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 Some functionalities in this file were developed as part of a software project 33 with students. We would like to thank all contributors for their help: 34 35 Winter semester 2023/2024: 36 Matti Kirchbach 37 */ 38 39 /*global JXG: true, define: true*/ 40 /*jslint nomen: true, plusplus: true*/ 41 42 /** 43 * @fileoverview The geometry object Line is defined in this file. Line stores all 44 * style and functional properties that are required to draw and move a line on 45 * a board. 46 */ 47 48 import JXG from "../jxg.js"; 49 import Mat from "../math/math.js"; 50 import Geometry from "../math/geometry.js"; 51 import Numerics from "../math/numerics.js"; 52 import Statistics from "../math/statistics.js"; 53 import Const from "./constants.js"; 54 import Coords from "./coords.js"; 55 import GeometryElement from "./element.js"; 56 import Type from "../utils/type.js"; 57 58 /** 59 * The Line class is a basic class for all kind of line objects, e.g. line, arrow, and axis. It is usually defined by two points and can 60 * be intersected with some other geometry elements. 61 * @class Creates a new basic line object. Do not use this constructor to create a line. 62 * Use {@link JXG.Board#create} with 63 * type {@link Line}, {@link Arrow}, or {@link Axis} instead. 64 * @constructor 65 * @augments JXG.GeometryElement 66 * @param {String|JXG.Board} board The board the new line is drawn on. 67 * @param {Point} p1 Startpoint of the line. 68 * @param {Point} p2 Endpoint of the line. 69 * @param {Object} attributes Javascript object containing attributes like name, id and colors. 70 */ 71 JXG.Line = function (board, p1, p2, attributes) { 72 this.constructor(board, attributes, Const.OBJECT_TYPE_LINE, Const.OBJECT_CLASS_LINE); 73 74 /** 75 * Startpoint of the line. You really should not set this field directly as it may break JSXGraph's 76 * update system so your construction won't be updated properly. 77 * @type JXG.Point 78 */ 79 this.point1 = this.board.select(p1); 80 81 /** 82 * Endpoint of the line. Just like {@link JXG.Line.point1} you shouldn't write this field directly. 83 * @type JXG.Point 84 */ 85 this.point2 = this.board.select(p2); 86 87 /** 88 * Array of ticks storing all the ticks on this line. Do not set this field directly and use 89 * {@link JXG.Line#addTicks} and {@link JXG.Line#removeTicks} to add and remove ticks to and from the line. 90 * @type Array 91 * @see JXG.Ticks 92 */ 93 this.ticks = []; 94 95 /** 96 * Reference of the ticks created automatically when constructing an axis. 97 * @type JXG.Ticks 98 * @see JXG.Ticks 99 */ 100 this.defaultTicks = null; 101 102 /** 103 * If the line is the border of a polygon, the polygon object is stored, otherwise null. 104 * @type JXG.Polygon 105 * @default null 106 * @private 107 */ 108 this.parentPolygon = null; 109 110 /* Register line at board */ 111 this.id = this.board.setId(this, "L"); 112 this.board.renderer.drawLine(this); 113 this.board.finalizeAdding(this); 114 115 this.elType = "line"; 116 117 /* Add line as child to defining points */ 118 if (this.point1._is_new) { 119 this.addChild(this.point1); 120 delete this.point1._is_new; 121 } else { 122 this.point1.addChild(this); 123 } 124 if (this.point2._is_new) { 125 this.addChild(this.point2); 126 delete this.point2._is_new; 127 } else { 128 this.point2.addChild(this); 129 } 130 131 this.inherits.push(this.point1, this.point2); 132 133 this.updateStdform(); // This is needed in the following situation: 134 // * the line is defined by three coordinates 135 // * and it will have a glider 136 // * and board.suspendUpdate() has been called. 137 138 // create Label 139 this.createLabel(); 140 141 this.methodMap = JXG.deepCopy(this.methodMap, { 142 point1: "point1", 143 point2: "point2", 144 getSlope: "Slope", 145 Slope: "Slope", 146 Direction: "Direction", 147 getRise: "getRise", 148 Rise: "getRise", 149 getYIntersect: "getRise", 150 YIntersect: "getRise", 151 getAngle: "getAngle", 152 Angle: "getAngle", 153 L: "L", 154 length: "L", 155 setFixedLength: "setFixedLength", 156 setStraight: "setStraight" 157 }); 158 }; 159 160 JXG.Line.prototype = new GeometryElement(); 161 162 JXG.extend( 163 JXG.Line.prototype, 164 /** @lends JXG.Line.prototype */ { 165 /** 166 * Checks whether (x,y) is near the line. 167 * @param {Number} x Coordinate in x direction, screen coordinates. 168 * @param {Number} y Coordinate in y direction, screen coordinates. 169 * @returns {Boolean} True if (x,y) is near the line, False otherwise. 170 */ 171 hasPoint: function (x, y) { 172 // Compute the stdform of the line in screen coordinates. 173 var c = [], 174 v = [1, x, y], 175 s, vnew, p1c, p2c, d, pos, i, prec, type, 176 sw = this.evalVisProp('strokewidth'); 177 178 if (Type.isObject(this.evalVisProp('precision'))) { 179 type = this.board._inputDevice; 180 prec = this.evalVisProp('precision.' + type); 181 } else { 182 // 'inherit' 183 prec = this.board.options.precision.hasPoint; 184 } 185 prec += sw * 0.5; 186 187 c[0] = 188 this.stdform[0] - 189 (this.stdform[1] * this.board.origin.scrCoords[1]) / this.board.unitX + 190 (this.stdform[2] * this.board.origin.scrCoords[2]) / this.board.unitY; 191 c[1] = this.stdform[1] / this.board.unitX; 192 c[2] = this.stdform[2] / -this.board.unitY; 193 194 s = Geometry.distPointLine(v, c); 195 if (isNaN(s) || s > prec) { 196 return false; 197 } 198 199 if ( 200 this.evalVisProp('straightfirst') && 201 this.evalVisProp('straightlast') 202 ) { 203 return true; 204 } 205 206 // If the line is a ray or segment we have to check if the projected point is between P1 and P2. 207 p1c = this.point1.coords; 208 p2c = this.point2.coords; 209 210 // Project the point orthogonally onto the line 211 vnew = [0, c[1], c[2]]; 212 // Orthogonal line to c through v 213 vnew = Mat.crossProduct(vnew, v); 214 // Intersect orthogonal line with line 215 vnew = Mat.crossProduct(vnew, c); 216 217 // Normalize the projected point 218 vnew[1] /= vnew[0]; 219 vnew[2] /= vnew[0]; 220 vnew[0] = 1; 221 222 vnew = new Coords(Const.COORDS_BY_SCREEN, vnew.slice(1), this.board).usrCoords; 223 d = p1c.distance(Const.COORDS_BY_USER, p2c); 224 p1c = p1c.usrCoords.slice(0); 225 p2c = p2c.usrCoords.slice(0); 226 227 // The defining points are identical 228 if (d < Mat.eps) { 229 pos = 0; 230 } else { 231 /* 232 * Handle the cases, where one of the defining points is an ideal point. 233 * d is set to something close to infinity, namely 1/eps. 234 * The ideal point is (temporarily) replaced by a finite point which has 235 * distance d from the other point. 236 * This is accomplished by extracting the x- and y-coordinates (x,y)=:v of the ideal point. 237 * v determines the direction of the line. v is normalized, i.e. set to length 1 by dividing through its length. 238 * Finally, the new point is the sum of the other point and v*d. 239 * 240 */ 241 242 // At least one point is an ideal point 243 if (d === Number.POSITIVE_INFINITY) { 244 d = 1 / Mat.eps; 245 246 // The second point is an ideal point 247 if (Math.abs(p2c[0]) < Mat.eps) { 248 d /= Geometry.distance([0, 0, 0], p2c); 249 p2c = [1, p1c[1] + p2c[1] * d, p1c[2] + p2c[2] * d]; 250 // The first point is an ideal point 251 } else { 252 d /= Geometry.distance([0, 0, 0], p1c); 253 p1c = [1, p2c[1] + p1c[1] * d, p2c[2] + p1c[2] * d]; 254 } 255 } 256 i = 1; 257 d = p2c[i] - p1c[i]; 258 259 if (Math.abs(d) < Mat.eps) { 260 i = 2; 261 d = p2c[i] - p1c[i]; 262 } 263 pos = (vnew[i] - p1c[i]) / d; 264 } 265 266 if (!this.evalVisProp('straightfirst') && pos < 0) { 267 return false; 268 } 269 270 return !(!this.evalVisProp('straightlast') && pos > 1); 271 }, 272 273 // documented in base/element 274 update: function () { 275 var funps; 276 277 if (!this.needsUpdate) { 278 return this; 279 } 280 281 if (this.constrained) { 282 if (Type.isFunction(this.funps)) { 283 funps = this.funps(); 284 if (funps && funps.length && funps.length === 2) { 285 this.point1 = funps[0]; 286 this.point2 = funps[1]; 287 } 288 } else { 289 if (Type.isFunction(this.funp1)) { 290 funps = this.funp1(); 291 if (Type.isPoint(funps)) { 292 this.point1 = funps; 293 } else if (funps && funps.length && funps.length === 2) { 294 this.point1.setPositionDirectly(Const.COORDS_BY_USER, funps); 295 } 296 } 297 298 if (Type.isFunction(this.funp2)) { 299 funps = this.funp2(); 300 if (Type.isPoint(funps)) { 301 this.point2 = funps; 302 } else if (funps && funps.length && funps.length === 2) { 303 this.point2.setPositionDirectly(Const.COORDS_BY_USER, funps); 304 } 305 } 306 } 307 } 308 309 this.updateSegmentFixedLength(); 310 this.updateStdform(); 311 312 if (this.evalVisProp('trace')) { 313 this.cloneToBackground(true); 314 } 315 316 return this; 317 }, 318 319 /** 320 * Update segments with fixed length and at least one movable point. 321 * @private 322 */ 323 updateSegmentFixedLength: function () { 324 var d, d_new, d1, d2, drag1, drag2, x, y; 325 326 if (!this.hasFixedLength) { 327 return this; 328 } 329 330 // Compute the actual length of the segment 331 d = this.point1.Dist(this.point2); 332 // Determine the length the segment ought to have 333 d_new = (this.evalVisProp('nonnegativeonly')) ? 334 Math.max(0.0, this.fixedLength()) : 335 Math.abs(this.fixedLength()); 336 337 // Distances between the two points and their respective 338 // position before the update 339 d1 = this.fixedLengthOldCoords[0].distance( 340 Const.COORDS_BY_USER, 341 this.point1.coords 342 ); 343 d2 = this.fixedLengthOldCoords[1].distance( 344 Const.COORDS_BY_USER, 345 this.point2.coords 346 ); 347 348 // If the position of the points or the fixed length function has been changed we have to work. 349 if (d1 > Mat.eps || d2 > Mat.eps || d !== d_new) { 350 drag1 = 351 this.point1.isDraggable && 352 this.point1.type !== Const.OBJECT_TYPE_GLIDER && 353 !this.point1.evalVisProp('fixed'); 354 drag2 = 355 this.point2.isDraggable && 356 this.point2.type !== Const.OBJECT_TYPE_GLIDER && 357 !this.point2.evalVisProp('fixed'); 358 359 // First case: the two points are different 360 // Then we try to adapt the point that was not dragged 361 // If this point can not be moved (e.g. because it is a glider) 362 // we try move the other point 363 if (d > Mat.eps) { 364 if ((d1 > d2 && drag2) || (d1 <= d2 && drag2 && !drag1)) { 365 this.point2.setPositionDirectly(Const.COORDS_BY_USER, [ 366 this.point1.X() + ((this.point2.X() - this.point1.X()) * d_new) / d, 367 this.point1.Y() + ((this.point2.Y() - this.point1.Y()) * d_new) / d 368 ]); 369 this.point2.fullUpdate(); 370 } else if ((d1 <= d2 && drag1) || (d1 > d2 && drag1 && !drag2)) { 371 this.point1.setPositionDirectly(Const.COORDS_BY_USER, [ 372 this.point2.X() + ((this.point1.X() - this.point2.X()) * d_new) / d, 373 this.point2.Y() + ((this.point1.Y() - this.point2.Y()) * d_new) / d 374 ]); 375 this.point1.fullUpdate(); 376 } 377 // Second case: the two points are identical. In this situation 378 // we choose a random direction. 379 } else { 380 x = Math.random() - 0.5; 381 y = Math.random() - 0.5; 382 d = Mat.hypot(x, y); 383 384 if (drag2) { 385 this.point2.setPositionDirectly(Const.COORDS_BY_USER, [ 386 this.point1.X() + (x * d_new) / d, 387 this.point1.Y() + (y * d_new) / d 388 ]); 389 this.point2.fullUpdate(); 390 } else if (drag1) { 391 this.point1.setPositionDirectly(Const.COORDS_BY_USER, [ 392 this.point2.X() + (x * d_new) / d, 393 this.point2.Y() + (y * d_new) / d 394 ]); 395 this.point1.fullUpdate(); 396 } 397 } 398 // Finally, we save the position of the two points. 