0;
    752             }
    753             return (x[0] >= m && x[0] <= cw - m && y[0] >= m && y[0] <= ch - m) ||
    754                     (x[1] >= m && x[1] <= cw - m && y[1] >= m && y[1] <= ch - m);
    755         },
    756
    757         /**
    758          * @param {JXG.Coords} coords Coordinates of the tick on the line.
    759          * @param {Boolean} major True if tick is major tick.
    760          * @returns {Array} Array of length 3 containing start and end coordinates in screen coordinates
    761          *                 of the tick (arrays of length 2). 3rd entry is true if major tick otherwise false.
    762          *                 If the tick is outside of the canvas, the return array is empty.
    763          * @private
    764          */
    765         tickEndings: function (coords, major) {
    766             var c, lineStdForm, intersection,
    767                 dxs, dys,
    768                 style,
    769                 x = [-2000000, -2000000],
    770                 y = [-2000000, -2000000];
    771
    772             c = coords.scrCoords;
    773             if (major) {
    774                 dxs = this.dxMaj;
    775                 dys = this.dyMaj;
    776                 style = this.majStyle;
    777             } else {
    778                 dxs = this.dxMin;
    779                 dys = this.dyMin;
    780                 style = this.minStyle;
    781             }
    782             lineStdForm = [-dys * c[1] - dxs * c[2], dys, dxs];
    783
    784             // For all ticks regardless if of finite or infinite
    785             // tick length the intersection with the canvas border is
    786             // computed.
    787             if (style === 'infinite') {
    788                 intersection = Geometry.meetLineBoard(lineStdForm, this.board);
    789                 x[0] = intersection[0].scrCoords[1];
    790                 x[1] = intersection[1].scrCoords[1];
    791                 y[0] = intersection[0].scrCoords[2];
    792                 y[1] = intersection[1].scrCoords[2];
    793             } else {
    794                 x[0] = c[1] + dxs * Type.evaluate(this.visProp.tickendings[0]);
    795                 y[0] = c[2] - dys * Type.evaluate(this.visProp.tickendings[0]);
    796                 x[1] = c[1] - dxs * Type.evaluate(this.visProp.tickendings[1]);
    797                 y[1] = c[2] + dys * Type.evaluate(this.visProp.tickendings[1]);
    798             }
    799
    800             // Check if (parts of) the tick is inside the canvas.
    801             if (this._isInsideCanvas(x, y)) {
    802                 return [x, y, major];
    803             }
    804
    805             return [];
    806         },
    807
    808         /**
    809          * Format label texts. Show the desired number of digits
    810          * and use utf-8 minus sign.
    811          * @param  {Number} value Number to be displayed
    812          * @return {String}       The value converted into a string.
    813          * @private
    814          */
    815         formatLabelText: function(value) {
    816             var labelText = value.toString(),
    817                 ev_s = Type.evaluate(this.visProp.scalesymbol);
    818
    819             // if value is Number
    820             if (Type.isNumber(value)) {
    821                 if (labelText.length > Type.evaluate(this.visProp.maxlabellength) ||
    822                         labelText.indexOf('e') !== -1) {
    823                     labelText = value.toPrecision(Type.evaluate(this.visProp.precision)).toString();
    824                 }
    825                 if (labelText.indexOf('.') > -1 && labelText.indexOf('e') === -1) {
    826                     // trim trailing zeros
    827                     labelText = labelText.replace(/0+$/, '');
    828                     // trim trailing .