399 this.fixedLengthOldCoords[0].setCoordinates( 400 Const.COORDS_BY_USER, 401 this.point1.coords.usrCoords 402 ); 403 this.fixedLengthOldCoords[1].setCoordinates( 404 Const.COORDS_BY_USER, 405 this.point2.coords.usrCoords 406 ); 407 } 408 409 return this; 410 }, 411 412 /** 413 * Updates the stdform derived from the parent point positions. 414 * @private 415 */ 416 updateStdform: function () { 417 var v = Mat.crossProduct( 418 this.point1.coords.usrCoords, 419 this.point2.coords.usrCoords 420 ); 421 422 this.stdform[0] = v[0]; 423 this.stdform[1] = v[1]; 424 this.stdform[2] = v[2]; 425 this.stdform[3] = 0; 426 427 this.normalize(); 428 }, 429 430 /** 431 * Uses the boards renderer to update the line. 432 * @private 433 */ 434 updateRenderer: function () { 435 //var wasReal; 436 437 if (!this.needsUpdate) { 438 return this; 439 } 440 441 if (this.visPropCalc.visible) { 442 // wasReal = this.isReal; 443 this.isReal = 444 !isNaN( 445 this.point1.coords.usrCoords[1] + 446 this.point1.coords.usrCoords[2] + 447 this.point2.coords.usrCoords[1] + 448 this.point2.coords.usrCoords[2] 449 ) && Mat.innerProduct(this.stdform, this.stdform, 3) >= Mat.eps * Mat.eps; 450 451 if ( 452 //wasReal && 453 !this.isReal 454 ) { 455 this.updateVisibility(false); 456 } 457 } 458 459 if (this.visPropCalc.visible) { 460 this.board.renderer.updateLine(this); 461 } 462 463 /* Update the label if visible. */ 464 if ( 465 this.hasLabel && 466 this.visPropCalc.visible && 467 this.label && 468 this.label.visPropCalc.visible && 469 this.isReal 470 ) { 471 this.label.update(); 472 this.board.renderer.updateText(this.label); 473 } 474 475 // Update rendNode display 476 this.setDisplayRendNode(); 477 478 this.needsUpdate = false; 479 return this; 480 }, 481 482 // /** 483 // * Used to generate a polynomial for a point p that lies on this line, i.e. p is collinear to 484 // * {@link JXG.Line#point1} and {@link JXG.Line#point2}. 485 // * 486 // * @param {JXG.Point} p The point for that the polynomial is generated. 487 // * @returns {Array} An array containing the generated polynomial. 488 // * @private 489 // */ 490 generatePolynomial: function (p) { 491 var u1 = this.point1.symbolic.x, 492 u2 = this.point1.symbolic.y, 493 v1 = this.point2.symbolic.x, 494 v2 = this.point2.symbolic.y, 495 w1 = p.symbolic.x, 496 w2 = p.symbolic.y; 497 498 /* 499 * The polynomial in this case is determined by three points being collinear: 500 * 501 * U (u1,u2) W (w1,w2) V (v1,v2) 502 * ----x--------------x------------------------x---------------- 503 * 504 * The collinearity condition is 505 * 506 * u2-w2 w2-v2 507 * ------- = ------- (1) 508 * u1-w1 w1-v1 509 * 510 * Multiplying (1) with denominators and simplifying is 511 * 512 * u2w1 - u2v1 + w2v1 - u1w2 + u1v2 - w1v2 = 0 513 */ 514 515 return [ 516 [ 517 "(", u2, ")*(", w1, ")-(", u2, ")*(", v1, ")+(", w2, ")*(", v1, ")-(", u1, ")*(", w2, ")+(", u1, ")*(", v2, ")-(", w1, ")*(", v2, ")" 518 ].join("") 519 ]; 520 }, 521 522 /** 523 * Calculates the y intersect of the line. 524 * @returns {Number} The y intersect. 525 */ 526 getRise: function () { 527 if (Math.abs(this.stdform[2]) >= Mat.eps) { 528 return -this.stdform[0] / this.stdform[2]; 529 } 530 531 return Infinity; 532 }, 533 534 /** 535 * Calculates the slope of the line. 536 * @returns {Number} The slope of the line or Infinity if the line is parallel to the y-axis. 537 */ 538 Slope: function () { 539 if (Math.abs(this.stdform[2]) >= Mat.eps) { 540 return -this.stdform[1] / this.stdform[2]; 541 } 542 543 return Infinity; 544 }, 545 546 /** 547 * Alias for line.Slope 548 * @returns {Number} The slope of the line or Infinity if the line is parallel to the y-axis. 549 * @deprecated 550 * @see Line#Slope 551 */ 552 getSlope: function () { 553 return this.Slope(); 554 }, 555 556 /** 557 * Determines the angle between the positive x axis and the line. 558 * @returns {Number} 559 */ 560 getAngle: function () { 561 return Math.atan2(-this.stdform[1], this.stdform[2]); 562 }, 563 564 /** 565 * Returns the direction vector of the line. This is an array of length two 566 * containing the direction vector as [x, y]. It is defined as 567 * <li> the difference of the x- and y-coordinate of the second and first point, in case both points are finite or both points are infinite. 568 * <li> [x, y] coordinates of point2, in case only point2 is infinite. 569 * <li> [-x, -y] coordinates of point1, in case only point1 is infinite. 570 * @function 571 * @returns {Array} of length 2. 572 */ 573 Direction: function () { 574 var coords1 = this.point1.coords.usrCoords, 575 coords2 = this.point2.coords.usrCoords; 576 577 if (coords2[0] === 0 && coords1[0] !== 0) { 578 return coords2.slice(1); 579 } 580 581 if (coords1[0] === 0 && coords2[0] !== 0) { 582 return [-coords1[1], -coords1[2]]; 583 } 584 585 return [ 586 coords2[1] - coords1[1], 587 coords2[2] - coords1[2] 588 ]; 589 }, 590 591 /** 592 * Returns true, if the line is vertical (if the x coordinate of the direction vector is 0). 593 * @function 594 * @returns {Boolean} 595 */ 596 isVertical: function () { 597 var dir = this.Direction(); 598 return dir[0] === 0 && dir[1] !== 0; 599 }, 600 601 /** 602 * Returns true, if the line is horizontal (if the y coordinate of the direction vector is 0). 603 * @function 604 * @returns {Boolean} 605 */ 606 isHorizontal: function () { 607 var dir = this.Direction(); 608 return dir[1] === 0 && dir[0] !== 0; 609 }, 610 611 /** 612 * Determines whether the line is drawn beyond {@link JXG.Line#point1} and 613 * {@link JXG.Line#point2} and updates the line. 614 * @param {Boolean} straightFirst True if the Line shall be drawn beyond 615 * {@link JXG.Line#point1}, false otherwise. 616 * @param {Boolean} straightLast True if the Line shall be drawn beyond 617 * {@link JXG.Line#point2}, false otherwise. 618 * @see Line#straightFirst 619 * @see Line#straightLast 620 * @private 621 */ 622 setStraight: function (straightFirst, straightLast) { 623 this.visProp.straightfirst = straightFirst; 624 this.visProp.straightlast = straightLast; 625 626 this.board.renderer.updateLine(this); 627 return this; 628 }, 629 630 // documented in geometry element 631 getTextAnchor: function () { 632 return new Coords( 633 Const.COORDS_BY_USER, 634 [ 635 0.5 * (this.point2.X() + this.point1.X()), 636 0.5 * (this.point2.Y() + this.point1.Y()) 637 ], 638 this.board 639 ); 640 }, 641 642 /** 643 * Adjusts Label coords relative to Anchor. DESCRIPTION 644 * @private 645 */ 646 setLabelRelativeCoords: function (relCoords) { 647 if (Type.exists(this.label)) { 648 this.label.relativeCoords = new Coords( 649 Const.COORDS_BY_SCREEN, 650 [relCoords[0], -relCoords[1]], 651 this.board 652 ); 653 } 654 }, 655 656 // documented in geometry element 657 getLabelAnchor: function () { 658 var x, y, pos, 659 xy, lbda, dx, dy, d, 660 dist = 1.5, 661 fs = 0, 662 c1 = new Coords(Const.COORDS_BY_USER, this.point1.coords.usrCoords, this.board), 663 c2 = new Coords(Const.COORDS_BY_USER, this.point2.coords.usrCoords, this.board), 664 ev_sf = this.evalVisProp('straightfirst'), 665 ev_sl = this.evalVisProp('straightlast'); 666 667 if (ev_sf || ev_sl) { 668 Geometry.calcStraight(this, c1, c2, 0); 669 } 670 671 c1 = c1.scrCoords; 672 c2 = c2.scrCoords; 673 674 if (!Type.exists(this.label)) { 675 return new Coords(Const.COORDS_BY_SCREEN, [NaN, NaN], this.board); 676 } 677 678 pos = this.label.evalVisProp('position'); 679 if (!Type.isString(pos)) { 680 return new Coords(Const.COORDS_BY_SCREEN, [NaN, NaN], this.board); 681 } 682 683 if (pos.indexOf('right') < 0 && pos.indexOf('left') < 0) { 684 // Old positioning commands 685 switch (pos) { 686 case 'last': 687 x = c2[1]; 688 y = c2[2]; 689 break; 690 case 'first': 691 x = c1[1]; 692 y = c1[2]; 693 break; 694 case "lft": 695 case "llft": 696 case "ulft": 697 if (c1[1] < c2[1] + Mat.eps) { 698 x = c1[1]; 699 y = c1[2]; 700 } else { 701 x = c2[1]; 702 y = c2[2]; 703 } 704 break; 705 case "rt": 706 case "lrt": 707 case "urt": 708 if (c1[1] > c2[1] + Mat.eps) { 709 x = c1[1]; 710 y = c1[2]; 711 } else { 712 x = c2[1]; 713 y = c2[2]; 714 } 715 break; 716 default: 717 x = 0.5 * (c1[1] + c2[1]); 718 y = 0.5 * (c1[2] + c2[2]); 719 } 720 } else { 721 // New positioning 722 xy = Type.parsePosition(pos); 723 lbda = Type.parseNumber(xy.pos, 1, 1); 724 725 dx = c2[1] - c1[1]; 726 dy = c2[2] - c1[2]; 727 d = Mat.hypot(dx, dy); 728 729 if (xy.pos.indexOf('px') >= 0 || 730 xy.pos.indexOf('fr') >= 0 || 731 xy.pos.indexOf('%') >= 0) { 732 // lbda is interpreted in screen coords 733 734 if (xy.pos.indexOf('px') >= 0) { 735 // Pixel values are supported 736 lbda /= d; 737 } 738 739 // Position along the line 740 x = c1[1] + lbda * dx; 741 y = c1[2] + lbda * dy; 742 } else { 743 // lbda is given as number or as a number string 744 // Then, lbda is interpreted in user coords 745 x = c1[1] + lbda * this.board.unitX * dx / d; 746 y = c1[2] + lbda * this.board.unitY * dy / d; 747 } 748 749 // Position left or right 750 if (xy.side === 'left') { 751 dx *= -1; 752 } else { 753 dy *= -1; 754 } 755 if (Type.exists(this.label)) { 756 dist = 0.5 * this.label.evalVisProp('distance') / d; 757 } 758 x += dy * this.label.size[0] * dist; 759 y += dx * this.label.size[1] * dist; 760 } 761 762 // Correct coordinates if the label seems to be outside of canvas. 763 if (ev_sf || ev_sl) { 764 if (Type.exists(this.label)) { 765 // Does not exist during createLabel 766 fs = this.label.evalVisProp('fontsize'); 767 } 768 769 if (Math.abs(x) < Mat.eps) { 770 x = fs; 771 } else if ( 772 this.board.canvasWidth + Mat.eps > x && 773 x > this.board.canvasWidth - fs - Mat.eps 774 ) { 775 x = this.board.canvasWidth - fs; 776 } 777 778 if (Mat.eps + fs > y && y > -Mat.eps) { 779 y = fs; 780 } else if ( 781 this.board.canvasHeight + Mat.eps > y && 782 y > this.board.canvasHeight - fs - Mat.eps 783 ) { 784 y = this.board.canvasHeight - fs; 785 } 786 } 787 788 return new Coords(Const.COORDS_BY_SCREEN, [x, y], this.board); 789 }, 790 791 // documented in geometry element 792 cloneToBackground: function () { 793 var copy = Type.getCloneObject(this), 794 r, s, 795 er; 796 797 copy.point1 = this.point1; 798 copy.point2 = this.point2; 799 copy.stdform = this.stdform; 800 801 s = this.getSlope(); 802 r = this.getRise(); 803 copy.getSlope = function () { 804 return s; 805 }; 806 copy.getRise = function () { 807 return r; 808 }; 809 810 er = this.board.renderer.enhancedRendering; 811 this.board.renderer.enhancedRendering = true; 812 this.board.renderer.drawLine(copy); 813 this.board.renderer.enhancedRendering = er; 814 this.traces[copy.id] = copy.rendNode; 815 816 return this; 817 }, 818 819 /** 820 * Add transformations to this line. 821 * @param {JXG.Transformation|Array} transform Either one {@link JXG.Transformation} or an array of 822 * {@link JXG.Transformation}s. 823 * @returns {JXG.Line} Reference to this line object. 824 */ 825 addTransform: function (transform) { 826 var i, 827 list = Type.isArray(transform) ? transform : [transform], 828 len = list.length; 829 830 for (i = 0; i < len; i++) { 831 this.point1.transformations.push(list[i]); 832 this.point2.transformations.push(list[i]); 833 } 834 835 // Why not like this? 836 // The difference is in setting baseElement 837 // var list = Type.isArray(transform) ? transform : [transform]; 838 // this.point1.addTransform(this, list); 839 // this.point2.addTransform(this, list); 840 841 return this; 842 }, 843 844 // see GeometryElement.js 845 snapToGrid: function (pos) { 846 var c1, c2, dc, t, ticks, x, y, sX, sY; 847 848 if (this.evalVisProp('snaptogrid')) { 849 if (this.parents.length < 3) { 850 // Line through two points 851 this.point1.handleSnapToGrid(true, true); 852 this.point2.handleSnapToGrid(true, true); 853 } else if (Type.exists(pos)) { 854 // Free line 855 sX = this.evalVisProp('snapsizex'); 856 sY = this.evalVisProp('snapsizey'); 857 858 c1 = new Coords(Const.COORDS_BY_SCREEN, [pos.Xprev, pos.Yprev], this.board); 859 860 x = c1.usrCoords[1]; 861 y = c1.usrCoords[2]; 862 863 if ( 864 sX <= 0 && 865 this.board.defaultAxes && 866 this.board.defaultAxes.x.defaultTicks 867 ) { 868 ticks = this.board.defaultAxes.x.defaultTicks; 869 sX = ticks.ticksDelta * (ticks.evalVisProp('minorticks') + 1); 870 } 871 if ( 872 sY <= 0 && 873 this.board.defaultAxes && 874 this.board.defaultAxes.y.defaultTicks 875 ) { 876 ticks = this.board.defaultAxes.y.defaultTicks; 877 sY = ticks.ticksDelta * (ticks.evalVisProp('minorticks') + 1); 878 } 879 880 // if no valid snap sizes are available, don't change the coords. 881 if (sX > 0 && sY > 0) { 882 // projectCoordsToLine 883 /* 884 v = [0, this.stdform[1], this.stdform[2]]; 885 v = Mat.crossProduct(v, c1.usrCoords); 886 c2 = Geometry.meetLineLine(v, this.stdform, 0, this.board); 887 */ 888 c2 = Geometry.projectPointToLine({ coords: c1 }, this, this.board); 889 890 dc = Statistics.subtract( 891 [1, Math.round(x / sX) * sX, Math.round(y / sY) * sY], 892 c2.usrCoords 893 ); 894 t = this.board.create("transform", dc.slice(1), { 895 type: "translate" 896 }); 897 t.applyOnce([this.point1, this.point2]); 898 } 899 } 900 } else { 901 this.point1.handleSnapToGrid(false, true); 902 this.point2.handleSnapToGrid(false, true); 903 } 904 905 return this; 906 }, 907 908 // see element.js 909 snapToPoints: function () { 910 var forceIt = this.evalVisProp('snaptopoints'); 911 912 if (this.parents.length < 3) { 913 // Line through two points 914 this.point1.handleSnapToPoints(forceIt); 915 this.point2.handleSnapToPoints(forceIt); 916 } 917 918 return this; 919 }, 920 921 /** 922 * Treat the line as parametric curve in homogeneous coordinates, where the parameter t runs from 0 to 1. 923 * First we transform the interval [0,1] to [-1,1]. 924 * If the line has homogeneous coordinates [c, a, b] = stdform[] then the direction of the line is [b, -a]. 925 * Now, we take one finite point that defines the line, i.e. we take either point1 or point2 926 * (in case the line is not the ideal line). 927 * Let the coordinates of that point be [z, x, y]. 928 * Then, the curve runs linearly from 929 * [0, b, -a] (t=-1) to [z, x, y] (t=0) 930 * and 931 * [z, x, y] (t=0) to [0, -b, a] (t=1) 932 * 933 * @param {Number} t Parameter running from 0 to 1. 934 * @returns {Number} X(t) x-coordinate of the line treated as parametric curve. 935 * */ 936 X: function (t) { 937 var x, 938 b = this.stdform[2]; 939 940 x = 941 Math.abs(this.point1.coords.usrCoords[0]) > Mat.eps 942 ? this.point1.coords.usrCoords[1] 943 : this.point2.coords.usrCoords[1]; 944 945 t = (t - 0.5) * 2; 946 947 return (1 - Math.abs(t)) * x - t * b; 948 }, 949 950 /** 951 * Treat the line as parametric curve in homogeneous coordinates. 952 * See {@link JXG.Line#X} for a detailed description. 953 * @param {Number} t Parameter running from 0 to 1. 954 * @returns {Number} Y(t) y-coordinate of the line treated as parametric curve. 955 */ 956 Y: function (t) { 957 var y, 958 a = this.stdform[1]; 959 960 y = 961 Math.abs(this.point1.coords.usrCoords[0]) > Mat.eps 962 ? this.point1.coords.usrCoords[2] 963 : this.point2.coords.usrCoords[2]; 964 965 t = (t - 0.5) * 2; 966 967 return (1 - Math.abs(t)) * y + t * a; 968 }, 969 970 /** 971 * Treat the line as parametric curve in homogeneous coordinates. 972 * See {@link JXG.Line#X} for a detailed description. 973 * 974 * @param {Number} t Parameter running from 0 to 1. 975 * @returns {Number} Z(t) z-coordinate of the line treated as parametric curve. 976 */ 977 Z: function (t) { 978 var z = 979 Math.abs(this.point1.coords.usrCoords[0]) > Mat.eps 980 ? this.point1.coords.usrCoords[0] 981 : this.point2.coords.usrCoords[0]; 982 983 t = (t - 0.5) * 2; 984 985 return (1 - Math.abs(t)) * z; 986 }, 987 988 /** 989 * The distance between the two points defining the line. 990 * @returns {Number} 991 */ 992 L: function () { 993 return this.point1.Dist(this.point2); 994 }, 995 996 /** 997 * Set a new fixed length, then update the board. 998 * @param {String|Number|function} l A string, function or number describing the new length. 999 * @returns {JXG.Line} Reference to this line 1000 */ 1001 setFixedLength: function (l) { 1002 if (!this.hasFixedLength) { 1003 return this; 1004 } 1005 1006 this.fixedLength = Type.createFunction(l, this.board); 1007 this.hasFixedLength = true; 1008 this.addParentsFromJCFunctions([this.fixedLength]); 1009 this.board.update(); 1010 1011 return this; 1012 }, 1013 1014 /** 1015 * Treat the element as a parametric curve 1016 * @private 1017 */ 1018 minX: function () { 1019 return 0.0; 1020 }, 1021 1022 /** 1023 * Treat the element as parametric curve 1024 * @private 1025 */ 1026 maxX: function () { 1027 return 1.0; 1028 }, 1029 1030 // documented in geometry element 1031 bounds: function () { 1032 var p1c = this.point1.coords.usrCoords, 1033 p2c = this.point2.coords.usrCoords; 1034 1035 return [ 1036 Math.min(p1c[1], p2c[1]), 1037 Math.max(p1c[2], p2c[2]), 1038 Math.max(p1c[1], p2c[1]), 1039 Math.min(p1c[2], p2c[2]) 1040 ]; 1041 }, 1042 1043 // documented in GeometryElement.js 1044 remove: function () { 1045 this.removeAllTicks(); 1046 GeometryElement.prototype.remove.call(this); 1047 } 1048 1049 // hideElement: function () { 1050 // var i; 1051 // 1052 // GeometryElement.prototype.hideElement.call(this); 1053 // 1054 // for (i = 0; i < this.ticks.length; i++) { 1055 // this.ticks[i].hideElement(); 1056 // } 1057 // }, 1058 // 1059 // showElement: function () { 1060 // var i; 1061 // GeometryElement.prototype.showElement.call(this); 1062 // 1063 // for (i = 0; i < this.ticks.length; i++) { 1064 // this.ticks[i].showElement(); 1065 // } 1066 // } 1067 1068 } 1069 ); 1070 1071 /** 1072 * @class This element is used to provide a constructor for a general line. A general line is given by two points. By setting additional properties 1073 * a line can be used as an arrow and/or axis. 1074 * @pseudo 1075 * @name Line 1076 * @augments JXG.Line 1077 * @constructor 1078 * @type JXG.Line 1079 * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown. 1080 * @param {JXG.Point,array,function_JXG.Point,array,function} point1,point2 Parent elements can be two elements either of type {@link JXG.Point} or array of 1081 * numbers describing the coordinates of a point. In the latter case the point will be constructed automatically as a fixed invisible point. 1082 * It is possible to provide a function returning an array or a point, instead of providing an array or a point. 1083 * @param {Number,function_Number,function_Number,function} a,b,c A line can also be created providing three numbers. The line is then described by 1084 * the set of solutions of the equation <tt>a*z+b*x+c*y = 0</tt>. For all finite points, z is normalized to the value 1. 1085 * It is possible to provide three functions returning numbers, too. 1086 * @param {function} f This function must return an array containing three numbers forming the line's homogeneous coordinates. 1087 * <p> 1088 * Additionally, a line can be created by providing a line and a transformation (or an array of transformations). 1089 * Then, the result is a line which is the transformation of the supplied line. 1090 * @example 1091 * // Create a line using point and coordinates/ 1092 * // The second point will be fixed and invisible. 1093 * var p1 = board.create('point', [4.5, 2.0]); 1094 * var l1 = board.create('line', [p1, [1.0, 1.0]]); 1095 * </pre><div class="jxgbox" id="JXGc0ae3461-10c4-4d39-b9be-81d74759d122" style="width: 300px; height: 300px;"></div> 1096 * <script type="text/javascript"> 1097 * var glex1_board = JXG.JSXGraph.initBoard('JXGc0ae3461-10c4-4d39-b9be-81d74759d122', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}); 1098 * var glex1_p1 = glex1_board.create('point', [4.5, 2.0]); 1099 * var glex1_l1 = glex1_board.create('line', [glex1_p1, [1.0, 1.0]]); 1100 * </script><pre> 1101 * @example 1102 * // Create a line using three coordinates 1103 * var l1 = board.create('line', [1.0, -2.0, 3.0]); 1104 * </pre><div class="jxgbox" id="JXGcf45e462-f964-4ba4-be3a-c9db94e2593f" style="width: 300px; height: 300px;"></div> 1105 * <script type="text/javascript"> 1106 * var glex2_board = JXG.JSXGraph.initBoard('JXGcf45e462-f964-4ba4-be3a-c9db94e2593f', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}); 1107 * var glex2_l1 = glex2_board.create('line', [1.0, -2.0, 3.0]); 1108 * </script><pre> 1109 * @example 1110 * // Create a line (l2) as reflection of another line (l1) 1111 * // reflection line 1112 * var li = board.create('line', [1,1,1], {strokeColor: '#aaaaaa'}); 1113 * var reflect = board.create('transform', [li], {type: 'reflect'}); 1114 * 1115 * var l1 = board.create('line', [1,-5,1]); 1116 * var l2 = board.create('line', [l1, reflect]); 1117 * 1118 * </pre><div id="JXGJXGa00d7dd6-d38c-11e7-93b3-901b0e1b8723" class="jxgbox" style="width: 300px; height: 300px;"></div> 1119 * <script type="text/javascript"> 1120 * (function() { 1121 * var board = JXG.JSXGraph.initBoard('JXGJXGa00d7dd6-d38c-11e7-93b3-901b0e1b8723', 1122 * {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false}); 1123 * // reflection line 1124 * var li = board.create('line', [1,1,1], {strokeColor: '#aaaaaa'}); 1125 * var reflect = board.create('transform', [li], {type: 'reflect'}); 1126 * 1127 * var l1 = board.create('line', [1,-5,1]); 1128 * var l2 = board.create('line', [l1, reflect]); 1129 * })(); 1130 * 1131 * </script><pre> 1132 * 1133 * @example 1134 * var t = board.create('transform', [2, 1.5], {type: 'scale'}); 1135 * var l1 = board.create('line', [1, -5, 1]); 1136 * var l2 = board.create('line', [l1, t]); 1137 * 1138 * </pre><div id="d16d5b58-6338-11e8-9fb9-901b0e1b8723" class="jxgbox" style="width: 300px; height: 300px;"></div> 1139 * <script type="text/javascript"> 1140 * (function() { 1141 * var board = JXG.JSXGraph.initBoard('d16d5b58-6338-11e8-9fb9-901b0e1b8723', 1142 * {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false}); 1143 * var t = board.create('transform', [2, 1.5], {type: 'scale'}); 1144 * var l1 = board.create('line', [1, -5, 1]); 1145 * var l2 = board.create('line', [l1, t]); 1146 * 1147 * })(); 1148 * 1149 * </script><pre> 1150 * 1151 * @example 1152 * //create line between two points 1153 * var p1 = board.create('point', [0,0]); 1154 * var p2 = board.create('point', [2,2]); 1155 * var l1 = board.create('line', [p1,p2], {straightFirst:false, straightLast:false}); 1156 * </pre><div id="d21d5b58-6338-11e8-9fb9-901b0e1b8723" class="jxgbox" style="width: 300px; height: 300px;"></div> 1157 * <script type="text/javascript"> 1158 * (function() { 1159 * var board = JXG.JSXGraph.initBoard('d21d5b58-6338-11e8-9fb9-901b0e1b8723', 1160 * {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false}); 1161 * var ex5p1 = board.create('point', [0,0]); 1162 * var ex5p2 = board.create('point', [2,2]); 1163 * var ex5l1 = board.create('line', [ex5p1,ex5p2], {straightFirst:false, straightLast:false}); 1164 * })(); 1165 * 1166 * </script><pre> 1167 */ 1168 JXG.createLine = function (board, parents, attributes) { 1169 var ps, el, p1, p2, i, attr, 1170 c = [], 1171 doTransform = false, 1172 constrained = false, 1173 isDraggable; 1174 1175 if (parents.length === 2) { 1176 // The line is defined by two points or coordinates of two points. 1177 // In the latter case, the points are created. 