    829                     labelText = labelText.replace(/\.$/, '');
    830                 }
    831             }
    832
    833             if (ev_s.length > 0) {
    834                 if (labelText === '1') {
    835                     labelText = ev_s;
    836                 } else if (labelText === '-1') {
    837                     labelText = '-' + ev_s;
    838                 } else if (labelText !== '0') {
    839                     labelText = labelText + ev_s;
    840                 }
    841             }
    842
    843             if (Type.evaluate(this.visProp.useunicodeminus)) {
    844                 labelText = labelText.replace(/-/g, '\u2212');
    845             }
    846             return labelText;
    847         },
    848
    849         /**
    850          * Creates the label text for a given tick. A value for the text can be provided as a number or string
    851          *
    852          * @param  {JXG.Coords}    tick  The Coords-object of the tick to create a label for
    853          * @param  {JXG.Coords}    zero  The Coords-object of line's zero
    854          * @param  {Number|String} value A predefined value for this tick
    855          * @returns {String}
    856          * @private
    857          */
    858         generateLabelText: function (tick, zero, value) {
    859             var labelText,
    860                 distance = this.getDistanceFromZero(zero, tick);
    861
    862             if (Math.abs(distance) < Mat.eps) { // Point is zero
    863                 labelText = '0';
    864             } else {
    865                 // No value provided, equidistant, so assign distance as value
    866                 if (!Type.exists(value)) { // could be null or undefined
    867                     value = distance / Type.evaluate(this.visProp.scale);
    868                 }
    869
    870                 labelText = this.formatLabelText(value);
    871             }
    872
    873             return labelText;
    874         },
    875
    876         /**
    877          * Create a tick label data, i.e. text and coordinates
    878          * @param  {String}     labelText
    879          * @param  {JXG.Coords} tick
    880          * @param  {Number}     tickNumber
    881          * @returns {Object} with properties 'x', 'y', 't' (text), 'i' (tick number) or null in case of o label
    882          * @private
    883          */
    884          generateLabelData: function (labelText, tick, tickNumber) {
    885              var xa, ya, m, fs;
    886
    887              // Test if large portions of the label are inside of the canvas
    888              // This is the last chance to abandon the creation of the label if it is mostly
    889              // outside of the canvas.
    890              fs = Type.evaluate(this.visProp.label.fontsize);
    891              xa = [tick.scrCoords[1], tick.scrCoords[1]];
    892              ya = [tick.scrCoords[2], tick.scrCoords[2]];
    893              m = (fs === undefined) ? 12 : fs;
    894              m *= 1.5;
    895              if (!this._isInsideCanvas(xa, ya, m)) {
    896                  return null;
    897              }
    898
    899              xa = Type.evaluate(this.visProp.label.offset[0]);
    900              ya = Type.evaluate(this.visProp.label.offset[1]);
    901
    902              return {
    903                  x: tick.usrCoords[1] + xa / (this.board.unitX),
    904                  y: tick.usrCoords[2] + ya / (this.board.unitY),
    905                  t: labelText,
    906                  i: tickNumber
    907              };
    908          },
    909
    910         /**
    911          * Recalculate the tick positions and the labels.
    912          * @returns {JXG.Ticks}
    913          */
    914         update: function () {
    915             if (this.needsUpdate) {
    916                 //this.visPropCalc.visible = Type.evaluate(this.visProp.visible);
    917                 // A canvas with no width or height will create an endless loop, so ignore it
    918                 if (this.board.canvasWidth !== 0 && this.board.canvasHeight !== 0) {
    919                     this.calculateTicksCoordinates();
    920                 }
    921                 // this.updateVisibility(this.line.visPropCalc.visible);
    922                 //
    923                 // for (var i = 0; i < this.labels.length; i++) {
    924                 //     if (this.labels[i] !== null) {
    925                 //         this.labels[i].prepareUpdate()
    926                 //             .updateVisibility(this.line.visPropCalc.visible)
    927                 //             .updateRenderer();
    928                 //     }
    929                 // }
    930             }
    931
    932             return this;
    933         },
    934
    935         /**
    936          * Uses the boards renderer to update the arc.
    937          * @returns {JXG.Ticks} Reference to the object.