1178 attr = Type.copyAttributes(attributes, board.options, "line", "point1"); 1179 if (Type.isArray(parents[0]) && parents[0].length > 1) { 1180 p1 = board.create("point", parents[0], attr); 1181 } else if (Type.isString(parents[0]) || Type.isPoint(parents[0])) { 1182 p1 = board.select(parents[0]); 1183 } else if (Type.isFunction(parents[0]) && Type.isPoint(parents[0]())) { 1184 p1 = parents[0](); 1185 constrained = true; 1186 } else if ( 1187 Type.isFunction(parents[0]) && 1188 parents[0]().length && 1189 parents[0]().length >= 2 1190 ) { 1191 p1 = JXG.createPoint(board, parents[0](), attr); 1192 constrained = true; 1193 } else if (Type.isObject(parents[0]) && Type.isTransformationOrArray(parents[1])) { 1194 doTransform = true; 1195 p1 = board.create("point", [parents[0].point1, parents[1]], attr); 1196 } else { 1197 throw new Error( 1198 "JSXGraph: Can't create line with parent types '" + 1199 typeof parents[0] + 1200 "' and '" + 1201 typeof parents[1] + 1202 "'." + 1203 "\nPossible parent types: [point,point], [[x1,y1],[x2,y2]], [a,b,c]" 1204 ); 1205 } 1206 1207 // point 2 given by coordinates 1208 attr = Type.copyAttributes(attributes, board.options, "line", "point2"); 1209 if (doTransform) { 1210 p2 = board.create("point", [parents[0].point2, parents[1]], attr); 1211 } else if (Type.isArray(parents[1]) && parents[1].length > 1) { 1212 p2 = board.create("point", parents[1], attr); 1213 } else if (Type.isString(parents[1]) || Type.isPoint(parents[1])) { 1214 p2 = board.select(parents[1]); 1215 } else if (Type.isFunction(parents[1]) && Type.isPoint(parents[1]())) { 1216 p2 = parents[1](); 1217 constrained = true; 1218 } else if ( 1219 Type.isFunction(parents[1]) && 1220 parents[1]().length && 1221 parents[1]().length >= 2 1222 ) { 1223 p2 = JXG.createPoint(board, parents[1](), attr); 1224 constrained = true; 1225 } else { 1226 throw new Error( 1227 "JSXGraph: Can't create line with parent types '" + 1228 typeof parents[0] + 1229 "' and '" + 1230 typeof parents[1] + 1231 "'." + 1232 "\nPossible parent types: [point,point], [[x1,y1],[x2,y2]], [a,b,c]" 1233 ); 1234 } 1235 1236 attr = Type.copyAttributes(attributes, board.options, "line"); 1237 el = new JXG.Line(board, p1, p2, attr); 1238 1239 if (constrained) { 1240 el.constrained = true; 1241 el.funp1 = parents[0]; 1242 el.funp2 = parents[1]; 1243 } else if (!doTransform) { 1244 el.isDraggable = true; 1245 } 1246 1247 //if (!el.constrained) { 1248 el.setParents([p1.id, p2.id]); 1249 //} 1250 1251 } else if (parents.length === 3) { 1252 // Free line: 1253 // Line is defined by three homogeneous coordinates. 1254 // Also in this case points are created. 1255 isDraggable = true; 1256 for (i = 0; i < 3; i++) { 1257 if (Type.isNumber(parents[i])) { 1258 // createFunction will just wrap a function around our constant number 1259 // that does nothing else but to return that number. 1260 c[i] = Type.createFunction(parents[i]); 1261 } else if (Type.isFunction(parents[i])) { 1262 c[i] = parents[i]; 1263 isDraggable = false; 1264 } else { 1265 throw new Error( 1266 "JSXGraph: Can't create line with parent types '" + 1267 typeof parents[0] + 1268 "' and '" + 1269 typeof parents[1] + 1270 "' and '" + 1271 typeof parents[2] + 1272 "'." + 1273 "\nPossible parent types: [point,point], [[x1,y1],[x2,y2]], [a,b,c]" 1274 ); 1275 } 1276 } 1277 1278 // point 1 is the midpoint between (0, c, -b) and point 2. => point1 is finite. 1279 attr = Type.copyAttributes(attributes, board.options, "line", "point1"); 1280 if (isDraggable) { 1281 p1 = board.create("point", [ 1282 c[2]() * c[2]() + c[1]() * c[1](), 1283 c[2]() - c[1]() * c[0]() + c[2](), 1284 -c[1]() - c[2]() * c[0]() - c[1]() 1285 ], attr); 1286 } else { 1287 p1 = board.create("point", [ 1288 function () { 1289 return (c[2]() * c[2]() + c[1]() * c[1]()) * 0.5; 1290 }, 1291 function () { 1292 return (c[2]() - c[1]() * c[0]() + c[2]()) * 0.5; 1293 }, 1294 function () { 1295 return (-c[1]() - c[2]() * c[0]() - c[1]()) * 0.5; 1296 } 1297 ], attr); 1298 } 1299 1300 // point 2: (b^2+c^2,-ba+c,-ca-b) 1301 attr = Type.copyAttributes(attributes, board.options, "line", "point2"); 1302 if (isDraggable) { 1303 p2 = board.create("point", [ 1304 c[2]() * c[2]() + c[1]() * c[1](), 1305 -c[1]() * c[0]() + c[2](), 1306 -c[2]() * c[0]() - c[1]() 1307 ], attr); 1308 } else { 1309 p2 = board.create("point", [ 1310 function () { 1311 return c[2]() * c[2]() + c[1]() * c[1](); 1312 }, 1313 function () { 1314 return -c[1]() * c[0]() + c[2](); 1315 }, 1316 function () { 1317 return -c[2]() * c[0]() - c[1](); 1318 } 1319 ], attr); 1320 } 1321 1322 // If the line will have a glider and board.suspendUpdate() has been called, we 1323 // need to compute the initial position of the two points p1 and p2. 1324 p1.prepareUpdate().update(); 1325 p2.prepareUpdate().update(); 1326 attr = Type.copyAttributes(attributes, board.options, "line"); 1327 el = new JXG.Line(board, p1, p2, attr); 1328 // Not yet working, because the points are not draggable. 1329 el.isDraggable = isDraggable; 1330 el.setParents([p1, p2]); 1331 1332 } else if ( 1333 // The parent array contains a function which returns two points. 1334 parents.length === 1 && 1335 Type.isFunction(parents[0]) && 1336 parents[0]().length === 2 && 1337 Type.isPoint(parents[0]()[0]) && 1338 Type.isPoint(parents[0]()[1]) 1339 ) { 1340 ps = parents[0](); 1341 attr = Type.copyAttributes(attributes, board.options, "line"); 1342 el = new JXG.Line(board, ps[0], ps[1], attr); 1343 el.constrained = true; 1344 el.funps = parents[0]; 1345 el.setParents(ps); 1346 } else if ( 1347 parents.length === 1 && 1348 Type.isFunction(parents[0]) && 1349 parents[0]().length === 3 && 1350 Type.isNumber(parents[0]()[0]) && 1351 Type.isNumber(parents[0]()[1]) && 1352 Type.isNumber(parents[0]()[2]) 1353 ) { 1354 ps = parents[0]; 1355 1356 attr = Type.copyAttributes(attributes, board.options, "line", "point1"); 1357 p1 = board.create("point", [ 1358 function () { 1359 var c = ps(); 1360 1361 return [ 1362 (c[2] * c[2] + c[1] * c[1]) * 0.5, 1363 (c[2] - c[1] * c[0] + c[2]) * 0.5, 1364 (-c[1] - c[2] * c[0] - c[1]) * 0.5 1365 ]; 1366 } 1367 ], attr); 1368 1369 attr = Type.copyAttributes(attributes, board.options, "line", "point2"); 1370 p2 = board.create("point", [ 1371 function () { 1372 var c = ps(); 1373 1374 return [ 1375 c[2] * c[2] + c[1] * c[1], 1376 -c[1] * c[0] + c[2], 1377 -c[2] * c[0] - c[1] 1378 ]; 1379 } 1380 ], attr); 1381 1382 attr = Type.copyAttributes(attributes, board.options, "line"); 1383 el = new JXG.Line(board, p1, p2, attr); 1384 1385 el.constrained = true; 1386 el.funps = parents[0]; 1387 el.setParents([p1, p2]); 1388 } else { 1389 throw new Error( 1390 "JSXGraph: Can't create line with parent types '" + 1391 typeof parents[0] + 1392 "' and '" + 1393 typeof parents[1] + 1394 "'." + 1395 "\nPossible parent types: [point,point], [[x1,y1],[x2,y2]], [a,b,c]" 1396 ); 1397 } 1398 1399 return el; 1400 }; 1401 1402 JXG.registerElement("line", JXG.createLine); 1403 1404 /** 1405 * @class This element is used to provide a constructor for a segment. 1406 * It's strictly spoken just a wrapper for element {@link Line} with {@link Line#straightFirst} 1407 * and {@link Line#straightLast} properties set to false. If there is a third variable then the 1408 * segment has a fixed length (which may be a function, too) determined by the absolute value of 1409 * that number. 1410 * @pseudo 1411 * @name Segment 1412 * @augments JXG.Line 1413 * @constructor 1414 * @type JXG.Line 1415 * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown. 1416 * @param {JXG.Point,array_JXG.Point,array} point1,point2 Parent elements can be two elements either of type {@link JXG.Point} 1417 * or array of numbers describing the 1418 * coordinates of a point. In the latter case the point will be constructed automatically as a fixed invisible point. 1419 * @param {number,function} [length] The points are adapted - if possible - such that their distance 1420 * is equal to the absolute value of this number. 1421 * @see Line 1422 * @example 1423 * // Create a segment providing two points. 1424 * var p1 = board.create('point', [4.5, 2.0]); 1425 * var p2 = board.create('point', [1.0, 1.0]); 1426 * var l1 = board.create('segment', [p1, p2]); 1427 * </pre><div class="jxgbox" id="JXGd70e6aac-7c93-4525-a94c-a1820fa38e2f" style="width: 300px; height: 300px;"></div> 1428 * <script type="text/javascript"> 1429 * var slex1_board = JXG.JSXGraph.initBoard('JXGd70e6aac-7c93-4525-a94c-a1820fa38e2f', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}); 1430 * var slex1_p1 = slex1_board.create('point', [4.5, 2.0]); 1431 * var slex1_p2 = slex1_board.create('point', [1.0, 1.0]); 1432 * var slex1_l1 = slex1_board.create('segment', [slex1_p1, slex1_p2]); 1433 * </script><pre> 1434 * 1435 * @example 1436 * // Create a segment providing two points. 1437 * var p1 = board.create('point', [4.0, 1.0]); 1438 * var p2 = board.create('point', [1.0, 1.0]); 1439 * // AB 1440 * var l1 = board.create('segment', [p1, p2]); 1441 * var p3 = board.create('point', [4.0, 2.0]); 1442 * var p4 = board.create('point', [1.0, 2.0]); 1443 * // CD 1444 * var l2 = board.create('segment', [p3, p4, 3]); // Fixed length 1445 * var p5 = board.create('point', [4.0, 3.0]); 1446 * var p6 = board.create('point', [1.0, 4.0]); 1447 * // EF 1448 * var l3 = board.create('segment', [p5, p6, function(){ return l1.L();} ]); // Fixed, but dependent length 1449 * </pre><div class="jxgbox" id="JXG617336ba-0705-4b2b-a236-c87c28ef25be" style="width: 300px; height: 300px;"></div> 1450 * <script type="text/javascript"> 1451 * var slex2_board = JXG.JSXGraph.initBoard('JXG617336ba-0705-4b2b-a236-c87c28ef25be', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}); 1452 * var slex2_p1 = slex2_board.create('point', [4.0, 1.0]); 1453 * var slex2_p2 = slex2_board.create('point', [1.0, 1.0]); 1454 * var slex2_l1 = slex2_board.create('segment', [slex2_p1, slex2_p2]); 1455 * var slex2_p3 = slex2_board.create('point', [4.0, 2.0]); 1456 * var slex2_p4 = slex2_board.create('point', [1.0, 2.0]); 1457 * var slex2_l2 = slex2_board.create('segment', [slex2_p3, slex2_p4, 3]); 1458 * var slex2_p5 = slex2_board.create('point', [4.0, 2.0]); 1459 * var slex2_p6 = slex2_board.create('point', [1.0, 2.0]); 1460 * var slex2_l3 = slex2_board.create('segment', [slex2_p5, slex2_p6, function(){ return slex2_l1.L();}]); 1461 * </script><pre> 1462 * 1463 */ 1464 JXG.createSegment = function (board, parents, attributes) { 1465 var el, attr; 1466 1467 attributes.straightFirst = false; 1468 attributes.straightLast = false; 1469 attr = Type.copyAttributes(attributes, board.options, "segment"); 1470 1471 el = board.create("line", parents.slice(0, 2), attr); 1472 1473 if (parents.length === 3) { 1474 try { 1475 el.hasFixedLength = true; 1476 el.fixedLengthOldCoords = []; 1477 el.fixedLengthOldCoords[0] = new Coords( 1478 Const.COORDS_BY_USER, 1479 el.point1.coords.usrCoords.slice(1, 3), 1480 board 1481 ); 1482 el.fixedLengthOldCoords[1] = new Coords( 1483 Const.COORDS_BY_USER, 1484 el.point2.coords.usrCoords.slice(1, 3), 1485 board 1486 ); 1487 1488 el.setFixedLength(parents[2]); 1489 } catch (err) { 1490 throw new Error( 1491 "JSXGraph: Can't create segment with third parent type '" + 1492 typeof parents[2] + 1493 "'." + 1494 "\nPossible third parent types: number or function" 1495 ); 1496 } 1497 // if (Type.isNumber(parents[2])) { 1498 // el.fixedLength = function () { 1499 // return parents[2]; 1500 // }; 1501 // } else if (Type.isFunction(parents[2])) { 1502 // el.fixedLength = Type.createFunction(parents[2], this.board); 1503 // } else { 1504 // throw new Error( 1505 // "JSXGraph: Can't create segment with third parent type '" + 1506 // typeof parents[2] + 1507 // "'." + 1508 // "\nPossible third parent types: number or function" 1509 // ); 1510 // } 1511 1512 el.getParents = function () { 1513 return this.parents.concat(this.fixedLength()); 1514 }; 1515 1516 } 1517 1518 el.elType = "segment"; 1519 1520 return el; 1521 }; 1522 1523 JXG.registerElement("segment", JXG.createSegment); 1524 1525 /** 1526 * @class This element is used to provide a constructor for arrow, which is just a wrapper for element 1527 * {@link Line} with {@link Line#straightFirst} 1528 * and {@link Line#straightLast} properties set to false and {@link Line#lastArrow} set to true. 1529 * @pseudo 1530 * @name Arrow 1531 * @augments JXG.Line 1532 * @constructor 1533 * @type JXG.Line 1534 * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown. 1535 * @param {JXG.Point,array_JXG.Point,array} point1,point2 Parent elements can be two elements either of type {@link JXG.Point} or array of numbers describing the 1536 * coordinates of a point. In the latter case the point will be constructed automatically as a fixed invisible point. 1537 * @param {Number_Number_Number} a,b,c A line can also be created providing three numbers. The line is then described by the set of solutions 1538 * of the equation <tt>a*x+b*y+c*z = 0</tt>. 1539 * @see Line 1540 * @example 1541 * // Create an arrow providing two points. 1542 * var p1 = board.create('point', [4.5, 2.0]); 1543 * var p2 = board.create('point', [1.0, 1.0]); 1544 * var l1 = board.create('arrow', [p1, p2]); 1545 * </pre><div class="jxgbox" id="JXG1d26bd22-7d6d-4018-b164-4c8bc8d22ccf" style="width: 300px; height: 300px;"></div> 1546 * <script type="text/javascript"> 1547 * var alex1_board = JXG.JSXGraph.initBoard('JXG1d26bd22-7d6d-4018-b164-4c8bc8d22ccf', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}); 1548 * var alex1_p1 = alex1_board.create('point', [4.5, 2.0]); 1549 * var alex1_p2 = alex1_board.create('point', [1.0, 1.0]); 1550 * var alex1_l1 = alex1_board.create('arrow', [alex1_p1, alex1_p2]); 1551 * </script><pre> 1552 */ 1553 JXG.createArrow = function (board, parents, attributes) { 1554 var el, attr; 1555 1556 attributes.straightFirst = false; 1557 attributes.straightLast = false; 1558 attr = Type.copyAttributes(attributes, board.options, "arrow"); 1559 el = board.create("line", parents, attr); 1560 //el.setArrow(false, true); 1561 el.type = Const.OBJECT_TYPE_VECTOR; 1562 el.elType = "arrow"; 1563 1564 return el; 1565 }; 1566 1567 JXG.registerElement("arrow", JXG.createArrow); 1568 1569 /** 1570 * @class This element is used to provide a constructor for an axis. It's strictly spoken just a wrapper for element {@link Line} with {@link Line#straightFirst} 1571 * and {@link Line#straightLast} properties set to true. Additionally {@link Line#lastArrow} is set to true and default {@link Ticks} will be created. 1572 * @pseudo 1573 * @name Axis 1574 * @augments JXG.Line 1575 * @constructor 1576 * @type JXG.Line 1577 * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown. 1578 * @param {JXG.Point,array_JXG.Point,array} point1,point2 Parent elements can be two elements either of type {@link JXG.Point} or array of numbers describing the 1579 * coordinates of a point. In the latter case, the point will be constructed automatically as a fixed invisible point. 1580 * @param {Number_Number_Number} a,b,c A line can also be created providing three numbers. The line is then described by the set of solutions 1581 * of the equation <tt>a*x+b*y+c*z = 0</tt>. 1582 * @example 1583 * // Create an axis providing two coords pairs. 1584 * var l1 = board.create('axis', [[0.0, 1.0], [1.0, 1.3]]); 1585 * </pre><div class="jxgbox" id="JXG4f414733-624c-42e4-855c-11f5530383ae" style="width: 300px; height: 300px;"></div> 1586 * <script type="text/javascript"> 1587 * var axex1_board = JXG.JSXGraph.initBoard('JXG4f414733-624c-42e4-855c-11f5530383ae', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}); 1588 * var axex1_l1 = axex1_board.create('axis', [[0.0, 1.0], [1.0, 1.3]]); 1589 * </script><pre> 1590 * @example 1591 * // Create ticks labels as fractions 1592 * board.create('axis', [[0,1], [1,1]], { 1593 * ticks: { 1594 * label: { 1595 * toFraction: true, 1596 * useMathjax: false, 1597 * anchorX: 'middle', 1598 * offset: [0, -10] 1599 * } 1600 * } 1601 * }); 1602 * 1603 * 1604 * </pre><div id="JXG34174cc4-0050-4ab4-af69-e91365d0666f" class="jxgbox" style="width: 300px; height: 300px;"></div> 1605 * <script src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js" id="MathJax-script"></script> 1606 * <script type="text/javascript"> 1607 * (function() { 1608 * var board = JXG.JSXGraph.initBoard('JXG34174cc4-0050-4ab4-af69-e91365d0666f', 1609 * {boundingbox: [-1.2, 2.3, 1.2, -2.3], axis: true, showcopyright: false, shownavigation: false}); 1610 * board.create('axis', [[0,1], [1,1]], { 1611 * ticks: { 1612 * label: { 1613 * toFraction: true, 1614 * useMathjax: false, 1615 * anchorX: 'middle', 1616 * offset: [0, -10] 1617 * } 1618 * } 1619 * }); 1620 * 1621 * 1622 * })(); 1623 * 1624 * </script><pre> 1625 * 1626 */ 1627 JXG.createAxis = function (board, parents, attributes) { 1628 var axis, attr, 1629 ancestor, ticksDist; 1630 1631 // Create line 1632 attr = Type.copyAttributes(attributes, board.options, "axis"); 1633 try { 1634 axis = board.create("line", parents, attr); 1635 } catch (err) { 1636 throw new Error( 1637 "JSXGraph: Can't create axis with parent types '" + 1638 typeof parents[0] + 1639 "' and '" + 1640 typeof parents[1] + 1641 "'." + 1642 "\nPossible parent types: [point,point], [[x1,y1],[x2,y2]]" 1643 ); 1644 } 1645 1646 axis.type = Const.OBJECT_TYPE_AXIS; 1647 axis.isDraggable = false; 1648 axis.point1.isDraggable = false; 1649 axis.point2.isDraggable = false; 1650 1651 // Save usrCoords of points 1652 axis._point1UsrCoordsOrg = axis.point1.coords.usrCoords.slice(); 1653 axis._point2UsrCoordsOrg = axis.point2.coords.usrCoords.slice(); 1654 1655 for (ancestor in axis.ancestors) { 1656 if (axis.ancestors.hasOwnProperty(ancestor)) { 1657 axis.ancestors[ancestor].type = Const.OBJECT_TYPE_AXISPOINT; 1658 } 1659 } 1660 1661 // Create ticks 1662 // attrTicks = attr.ticks; 1663 if (Type.exists(attr.ticks.ticksdistance)) { 1664 ticksDist = attr.ticks.ticksdistance; 1665 } else if (Type.isArray(attr.ticks.ticks)) { 1666 ticksDist = attr.ticks.ticks; 1667 } else { 1668 ticksDist = 1.0; 1669 } 1670 1671 /** 1672 * The ticks attached to the axis. 1673 * @memberOf Axis.prototype 1674 * @name defaultTicks 1675 * @type JXG.Ticks 1676 */ 1677 axis.defaultTicks = board.create("ticks", [axis, ticksDist], attr.ticks); 1678 axis.defaultTicks.dump = false; 1679 axis.elType = "axis"; 1680 axis.subs = { 1681 ticks: axis.defaultTicks 1682 }; 1683 axis.inherits.push(axis.defaultTicks); 1684 1685 axis.update = function () { 1686 var bbox, 1687 position, i, 1688 direction, horizontal, vertical, 1689 ticksAutoPos, ticksAutoPosThres, dist, 1690 anchor, left, right, 1691 distUsr, 1692 newPosP1, newPosP2, 1693 locationOrg, 1694 visLabel, anchr, off; 1695 1696 if (!this.needsUpdate) { 1697 return this; 1698 } 1699 1700 bbox = this.board.getBoundingBox(); 1701 position = this.evalVisProp('position'); 1702 direction = this.Direction(); 1703 horizontal = this.isHorizontal(); 1704 vertical = this.isVertical(); 1705 ticksAutoPos = this.evalVisProp('ticksautopos'); 1706 ticksAutoPosThres = this.evalVisProp('ticksautoposthreshold'); 1707 1708 if (horizontal) { 1709 ticksAutoPosThres = Type.parseNumber(ticksAutoPosThres, Math.abs(bbox[1] - bbox[3]), 1 / this.board.unitX) * this.board.unitX; 1710 } else if (vertical) { 1711 ticksAutoPosThres = Type.parseNumber(ticksAutoPosThres, Math.abs(bbox[1] - bbox[3]), 1 / this.board.unitY) * this.board.unitY; 1712 } else { 1713 ticksAutoPosThres = Type.parseNumber(ticksAutoPosThres, 1, 1); 1714 } 1715 1716 anchor = this.evalVisProp('anchor'); 1717 left = anchor.indexOf('left') > -1; 1718 right = anchor.indexOf('right') > -1; 1719 1720 distUsr = this.evalVisProp('anchordist'); 1721 if (horizontal) { 1722 distUsr = Type.parseNumber(distUsr, Math.abs(bbox[1] - bbox[3]), 1 / this.board.unitX); 1723 } else if (vertical) { 1724 distUsr = Type.parseNumber(distUsr, Math.abs(bbox[0] - bbox[2]), 1 / this.board.unitY); 1725 } else { 1726 distUsr = 0; 1727 } 1728 1729 locationOrg = this.board.getPointLoc(this._point1UsrCoordsOrg, distUsr); 1730 1731 // Set position of axis 1732 newPosP1 = this.point1.coords.usrCoords.slice(); 1733 newPosP2 = this.point2.coords.usrCoords.slice(); 1734 1735 if (position === 'static' || (!vertical && !horizontal)) { 1736 // Do nothing 1737 1738 } else if (position === 'fixed') { 1739 if (horizontal) { // direction[1] === 0 1740 if ((direction[0] > 0 && right) || (direction[0] < 0 && left)) { 1741 newPosP1[2] = bbox[3] + distUsr; 1742 newPosP2[2] = bbox[3] + distUsr; 1743 } else if ((direction[0] > 0 && left) || (direction[0] < 0 && right)) { 1744 newPosP1[2] = bbox[1] - distUsr; 1745 newPosP2[2] = bbox[1] - distUsr; 1746 1747 } else { 1748 newPosP1 = this._point1UsrCoordsOrg.slice(); 1749 newPosP2 = this._point2UsrCoordsOrg.slice(); 1750 } 1751 } 1752 if (vertical) { // direction[0] === 0 1753 if ((direction[1] > 0 && left) || (direction[1] < 0 && right)) { 1754 newPosP1[1] = bbox[0] + distUsr; 1755 newPosP2[1] = bbox[0] + distUsr; 1756 1757 } else if ((direction[1] > 0 && right) || (direction[1] < 0 && left)) { 1758 newPosP1[1] = bbox[2] - distUsr; 1759 newPosP2[1] = bbox[2] - distUsr; 1760 1761 } else { 1762 newPosP1 = this._point1UsrCoordsOrg.slice(); 1763 newPosP2 = this._point2UsrCoordsOrg.slice(); 1764 } 1765 } 1766 1767 } else if (position === 'sticky') { 1768 if (horizontal) { // direction[1] === 0 1769 if (locationOrg[1] < 0 && ((direction[0] > 0 && right) || (direction[0] < 0 && left))) { 1770 newPosP1[2] = bbox[3] + distUsr; 1771 newPosP2[2] = bbox[3] + distUsr; 1772 1773 } else if (locationOrg[1] > 0 && ((direction[0] > 0 && left) || (direction[0] < 0 && right))) { 1774 newPosP1[2] = bbox[1] - distUsr; 1775 newPosP2[2] = bbox[1] - distUsr; 1776 1777 } else { 1778 newPosP1 = this._point1UsrCoordsOrg.slice(); 1779 newPosP2 = this._point2UsrCoordsOrg.slice(); 1780 } 1781 } 1782 if (vertical) { // direction[0] === 0 1783 if (locationOrg[0] < 0 && ((direction[1] > 0 && left) || (direction[1] < 0 && right))) { 1784 newPosP1[1] = bbox[0] + distUsr; 1785 newPosP2[1] = bbox[0] + distUsr; 1786 1787 } else if (locationOrg[0] > 0 && ((direction[1] > 0 && right) || (direction[1] < 0 && left))) { 1788 newPosP1[1] = bbox[2] - distUsr; 1789 newPosP2[1] = bbox[2] - distUsr; 1790 1791 } else { 1792 newPosP1 = this._point1UsrCoordsOrg.slice(); 1793 newPosP2 = this._point2UsrCoordsOrg.slice(); 1794 } 1795 } 1796 } 1797 1798 this.point1.setPositionDirectly(JXG.COORDS_BY_USER, newPosP1); 1799 this.point2.setPositionDirectly(JXG.COORDS_BY_USER, newPosP2); 1800 1801 // Set position of tick labels 1802 if (Type.exists(this.defaultTicks)) { 1803 visLabel = this.defaultTicks.visProp.label; 1804 if (ticksAutoPos && (horizontal || vertical)) { 1805 1806 if (!Type.exists(visLabel._anchorx_org)) { 1807 visLabel._anchorx_org = Type.def(visLabel.anchorx, this.board.options.text.anchorX); 1808 } 1809 if (!Type.exists(visLabel._anchory_org)) { 1810 visLabel._anchory_org = Type.def(visLabel.anchory, this.board.options.text.anchorY); 1811 } 1812 if (!Type.exists(visLabel._offset_org)) { 1813 visLabel._offset_org = visLabel.offset.slice(); 1814 } 1815 1816 off = visLabel.offset; 1817 if (horizontal) { 1818 dist = axis.point1.coords.scrCoords[2] - (this.board.canvasHeight * 0.5); 1819 1820 anchr = visLabel.anchory; 1821 1822 // The last position of the labels is stored in visLabel._side 1823 if (dist < 0 && Math.abs(dist) > ticksAutoPosThres) { 1824 // Put labels on top of the line 1825 if (visLabel._side === 'bottom') { 1826 // Switch position 1827 if (visLabel.anchory === 'top') { 1828 anchr = 'bottom'; 1829 } 1830 off[1] *= -1; 