    938          */
    939         updateRenderer: function () {
    940             if (!this.needsUpdate) {
    941                 return this;
    942             }
    943
    944             if (this.visPropCalc.visible) {
    945                 this.board.renderer.updateTicks(this);
    946             }
    947             this.updateRendererLabels();
    948
    949             this.setDisplayRendNode();
    950             // if (this.visPropCalc.visible != this.visPropOld.visible) {
    951             //     this.board.renderer.display(this, this.visPropCalc.visible);
    952             //     this.visPropOld.visible = this.visPropCalc.visible;
    953             // }
    954
    955             this.needsUpdate = false;
    956             return this;
    957         },
    958
    959         /**
    960          * Updates the label elements of the major ticks.
    961          *
    962          * @private
    963          * @returns {JXG.Ticks} Reference to the object.
    964          */
    965         updateRendererLabels: function() {
    966             var i, j,
    967                 lenData, lenLabels,
    968                 attr,
    969                 label, ld,
    970                 visible;
    971
    972             // The number of labels needed
    973             lenData = this.labelsData.length;
    974             // The number of labels which already exist
    975             lenLabels = this.labels.length;
    976
    977             for (i = 0, j = 0; i < lenData; i++) {
    978                 if (this.labelsData[i] === null) {
    979                     continue;
    980                 }
    981
    982                 ld = this.labelsData[i];
    983                 if (j < lenLabels) {
    984                     // Take an already existing text element
    985                     label = this.labels[j];
    986                     label.setText(ld.t);
    987                     label.setCoords(ld.x, ld.y);
    988                     j++;
    989                 } else {
    990                     // A new text element is needed
    991                     this.labelCounter += 1;
    992
    993                     attr = {
    994                         isLabel: true,
    995                         layer: this.board.options.layer.line,
    996                         highlightStrokeColor: this.board.options.text.strokeColor,
    997                         highlightStrokeWidth: this.board.options.text.strokeWidth,
    998                         highlightStrokeOpacity: this.board.options.text.strokeOpacity,
    999                         priv: this.visProp.priv
    1000                     };
    1001                     attr = Type.deepCopy(attr, this.visProp.label);
    1002                     attr.id = this.id + ld.i + 'Label' + this.labelCounter;
    1003
    1004                     label = Text.createText(this.board, [ld.x, ld.y, ld.t], attr);
    1005                     label.isDraggable = false;
    1006                     label.dump = false;
    1007                     this.labels.push(label);
    1008                 }
    1009
    1010                 visible = Type.evaluate(this.visProp.label.visible);
    1011                 if (visible === 'inherit') {
    1012                     visible = this.visPropCalc.visible;
    1013                 }
    1014                 label.prepareUpdate()
    1015                     .updateVisibility(visible)
    1016                     .updateRenderer();
    1017                 //this.board.renderer.display(label, visible);
    1018
    1019                 label.distanceX = Type.evaluate(this.visProp.label.offset[0]);
    1020                 label.distanceY = Type.evaluate(this.visProp.label.offset[1]);
    1021             }
    1022
    1023             // Hide unused labels
    1024             lenData = j;
    1025             for (j = lenData; j < lenLabels; j++) {
    1026                 this.board.renderer.display(this.labels[j], false);
    1027                 // Tick labels have the attribute "visible: 'inherit'"
    1028                 // This must explicitely set to false, otherwise
    1029                 // this labels would be set to visible in the upcoming
    1030                 // update of the labels.
    1031                 this.labels[j].visProp.visible = false;
    1032             }
    1033
    1034             return this;
    1035         },
    1036
    1037         hideElement: function () {
    1038             var i;
    1039
    1040             JXG.deprecated('Element.hideElement()', 'Element.setDisplayRendNode()');
    1041
    1042             this.visPropCalc.visible = false;
    1043             this.board.renderer.display(this, false);
    1044             for (i = 0; i < this.labels.length; i++) {
    1045                 if (Type.exists(this.labels[i])) {
    1046                     this.labels[i].hideElement();
    1047                 }
    1048             }
    1049
    1050             return this;
    1051         },
    1052
    1053         showElement: function () {
    1054             var i;
    1055
    1056             JXG.deprecated('Element.showElement()', 'Element.setDisplayRendNode()');
    1057
    1058             this.visPropCalc.visible = true;
    1059             this.board.renderer.display(this, false);
    1060
    1061             for (i = 0; i < this.labels.length; i++) {
    1062                 if (Type.exists(this.labels[i])) {
    1063                     this.labels[i].showElement();
    1064                 }
    1065             }
    1066
    1067             return this;
    1068         }
    1069     });
    1070
    1071     /**
    1072      * @class Ticks are used as distance markers on a line.