1831 visLabel._side = 'top'; 1832 } 1833 1834 } else if (dist > 0 && Math.abs(dist) > ticksAutoPosThres) { 1835 // Put labels below the line 1836 if (visLabel._side === 'top') { 1837 // Switch position 1838 if (visLabel.anchory === 'bottom') { 1839 anchr = 'top'; 1840 } 1841 off[1] *= -1; 1842 visLabel._side = 'bottom'; 1843 } 1844 1845 } else { 1846 // Put to original position 1847 anchr = visLabel._anchory_org; 1848 off = visLabel._offset_org.slice(); 1849 1850 if (anchr === 'top') { 1851 visLabel._side = 'bottom'; 1852 } else if (anchr === 'bottom') { 1853 visLabel._side = 'top'; 1854 } else if (off[1] < 0) { 1855 visLabel._side = 'bottom'; 1856 } else { 1857 visLabel._side = 'top'; 1858 } 1859 } 1860 1861 for (i = 0; i < axis.defaultTicks.labels.length; i++) { 1862 this.defaultTicks.labels[i].visProp.anchory = anchr; 1863 } 1864 visLabel.anchory = anchr; 1865 1866 } else if (vertical) { 1867 dist = axis.point1.coords.scrCoords[1] - (this.board.canvasWidth * 0.5); 1868 1869 if (dist < 0 && Math.abs(dist) > ticksAutoPosThres) { 1870 // Put labels to the left of the line 1871 if (visLabel._side === 'right') { 1872 // Switch position 1873 if (visLabel.anchorx === 'left') { 1874 anchr = 'right'; 1875 } 1876 off[0] *= -1; 1877 visLabel._side = 'left'; 1878 } 1879 1880 } else if (dist > 0 && Math.abs(dist) > ticksAutoPosThres) { 1881 // Put labels to the right of the line 1882 if (visLabel._side === 'left') { 1883 // Switch position 1884 if (visLabel.anchorx === 'right') { 1885 anchr = 'left'; 1886 } 1887 off[0] *= -1; 1888 visLabel._side = 'right'; 1889 } 1890 1891 } else { 1892 // Put to original position 1893 anchr = visLabel._anchorx_org; 1894 off = visLabel._offset_org.slice(); 1895 1896 if (anchr === 'left') { 1897 visLabel._side = 'right'; 1898 } else if (anchr === 'right') { 1899 visLabel._side = 'left'; 1900 } else if (off[0] < 0) { 1901 visLabel._side = 'left'; 1902 } else { 1903 visLabel._side = 'right'; 1904 } 1905 } 1906 1907 for (i = 0; i < axis.defaultTicks.labels.length; i++) { 1908 this.defaultTicks.labels[i].visProp.anchorx = anchr; 1909 } 1910 visLabel.anchorx = anchr; 1911 } 1912 visLabel.offset = off; 1913 1914 } else { 1915 delete visLabel._anchorx_org; 1916 delete visLabel._anchory_org; 1917 delete visLabel._offset_org; 1918 } 1919 this.defaultTicks.needsUpdate = true; 1920 } 1921 1922 JXG.Line.prototype.update.call(this); 1923 1924 return this; 1925 }; 1926 1927 return axis; 1928 }; 1929 1930 JXG.registerElement("axis", JXG.createAxis); 1931 1932 /** 1933 * @class With the element tangent the slope of a line, circle, conic, turtle, or curve in a certain point can be visualized. A tangent is always constructed 1934 * by a point on a line, circle, or curve and describes the tangent in the point on that line, circle, or curve. 1935 * <p> 1936 * If the point is not on the object (line, circle, conic, curve, turtle) the output depends on the type of the object. 1937 * For conics and circles, the polar line will be constructed. For function graphs, 1938 * the tangent of the vertical projection of the point to the function graph is constructed. For all other objects, the tangent 1939 * in the orthogonal projection of the point to the object will be constructed. 1940 * @pseudo 1941 * @name Tangent 1942 * @augments JXG.Line 1943 * @constructor 1944 * @type JXG.Line 1945 * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown. 1946 * @param {Glider} g A glider on a line, circle, or curve. 1947 * @param {JXG.GeometryElement} [c] Optional element for which the tangent is constructed 1948 * @example 1949 * // Create a tangent providing a glider on a function graph 1950 * var c1 = board.create('curve', [function(t){return t},function(t){return t*t*t;}]); 1951 * var g1 = board.create('glider', [0.6, 1.2, c1]); 1952 * var t1 = board.create('tangent', [g1]); 1953 * </pre><div class="jxgbox" id="JXG7b7233a0-f363-47dd-9df5-4018d0d17a98" style="width: 400px; height: 400px;"></div> 1954 * <script type="text/javascript"> 1955 * var tlex1_board = JXG.JSXGraph.initBoard('JXG7b7233a0-f363-47dd-9df5-4018d0d17a98', {boundingbox: [-6, 6, 6, -6], axis: true, showcopyright: false, shownavigation: false}); 1956 * var tlex1_c1 = tlex1_board.create('curve', [function(t){return t},function(t){return t*t*t;}]); 1957 * var tlex1_g1 = tlex1_board.create('glider', [0.6, 1.2, tlex1_c1]); 1958 * var tlex1_t1 = tlex1_board.create('tangent', [tlex1_g1]); 1959 * </script><pre> 1960 */ 1961 JXG.createTangent = function (board, parents, attributes) { 1962 var p, c, j, el, tangent, attr, 1963 getCurveTangentDir, 1964 res, isTransformed, 1965 slides = []; 1966 1967 if (parents.length === 1) { 1968 // One argument: glider on line, circle or curve 1969 p = parents[0]; 1970 c = p.slideObject; 1971 1972 } else if (parents.length === 2) { 1973 // Two arguments: (point,line|curve|circle|conic) or (line|curve|circle|conic,point). 1974 // In fact, for circles and conics it is the polar 1975 if (Type.isPoint(parents[0])) { 1976 p = parents[0]; 1977 c = parents[1]; 1978 } else if (Type.isPoint(parents[1])) { 1979 c = parents[0]; 1980 p = parents[1]; 1981 } else { 1982 throw new Error( 1983 "JSXGraph: Can't create tangent with parent types '" + 1984 typeof parents[0] + 1985 "' and '" + 1986 typeof parents[1] + 1987 "'." + 1988 "\nPossible parent types: [glider|point], [point,line|curve|circle|conic]" 1989 ); 1990 } 1991 } else { 1992 throw new Error( 1993 "JSXGraph: Can't create tangent with parent types '" + 1994 typeof parents[0] + 1995 "' and '" + 1996 typeof parents[1] + 1997 "'." + 1998 "\nPossible parent types: [glider|point], [point,line|curve|circle|conic]" 1999 ); 2000 } 2001 2002 attr = Type.copyAttributes(attributes, board.options, 'tangent'); 2003 if (c.elementClass === Const.OBJECT_CLASS_LINE) { 2004 tangent = board.create("line", [c.point1, c.point2], attr); 2005 tangent.glider = p; 2006 } else if ( 2007 c.elementClass === Const.OBJECT_CLASS_CURVE && 2008 c.type !== Const.OBJECT_TYPE_CONIC 2009 ) { 2010 res = c.getTransformationSource(); 2011 isTransformed = res[0]; 2012 if (isTransformed) { 2013 // Curve is result of a transformation 2014 // We recursively collect all curves from which 2015 // the curve is transformed. 2016 slides.push(c); 2017 while (res[0] && Type.exists(res[1]._transformationSource)) { 2018 slides.push(res[1]); 2019 res = res[1].getTransformationSource(); 2020 } 2021 } 2022 2023 if (c.evalVisProp('curvetype') !== "plot" || isTransformed) { 2024 // Functiongraph or parametric curve or 2025 // transformed curve thereof. 2026 tangent = board.create( 2027 "line", 2028 [ 2029 function () { 2030 var g = c.X, 2031 f = c.Y, 2032 df, dg, 2033 li, i, c_org, invMat, po, 2034 t; 2035 2036 if (p.type === Const.OBJECT_TYPE_GLIDER) { 2037 t = p.position; 2038 } else if (c.evalVisProp('curvetype') === 'functiongraph') { 2039 t = p.X(); 2040 } else { 2041 t = Geometry.projectPointToCurve(p, c, board)[1]; 2042 } 2043 2044 // po are the coordinates of the point 2045 // on the "original" curve. That is the curve or 2046 // the original curve which is transformed (maybe multiple times) 2047 // to this curve. 2048 // t is the position of the point on the "original" curve 2049 po = p.Coords(true); 2050 if (isTransformed) { 2051 c_org = slides[slides.length - 1]._transformationSource; 2052 g = c_org.X; 2053 f = c_org.Y; 2054 for (i = 0; i < slides.length; i++) { 2055 slides[i].updateTransformMatrix(); 2056 invMat = Mat.inverse(slides[i].transformMat); 2057 po = Mat.matVecMult(invMat, po); 2058 } 2059 2060 if (p.type !== Const.OBJECT_TYPE_GLIDER) { 2061 po[1] /= po[0]; 2062 po[2] /= po[0]; 2063 po[0] /= po[0]; 2064 t = Geometry.projectCoordsToCurve(po[1], po[2], 0, c_org, board)[1]; 2065 } 2066 } 2067 2068 // li are the coordinates of the line on the "original" curve 2069 df = Numerics.D(f)(t); 2070 dg = Numerics.D(g)(t); 2071 li = [ 2072 -po[1] * df + po[2] * dg, 2073 po[0] * df, 2074 -po[0] * dg 2075 ]; 2076 2077 if (isTransformed) { 2078 // Transform the line to the transformed curve 2079 for (i = slides.length - 1; i >= 0; i--) { 2080 invMat = Mat.transpose(Mat.inverse(slides[i].transformMat)); 2081 li = Mat.matVecMult(invMat, li); 2082 } 2083 } 2084 2085 return li; 2086 } 2087 ], 2088 attr 2089 ); 2090 2091 p.addChild(tangent); 2092 // this is required for the geogebra reader to display a slope 2093 tangent.glider = p; 2094 } else { 2095 // curveType 'plot': discrete data 2096 /** 2097 * @ignore 2098 * 2099 * In case of bezierDegree == 1: 2100 * Find two points p1, p2 enclosing the glider. 2101 * Then the equation of the line segment is: 0 = y*(x1-x2) + x*(y2-y1) + y1*x2-x1*y2, 2102 * which is the cross product of p1 and p2. 2103 * 2104 * In case of bezierDegree === 3: 2105 * The slope dy / dx of the tangent is determined. Then the 2106 * tangent is computed as cross product between 2107 * the glider p and [1, p.X() + dx, p.Y() + dy] 2108 * 2109 */ 2110 getCurveTangentDir = function (position, c, num) { 2111 var i = Math.floor(position), 2112 p1, p2, t, A, B, C, D, dx, dy, d, 2113 points, le; 2114 2115 if (c.bezierDegree === 1) { 2116 if (i === c.numberPoints - 1) { 2117 i--; 2118 } 2119 } else if (c.bezierDegree === 3) { 2120 // i is start of the Bezier segment 2121 // t is the position in the Bezier segment 2122 if (c.elType === 'sector') { 2123 points = c.points.slice(3, c.numberPoints - 3); 2124 le = points.length; 2125 } else { 2126 points = c.points; 2127 le = points.length; 2128 } 2129 i = Math.floor((position * (le - 1)) / 3) * 3; 2130 t = (position * (le - 1) - i) / 3; 2131 if (i >= le - 1) { 2132 i = le - 4; 2133 t = 1; 2134 } 2135 } else { 2136 return 0; 2137 } 2138 2139 if (i < 0) { 2140 return 1; 2141 } 2142 2143 // The curve points are transformed (if there is a transformation) 2144 // c.X(i) is not transformed. 2145 if (c.bezierDegree === 1) { 2146 p1 = c.points[i].usrCoords; 2147 p2 = c.points[i + 1].usrCoords; 2148 } else { 2149 A = points[i].usrCoords; 2150 B = points[i + 1].usrCoords; 2151 C = points[i + 2].usrCoords; 2152 D = points[i + 3].usrCoords; 2153 dx = (1 - t) * (1 - t) * (B[1] - A[1]) + 2154 2 * (1 - t) * t * (C[1] - B[1]) + 2155 t * t * (D[1] - C[1]); 2156 dy = (1 - t) * (1 - t) * (B[2] - A[2]) + 2157 2 * (1 - t) * t * (C[2] - B[2]) + 2158 t * t * (D[2] - C[2]); 2159 d = Mat.hypot(dx, dy); 2160 dx /= d; 2161 dy /= d; 2162 p1 = p.coords.usrCoords; 2163 p2 = [1, p1[1] + dx, p1[2] + dy]; 2164 } 2165 2166 switch (num) { 2167 case 0: 2168 return p1[2] * p2[1] - p1[1] * p2[2]; 2169 case 1: 2170 return p2[2] - p1[2]; 2171 case 2: 2172 return p1[1] - p2[1]; 2173 default: 2174 return [ 2175 p1[2] * p2[1] - p1[1] * p2[2], 2176 p2[2] - p1[2], 2177 p1[1] - p2[1] 2178 ]; 2179 } 2180 }; 2181 2182 tangent = board.create( 2183 "line", 2184 [ 2185 function () { 2186 var t; 2187 2188 if (p.type === Const.OBJECT_TYPE_GLIDER) { 2189 t = p.position; 2190 } else { 2191 t = Geometry.projectPointToCurve(p, c, board)[1]; 2192 } 2193 2194 return getCurveTangentDir(t, c); 2195 } 2196 ], 2197 attr 2198 ); 2199 2200 p.addChild(tangent); 2201 // this is required for the geogebra reader to display a slope 2202 tangent.glider = p; 2203 } 2204 } else if (c.type === Const.OBJECT_TYPE_TURTLE) { 2205 tangent = board.create( 2206 "line", 2207 [ 2208 function () { 2209 var i, t; 2210 if (p.type === Const.OBJECT_TYPE_GLIDER) { 2211 t = p.position; 2212 } else { 2213 t = Geometry.projectPointToTurtle(p, c, board)[1]; 2214 } 2215 2216 i = Math.floor(t); 2217 2218 // run through all curves of this turtle 2219 for (j = 0; j < c.objects.length; j++) { 2220 el = c.objects[j]; 2221 2222 if (el.type === Const.OBJECT_TYPE_CURVE) { 2223 if (i < el.numberPoints) { 2224 break; 2225 } 2226 2227 i -= el.numberPoints; 2228 } 2229 } 2230 2231 if (i === el.numberPoints - 1) { 2232 i--; 2233 } 2234 2235 if (i < 0) { 2236 return [1, 0, 0]; 2237 } 2238 2239 return [ 2240 el.Y(i) * el.X(i + 1) - el.X(i) * el.Y(i + 1), 2241 el.Y(i + 1) - el.Y(i), 2242 el.X(i) - el.X(i + 1) 2243 ]; 2244 } 2245 ], 2246 attr 2247 ); 2248 p.addChild(tangent); 2249 2250 // this is required for the geogebra reader to display a slope 2251 tangent.glider = p; 2252 } else if ( 2253 c.elementClass === Const.OBJECT_CLASS_CIRCLE || 2254 c.type === Const.OBJECT_TYPE_CONIC 2255 ) { 2256 // If p is not on c, the tangent is the polar. 2257 // This construction should work on conics, too. p has to lie on c. 2258 tangent = board.create( 2259 "line", 2260 [ 2261 function () { 2262 return Mat.matVecMult(c.quadraticform, p.coords.usrCoords); 2263 } 2264 ], 2265 attr 2266 ); 2267 2268 p.addChild(tangent); 2269 // this is required for the geogebra reader to display a slope 2270 tangent.glider = p; 2271 } 2272 2273 if (!Type.exists(tangent)) { 2274 throw new Error("JSXGraph: Couldn't create tangent with the given parents."); 2275 } 2276 2277 tangent.elType = "tangent"; 2278 tangent.type = Const.OBJECT_TYPE_TANGENT; 2279 tangent.setParents(parents); 2280 2281 return tangent; 2282 }; 2283 2284 /** 2285 * @class Constructs a normal. 2286 * @pseudo 2287 * @description A normal is a line through a given point on an element of type line, circle, curve, or turtle and orthogonal to that object. 2288 * @constructor 2289 * @name Normal 2290 * @type JXG.Line 2291 * @augments JXG.Line 2292 * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown. 2293 * @param {JXG.Line,JXG.Circle,JXG.Curve,JXG.Turtle_JXG.Point} o,p The constructed line contains p which lies on the object and is orthogonal 2294 * to the tangent to the object in the given point. 2295 * @param {Glider} p Works like above, however the object is given by {@link JXG.CoordsElement#slideObject}. 2296 * @example 2297 * // Create a normal to a circle. 2298 * var p1 = board.create('point', [2.0, 2.0]); 2299 * var p2 = board.create('point', [3.0, 2.0]); 2300 * var c1 = board.create('circle', [p1, p2]); 2301 * 2302 * var norm1 = board.create('normal', [c1, p2]); 2303 * </pre><div class="jxgbox" id="JXG4154753d-3d29-40fb-a860-0b08aa4f3743" style="width: 400px; height: 400px;"></div> 2304 * <script type="text/javascript"> 2305 * var nlex1_board = JXG.JSXGraph.initBoard('JXG4154753d-3d29-40fb-a860-0b08aa4f3743', {boundingbox: [-1, 9, 9, -1], axis: true, showcopyright: false, shownavigation: false}); 2306 * var nlex1_p1 = nlex1_board.create('point', [2.0, 2.0]); 2307 * var nlex1_p2 = nlex1_board.create('point', [3.0, 2.0]); 2308 * var nlex1_c1 = nlex1_board.create('circle', [nlex1_p1, nlex1_p2]); 2309 * 2310 * // var nlex1_p3 = nlex1_board.create('point', [1.0, 2.0]); 2311 * var nlex1_norm1 = nlex1_board.create('normal', [nlex1_c1, nlex1_p2]); 2312 * </script><pre> 2313 */ 2314 JXG.createNormal = function (board, parents, attributes) { 2315 var p, c, l, i, attr, pp, attrp, 2316 getCurveNormalDir, 2317 res, isTransformed, 2318 slides = []; 2319 2320 for (i = 0; i < parents.length; ++i) { 2321 parents[i] = board.select(parents[i]); 2322 } 2323 // One arguments: glider on line, circle or curve 2324 if (parents.length === 1) { 2325 p = parents[0]; 2326 c = p.slideObject; 2327 // Two arguments: (point,line), (point,circle), (line,point) or (circle,point) 2328 } else if (parents.length === 2) { 2329 if (Type.isPointType(board, parents[0])) { 2330 p = Type.providePoints(board, [parents[0]], attributes, "point")[0]; 2331 c = parents[1]; 2332 } else if (Type.isPointType(board, parents[1])) { 2333 c = parents[0]; 2334 p = Type.providePoints(board, [parents[1]], attributes, "point")[0]; 2335 } else { 2336 throw new Error( 2337 "JSXGraph: Can't create normal with parent types '" + 2338 typeof parents[0] + 2339 "' and '" + 2340 typeof parents[1] + 2341 "'." + 2342 "\nPossible parent types: [point,line], [point,circle], [glider]" 2343 ); 2344 } 2345 } else { 2346 throw new Error( 2347 "JSXGraph: Can't create normal with parent types '" + 2348 typeof parents[0] + 2349 "' and '" + 2350 typeof parents[1] + 2351 "'." + 2352 "\nPossible parent types: [point,line], [point,circle], [glider]" 2353 ); 2354 } 2355 2356 attr = Type.copyAttributes(attributes, board.options, "normal"); 2357 if (c.elementClass === Const.OBJECT_CLASS_LINE) { 2358 // Private point 2359 attrp = Type.copyAttributes(attributes, board.options, "normal", "point"); 2360 pp = board.create( 2361 "point", 2362 [ 2363 function () { 2364 var p = Mat.crossProduct([1, 0, 0], c.stdform); 2365 return [p[0], -p[2], p[1]]; 2366 } 2367 ], 2368 attrp 2369 ); 2370 pp.isDraggable = true; 2371 2372 l = board.create("line", [p, pp], attr); 2373 2374 /** 2375 * A helper point used to create a normal to a {@link JXG.Line} object. For normals to circles or curves this 2376 * element is <tt>undefined</tt>. 2377 * @type JXG.Point 2378 * @name point 2379 * @memberOf Normal.prototype 2380 */ 2381 l.point = pp; 2382 l.subs = { 2383 point: pp 2384 }; 2385 l.inherits.push(pp); 2386 } else if (c.elementClass === Const.OBJECT_CLASS_CIRCLE) { 2387 l = board.create("line", [c.midpoint, p], attr); 2388 } else if (c.elementClass === Const.OBJECT_CLASS_CURVE) { 2389 res = c.getTransformationSource(); 2390 isTransformed = res[0]; 2391 if (isTransformed) { 2392 // Curve is result of a transformation 2393 // We recursively collect all curves from which 2394 // the curve is transformed. 2395 slides.push(c); 2396 while (res[0] && Type.exists(res[1]._transformationSource)) { 2397 slides.push(res[1]); 2398 res = res[1].getTransformationSource(); 2399 } 2400 } 2401 2402 if (c.evalVisProp('curvetype') !== "plot" || isTransformed) { 2403 // Functiongraph or parametric curve or 2404 // transformed curve thereof. 2405 l = board.create( 2406 "line", 2407 [ 2408 function () { 2409 var g = c.X, 2410 f = c.Y, 2411 df, dg, 2412 li, i, c_org, invMat, po, 2413 t; 2414 2415 if (p.type === Const.OBJECT_TYPE_GLIDER) { 2416 t = p.position; 2417 } else if (c.evalVisProp('curvetype') === 'functiongraph') { 2418 t = p.X(); 2419 } else { 2420 t = Geometry.projectPointToCurve(p, c, board)[1]; 2421 } 2422 2423 // po are the coordinates of the point 2424 // on the "original" curve. That is the curve or 2425 // the original curve which is transformed (maybe multiple times) 2426 // to this curve. 2427 // t is the position of the point on the "original" curve 2428 po = p.Coords(true); 2429 if (isTransformed) { 2430 c_org = slides[slides.length - 1]._transformationSource; 2431 g = c_org.X; 2432 f = c_org.Y; 2433 for (i = 0; i < slides.length; i++) { 2434 slides[i].updateTransformMatrix(); 2435 invMat = Mat.inverse(slides[i].transformMat); 2436 po = Mat.matVecMult(invMat, po); 2437 } 2438 2439 if (p.type !== Const.OBJECT_TYPE_GLIDER) { 2440 po[1] /= po[0]; 2441 po[2] /= po[0]; 2442 po[0] /= po[0]; 2443 t = Geometry.projectCoordsToCurve(po[1], po[2], 0, c_org, board)[1]; 2444 } 2445 } 2446 2447 df = Numerics.D(f)(t); 2448 dg = Numerics.D(g)(t); 2449 li = [ 2450 -po[1] * dg - po[2] * df, 2451 po[0] * dg, 2452 po[0] * df 2453 ]; 2454 2455 if (isTransformed) { 2456 // Transform the line to the transformed curve 2457 for (i = slides.length - 1; i >= 0; i--) { 2458 invMat = Mat.transpose(Mat.inverse(slides[i].transformMat)); 2459 li = Mat.matVecMult(invMat, li); 2460 } 2461 } 2462 2463 return li; 2464 } 2465 ], 2466 attr 2467 ); 2468 } else { 2469 // curveType 'plot': discrete data 2470 getCurveNormalDir = function (position, c, num) { 2471 var i = Math.floor(position), 2472 lbda, 2473 p1, p2, t, A, B, C, D, dx, dy, d, 2474 li, p_org, pp, 2475 points, le; 2476 2477 2478 if (c.bezierDegree === 1) { 2479 if (i === c.numberPoints - 1) { 2480 i--; 2481 } 2482 t = position; 2483 } else if (c.bezierDegree === 3) { 2484 // i is start of the Bezier segment 2485 // t is the position in the Bezier segment 2486 if (c.elType === 'sector') { 2487 points = c.points.slice(3, c.numberPoints - 3); 2488 le = points.length; 2489 } else { 2490 points = c.points; 2491 le = points.length; 2492 } 2493 i = Math.floor((position * (le - 1)) / 3) * 3; 2494 t = (position * (le - 1) - i) / 3; 2495 if (i >= le - 1) { 2496 i = le - 4; 2497 t = 1; 2498 } 2499 } else { 2500 return 0; 2501 } 2502 2503 if (i < 0) { 2504 return 1; 2505 } 2506 2507 lbda = t - i; 2508 if (c.bezierDegree === 1) { 2509 p1 = c.points[i].usrCoords; 2510 p2 = c.points[i + 1].usrCoords; 2511 p_org = [ 2512 p1[0] + lbda * (p2[0] - p1[0]), 2513 p1[1] + lbda * (p2[1] - p1[1]), 2514 p1[2] + lbda * (p2[2] - p1[2]) 2515 ]; 2516 li = Mat.crossProduct(p1, p2); 2517 pp = Mat.crossProduct([1, 0, 0], li); 2518 pp = [pp[0], -pp[2], pp[1]]; 2519 li = Mat.crossProduct(p_org, pp); 2520 2521 } else { 2522 A = points[i].usrCoords; 2523 B = points[i + 1].usrCoords; 2524 C = points[i + 2].usrCoords; 2525 D = points[i + 3].usrCoords; 2526 dx = 2527 (1 - t) * (1 - t) * (B[1] - A[1]) + 2528 2 * (1 - t) * t * (C[1] - B[1]) + 2529 t * t * (D[1] - C[1]); 2530 dy = 2531 (1 - t) * (1 - t) * (B[2] - A[2]) + 2532 2 * (1 - t) * t * (C[2] - B[2]) + 2533 t * t * (D[2] - C[2]); 2534 d = Mat.hypot(dx, dy); 2535 dx /= d; 2536 dy /= d; 2537 p1 = p.coords.usrCoords; 2538 p2 = [1, p1[1] - dy, p1[2] + dx]; 2539 2540 li = [ 2541 p1[2] * p2[1] - p1[1] * p2[2], 2542 p2[2] - p1[2], 2543 p1[1] - p2[1] 2544 ]; 2545 } 2546 2547 switch (num) { 2548 case 0: 2549 return li[0]; 2550 case 1: 2551 return li[1]; 2552 case 2: 2553 return li[2]; 2554 default: 2555 return li; 2556 } 2557 }; 2558 2559 l = board.create( 2560 "line", 2561 [ 2562 function () { 2563 var t; 2564 2565 if (p.type === Const.OBJECT_TYPE_GLIDER) { 2566 t = p.position; 2567 } else { 2568 t = Geometry.projectPointToCurve(p, c, board)[1]; 2569 } 2570 2571 return getCurveNormalDir(t, c); 2572 } 2573 ], 2574 attr 2575 ); 2576 p.addChild(l); 2577 l.glider = p; 2578 } 2579 } else if (c.type === Const.OBJECT_TYPE_TURTLE) { 2580 l = board.create( 2581 "line", 2582 [ 2583 function () { 2584 var el, 2585 j, 2586 i = Math.floor(p.position), 2587 lbda = p.position - i; 2588 2589 // run through all curves of this turtle 2590 for (j = 0; j < c.objects.length; j++) { 2591 el = c.objects[j]; 2592 2593 if (el.type === Const.OBJECT_TYPE_CURVE) { 2594 if (i < el.numberPoints) { 2595 break; 2596 } 2597 2598 i -= el.numberPoints; 2599 } 2600 } 2601 2602 if (i === el.numberPoints - 1) { 2603 i -= 1; 2604 lbda = 1; 2605 } 2606 2607 if (i < 0) { 2608 return 1; 2609 } 2610 2611 return ( 2612 (el.Y(i) + lbda * (el.Y(i + 1) - el.Y(i))) * (el.Y(i) - el.Y(i + 1)) - 2613 (el.X(i) + lbda * (el.X(i + 1) - el.X(i))) * (el.X(i + 1) - el.X(i)) 2614 ); 2615 }, 2616 function () { 2617 var el, 2618 j, 2619 i = Math.floor(p.position); 2620 2621 // run through all curves of this turtle 2622 for (j = 0; j < c.objects.length; j++) { 2623 el = c.objects[j]; 2624 if (el.type === Const.OBJECT_TYPE_CURVE) { 2625 if (i < el.numberPoints) { 2626 break; 2627 } 2628 2629 i -= el.numberPoints; 2630 } 2631 } 2632 2633 if (i === el.numberPoints - 1) { 2634 i -= 1; 2635 } 2636 2637 if (i < 0) { 2638 return 0; 2639 } 2640 2641 return el.X(i + 1) - el.X(i); 2642 }, 2643 function () { 2644 var el, 2645 j, 2646 i = Math.floor(p.position); 2647 2648 // run through all curves of this turtle 2649 for (j = 0; j < c.objects.length; j++) { 2650 el = c.objects[j]; 2651 if (el.type === Const.OBJECT_TYPE_CURVE) { 2652 if (i < el.numberPoints) { 2653 break; 2654 } 2655 2656 i -= el.numberPoints; 2657 } 2658 } 2659 2660 if (i === el.numberPoints - 1) { 2661 i -= 1; 2662 } 2663 2664 if (i < 0) { 2665 return 0; 2666 } 2667 2668 return el.Y(i + 1) - el.Y(i); 2669 } 2670 ], 2671 attr 2672 ); 2673 } else { 2674 throw new Error( 2675 "JSXGraph: Can't create normal with parent types '" + 2676 typeof parents[0] + 2677 "' and '" + 2678 typeof parents[1] + 2679 "'." + 2680 "\nPossible parent types: [point,line], [point,circle], [glider]" 2681 ); 2682 } 2683 2684 l.elType = "normal"; 2685 l.setParents(parents); 2686 2687 if (Type.exists(p._is_new)) { 2688 l.addChild(p); 2689 delete p._is_new; 2690 } else { 2691 p.addChild(l); 2692 } 2693 c.addChild(l); 2694 2695 return l; 2696 }; 2697 2698 /** 2699 * @class This element is used to provide a constructor for the radical axis with respect to two circles with distinct centers. 