    1073      * @pseudo
    1074      * @description
    1075      * @name Ticks
    1076      * @augments JXG.Ticks
    1077      * @constructor
    1078      * @type JXG.Ticks
    1079      * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.
    1080      * @param {JXG.Line} line The parents consist of the line the ticks are going to be attached to.
    1081      * @param {Number} distance Number defining the distance between two major ticks or an
    1082      * array defining static ticks. Alternatively, the distance can be specified with the attribute
    1083      * "ticksDistance". For arbitrary lines (and not axes) a "zero coordinate" is determined
    1084      * which defines where the first tick is positioned. This zero coordinate
    1085      * can be altered with the attribute "anchor". Possible values are "left", "middle", "right" or a number.
    1086      * The default value is "middle".
    1087      *
    1088      * @example
    1089      * // Create an axis providing two coord pairs.
    1090      *   var p1 = board.create('point', [0, 3]);
    1091      *   var p2 = board.create('point', [1, 3]);
    1092      *   var l1 = board.create('line', [p1, p2]);
    1093      *   var t = board.create('ticks', [l1], {ticksDistance: 2});
    1094      * </pre><div class="jxgbox" id="ee7f2d68-75fc-4ec0-9931-c76918427e63" style="width: 300px; height: 300px;"></div>
    1095      * <script type="text/javascript">
    1096      * (function () {
    1097      *   var board = JXG.JSXGraph.initBoard('ee7f2d68-75fc-4ec0-9931-c76918427e63', {boundingbox: [-1, 7, 7, -1], showcopyright: false, shownavigation: false});
    1098      *   var p1 = board.create('point', [0, 3]);
    1099      *   var p2 = board.create('point', [1, 3]);
    1100      *   var l1 = board.create('line', [p1, p2]);
    1101      *   var t = board.create('ticks', [l1, 2], {ticksDistance: 2});
    1102      * })();
    1103      * </script><pre>
    1104      */
    1105     JXG.createTicks = function (board, parents, attributes) {
    1106         var el, dist,
    1107             attr = Type.copyAttributes(attributes, board.options, 'ticks');
    1108
    1109         if (parents.length < 2) {
    1110             dist = attr.ticksdistance;
    1111         } else {
    1112             dist = parents[1];
    1113         }
    1114
    1115         if (parents[0].elementClass === Const.OBJECT_CLASS_LINE) {
    1116             el = new JXG.Ticks(parents[0], dist, attr);
    1117         } else {
    1118             throw new Error("JSXGraph: Can't create Ticks with parent types '" + (typeof parents[0]) + "'.");
    1119         }
    1120
    1121         // deprecated
    1122         if (Type.isFunction(attr.generatelabelvalue)) {
    1123             el.generateLabelText = attr.generatelabelvalue;
    1124         }
    1125         if (Type.isFunction(attr.generatelabeltext)) {
    1126             el.generateLabelText = attr.generatelabeltext;
    1127         }
    1128
    1129         el.setParents(parents[0]);
    1130         el.isDraggable = true;
    1131         el.fullUpdate(parents[0].visPropCalc.visible);
    1132
    1133         return el;
    1134     };
    1135
    1136     /**
    1137      * @class Hashes can be used to mark congruent lines.
    1138      * @pseudo
    1139      * @description
    1140      * @name Hatch
    1141      * @augments JXG.Ticks
    1142      * @constructor
    1143      * @type JXG.Ticks
    1144      * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown.
    1145      * @param {JXG.Line} line The line the hatch marks are going to be attached to.
    1146      * @param {Number} numberofhashes Number of dashes.
    1147      * @example
    1148      * // Create an axis providing two coord pairs.
    1149      *   var p1 = board.create('point', [0, 3]);
    1150      *   var p2 = board.create('point', [1, 3]);
    1151      *   var l1 = board.create('line', [p1, p2]);
    1152      *   var t = board.create('hatch', [l1, 3]);
    1153      * </pre><div class="jxgbox" id="4a20af06-4395-451c-b7d1-002757cf01be" style="width: 300px; height: 300px;"></div>
    1154      * <script type="text/javascript">
    1155      * (function () {
    1156      *   var board = JXG.JSXGraph.initBoard('4a20af06-4395-451c-b7d1-002757cf01be', {boundingbox: [-1, 7, 7, -1], showcopyright: false, shownavigation: false});
    1157      *   var p1 = board.create('point', [0, 3]);
    1158      *   var p2 = board.create('point', [1, 3]);
    1159      *   var l1 = board.create('line', [p1, p2]);
    1160      *   var t = board.create('hatch', [l1, 3]);
    1161      * })();
    1162      * </script><pre>
    1163      *
    1164      * @example
    1165      * // Alter the position of the hatch
    1166      * var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-10, 10, 10, -5], keepaspectratio:true});
    1167      *
    1168      * var p = board.create('point', [-5, 0]);
    1169      * var q = board.create('point', [5, 0]);
    1170      * var li = board.create('line', [p, q]);
    1171      * var h = board.create('hatch', [li, 2], {anchor: 0.2});
    1172      *
    1173      * </pre><div id="05d720ee-99c9-11e6-a9c7-901b0e1b8723" class="jxgbox" style="width: 300px; height: 300px;"></div>
    1174      * <script type="text/javascript">
    1175      *     (function() {
    1176      *         var board = JXG.JSXGraph.initBoard('05d720ee-99c9-11e6-a9c7-901b0e1b8723',
    1177      *             {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false});
    1178      *     var board = JXG.JSXGraph.initBoard('jxgbox', {boundingbox: [-10, 10, 10, -5], keepaspectratio:true});
    1179      *
    1180      *     var p = board.create('point', [-5, 0]);
    1181      *     var q = board.create('point', [5, 0]);
    1182      *     var li = board.create('line', [p, q]);
    1183      *     var h = board.create('hatch', [li, 2], {anchor: 0.2});
    1184      *
    1185      *     })();
    1186      *
    1187      * </script><pre>
    1188      *
    1189      */
    1190     JXG.createHatchmark = function (board, parents, attributes) {
    1191         var num, i, base, width, totalwidth, el,
    1192             pos = [],
    1193             attr = Type.copyAttributes(attributes, board.options, 'hatch');
    1194
    1195         if (parents[0].elementClass !== Const.OBJECT_CLASS_LINE || typeof parents[1] !== 'number') {
    1196             throw new Error("JSXGraph: Can't create Hatch mark with parent types '" + (typeof parents[0]) + "' and '" + (typeof parents[1]) + " and ''" + (typeof parents[2]) + "'.");
    1197         }
    1198
    1199         num = parents[1];
    1200         width = attr.ticksdistance;
    1201         totalwidth = (num - 1) * width;
    1202         base = -totalwidth * 0.5;
    1203
    1204         for (i = 0; i < num; i++) {
    1205             pos[i] = base + i * width;
    1206         }
    1207
    1208         el = board.create('ticks', [parents[0], pos], attr);
    1209         el.elType = 'hatch';
    1210
    1211         return el;
    1212     };
    1213
    1214     JXG.registerElement('ticks', JXG.createTicks);
    1215     JXG.registerElement('hash', JXG.createHatchmark);
    1216     JXG.registerElement('hatch', JXG.createHatchmark);
    1217
    1218     return {
    1219         Ticks: JXG.Ticks,
    1220         createTicks: JXG.createTicks,
    1221         createHashmark: JXG.createHatchmark,
    1222         createHatchmark: JXG.createHatchmark
    1223     };
    1224 });
    1225