2700 * The angular bisector of the polar lines of the circle centers with respect to the other circle is always the radical axis. 2701 * The radical axis passes through the intersection points when the circles intersect. 2702 * When a circle about the midpoint of circle centers, passing through the circle centers, intersects the circles, the polar lines pass through those intersection points. 2703 * @pseudo 2704 * @name RadicalAxis 2705 * @augments JXG.Line 2706 * @constructor 2707 * @type JXG.Line 2708 * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown. 2709 * @param {JXG.Circle} circle Circle one of the two respective circles. 2710 * @param {JXG.Circle} circle Circle the other of the two respective circles. 2711 * @example 2712 * // Create the radical axis line with respect to two circles 2713 * var board = JXG.JSXGraph.initBoard('7b7233a0-f363-47dd-9df5-5018d0d17a98', {boundingbox: [-1, 9, 9, -1], axis: true, showcopyright: false, shownavigation: false}); 2714 * var p1 = board.create('point', [2, 3]); 2715 * var p2 = board.create('point', [1, 4]); 2716 * var c1 = board.create('circle', [p1, p2]); 2717 * var p3 = board.create('point', [6, 5]); 2718 * var p4 = board.create('point', [8, 6]); 2719 * var c2 = board.create('circle', [p3, p4]); 2720 * var r1 = board.create('radicalaxis', [c1, c2]); 2721 * </pre><div class="jxgbox" id="JXG7b7233a0-f363-47dd-9df5-5018d0d17a98" class="jxgbox" style="width:400px; height:400px;"></div> 2722 * <script type='text/javascript'> 2723 * var rlex1_board = JXG.JSXGraph.initBoard('JXG7b7233a0-f363-47dd-9df5-5018d0d17a98', {boundingbox: [-1, 9, 9, -1], axis: true, showcopyright: false, shownavigation: false}); 2724 * var rlex1_p1 = rlex1_board.create('point', [2, 3]); 2725 * var rlex1_p2 = rlex1_board.create('point', [1, 4]); 2726 * var rlex1_c1 = rlex1_board.create('circle', [rlex1_p1, rlex1_p2]); 2727 * var rlex1_p3 = rlex1_board.create('point', [6, 5]); 2728 * var rlex1_p4 = rlex1_board.create('point', [8, 6]); 2729 * var rlex1_c2 = rlex1_board.create('circle', [rlex1_p3, rlex1_p4]); 2730 * var rlex1_r1 = rlex1_board.create('radicalaxis', [rlex1_c1, rlex1_c2]); 2731 * </script><pre> 2732 */ 2733 JXG.createRadicalAxis = function (board, parents, attributes) { 2734 var el, el1, el2; 2735 2736 if ( 2737 parents.length !== 2 || 2738 parents[0].elementClass !== Const.OBJECT_CLASS_CIRCLE || 2739 parents[1].elementClass !== Const.OBJECT_CLASS_CIRCLE 2740 ) { 2741 // Failure 2742 throw new Error( 2743 "JSXGraph: Can't create 'radical axis' with parent types '" + 2744 typeof parents[0] + 2745 "' and '" + 2746 typeof parents[1] + 2747 "'." + 2748 "\nPossible parent type: [circle,circle]" 2749 ); 2750 } 2751 2752 el1 = board.select(parents[0]); 2753 el2 = board.select(parents[1]); 2754 2755 el = board.create( 2756 "line", 2757 [ 2758 function () { 2759 var a = el1.stdform, 2760 b = el2.stdform; 2761 2762 return Mat.matVecMult(Mat.transpose([a.slice(0, 3), b.slice(0, 3)]), [ 2763 b[3], 2764 -a[3] 2765 ]); 2766 } 2767 ], 2768 attributes 2769 ); 2770 2771 el.elType = "radicalaxis"; 2772 el.setParents([el1.id, el2.id]); 2773 2774 el1.addChild(el); 2775 el2.addChild(el); 2776 2777 return el; 2778 }; 2779 2780 /** 2781 * @class This element is used to provide a constructor for the polar line of a point with respect to a conic or a circle. 2782 * @pseudo 2783 * @description The polar line is the unique reciprocal relationship of a point with respect to a conic. 2784 * The lines through the intersections of a conic and the polar line of a point with respect to that conic and through that point are tangent to the conic. 2785 * A point on a conic has the polar line of that point with respect to that conic as the tangent line to that conic at that point. 2786 * See {@link https://en.wikipedia.org/wiki/Pole_and_polar} for more information on pole and polar. 2787 * @name PolarLine 2788 * @augments JXG.Line 2789 * @constructor 2790 * @type JXG.Line 2791 * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown. 2792 * @param {JXG.Conic,JXG.Circle_JXG.Point} el1,el2 or 2793 * @param {JXG.Point_JXG.Conic,JXG.Circle} el1,el2 The result will be the polar line of the point with respect to the conic or the circle. 2794 * @example 2795 * // Create the polar line of a point with respect to a conic 2796 * var p1 = board.create('point', [-1, 2]); 2797 * var p2 = board.create('point', [ 1, 4]); 2798 * var p3 = board.create('point', [-1,-2]); 2799 * var p4 = board.create('point', [ 0, 0]); 2800 * var p5 = board.create('point', [ 4,-2]); 2801 * var c1 = board.create('conic',[p1,p2,p3,p4,p5]); 2802 * var p6 = board.create('point', [-1, 1]); 2803 * var l1 = board.create('polarline', [c1, p6]); 2804 * </pre><div class="jxgbox" id="JXG7b7233a0-f363-47dd-9df5-6018d0d17a98" class="jxgbox" style="width:400px; height:400px;"></div> 2805 * <script type='text/javascript'> 2806 * var plex1_board = JXG.JSXGraph.initBoard('JXG7b7233a0-f363-47dd-9df5-6018d0d17a98', {boundingbox: [-3, 5, 5, -3], axis: true, showcopyright: false, shownavigation: false}); 2807 * var plex1_p1 = plex1_board.create('point', [-1, 2]); 2808 * var plex1_p2 = plex1_board.create('point', [ 1, 4]); 2809 * var plex1_p3 = plex1_board.create('point', [-1,-2]); 2810 * var plex1_p4 = plex1_board.create('point', [ 0, 0]); 2811 * var plex1_p5 = plex1_board.create('point', [ 4,-2]); 2812 * var plex1_c1 = plex1_board.create('conic',[plex1_p1,plex1_p2,plex1_p3,plex1_p4,plex1_p5]); 2813 * var plex1_p6 = plex1_board.create('point', [-1, 1]); 2814 * var plex1_l1 = plex1_board.create('polarline', [plex1_c1, plex1_p6]); 2815 * </script><pre> 2816 * @example 2817 * // Create the polar line of a point with respect to a circle. 2818 * var p1 = board.create('point', [ 1, 1]); 2819 * var p2 = board.create('point', [ 2, 3]); 2820 * var c1 = board.create('circle',[p1,p2]); 2821 * var p3 = board.create('point', [ 6, 6]); 2822 * var l1 = board.create('polarline', [c1, p3]); 2823 * </pre><div class="jxgbox" id="JXG7b7233a0-f363-47dd-9df5-7018d0d17a98" class="jxgbox" style="width:400px; height:400px;"></div> 2824 * <script type='text/javascript'> 2825 * var plex2_board = JXG.JSXGraph.initBoard('JXG7b7233a0-f363-47dd-9df5-7018d0d17a98', {boundingbox: [-3, 7, 7, -3], axis: true, showcopyright: false, shownavigation: false}); 2826 * var plex2_p1 = plex2_board.create('point', [ 1, 1]); 2827 * var plex2_p2 = plex2_board.create('point', [ 2, 3]); 2828 * var plex2_c1 = plex2_board.create('circle',[plex2_p1,plex2_p2]); 2829 * var plex2_p3 = plex2_board.create('point', [ 6, 6]); 2830 * var plex2_l1 = plex2_board.create('polarline', [plex2_c1, plex2_p3]); 2831 * </script><pre> 2832 */ 2833 JXG.createPolarLine = function (board, parents, attributes) { 2834 var el, 2835 el1, 2836 el2, 2837 firstParentIsConic, 2838 secondParentIsConic, 2839 firstParentIsPoint, 2840 secondParentIsPoint; 2841 2842 if (parents.length > 1) { 2843 firstParentIsConic = 2844 parents[0].type === Const.OBJECT_TYPE_CONIC || 2845 parents[0].elementClass === Const.OBJECT_CLASS_CIRCLE; 2846 secondParentIsConic = 2847 parents[1].type === Const.OBJECT_TYPE_CONIC || 2848 parents[1].elementClass === Const.OBJECT_CLASS_CIRCLE; 2849 2850 firstParentIsPoint = Type.isPoint(parents[0]); 2851 secondParentIsPoint = Type.isPoint(parents[1]); 2852 } 2853 2854 if ( 2855 parents.length !== 2 || 2856 !( 2857 (firstParentIsConic && secondParentIsPoint) || 2858 (firstParentIsPoint && secondParentIsConic) 2859 ) 2860 ) { 2861 // Failure 2862 throw new Error( 2863 "JSXGraph: Can't create 'polar line' with parent types '" + 2864 typeof parents[0] + 2865 "' and '" + 2866 typeof parents[1] + 2867 "'." + 2868 "\nPossible parent type: [conic|circle,point], [point,conic|circle]" 2869 ); 2870 } 2871 2872 if (secondParentIsPoint) { 2873 el1 = board.select(parents[0]); 2874 el2 = board.select(parents[1]); 2875 } else { 2876 el1 = board.select(parents[1]); 2877 el2 = board.select(parents[0]); 2878 } 2879 2880 // Polar lines have been already provided in the tangent element. 2881 el = board.create("tangent", [el1, el2], attributes); 2882 2883 el.elType = "polarline"; 2884 return el; 2885 }; 2886 2887 /** 2888 * 2889 * @class This element is used to provide a constructor for the tangent through a point to a conic or a circle. 2890 * @pseudo 2891 * @description Construct the tangent line through a point to a conic or a circle. There will be either two, one or no 2892 * such tangent, depending if the point is outside of the conic, on the conic, or inside of the conic. 2893 * Similar to the intersection of a line with a circle, the specific tangent can be chosen with a third (optional) parameter 2894 * <i>number</i>. 2895 * <p> 2896 * Attention: from a technical point of view, the point from which the tangent to the conic/circle is constructed is not an element of 2897 * the tangent line. 2898 * @name TangentTo 2899 * @augments JXG.Line 2900 * @constructor 2901 * @type JXG.Line 2902 * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown. 2903 * @param {JXG.Conic,JXG.Circle_JXG.Point_Number} conic,point,[number=0] The result will be the tangent line through 2904 * the point with respect to the conic or circle. 2905 * 2906 * @example 2907 * var c = board.create('circle', [[3, 0], [3, 4]]); 2908 * var p = board.create('point', [0, 6]); 2909 * var t0 = board.create('tangentto', [c, p, 0], { color: 'black', polar: {visible: true}, point: {visible: true} }); 2910 * var t1 = board.create('tangentto', [c, p, 1], { color: 'black' }); 2911 * 2912 * </pre><div id="JXGd4b359c7-3a29-44c3-a19d-d51b42a00c8b" class="jxgbox" style="width: 300px; height: 300px;"></div> 2913 * <script type="text/javascript"> 2914 * (function() { 2915 * var board = JXG.JSXGraph.initBoard('JXGd4b359c7-3a29-44c3-a19d-d51b42a00c8b', 2916 * {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false}); 2917 * var c = board.create('circle', [[3, 0], [3, 4]]); 2918 * var p = board.create('point', [0, 6]); 2919 * var t0 = board.create('tangentto', [c, p, 0], { color: 'black', polar: {visible: true}, point: {visible: true} }); 2920 * var t1 = board.create('tangentto', [c, p, 1], { color: 'black' }); 2921 * 2922 * })(); 2923 * 2924 * </script><pre> 2925 * 2926 * @example 2927 * var p = board.create('point', [0, 6]); 2928 * var ell = board.create('ellipse', [[-5, 1], [-2, -1], [-3, 2]]); 2929 * var t0 = board.create('tangentto', [ell, p, 0]); 2930 * var t1 = board.create('tangentto', [ell, p, 1]); 2931 * 2932 * </pre><div id="JXG6e625663-1c3e-4e08-a9df-574972a374e8" class="jxgbox" style="width: 300px; height: 300px;"></div> 2933 * <script type="text/javascript"> 2934 * (function() { 2935 * var board = JXG.JSXGraph.initBoard('JXG6e625663-1c3e-4e08-a9df-574972a374e8', 2936 * {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false}); 2937 * var p = board.create('point', [0, 6]); 2938 * var ell = board.create('ellipse', [[-5, 1], [-2, -1], [-3, 2]]); 2939 * var t0 = board.create('tangentto', [ell, p, 0]); 2940 * var t1 = board.create('tangentto', [ell, p, 1]); 2941 * 2942 * })(); 2943 * 2944 * </script><pre> 2945 * 2946 */ 2947 JXG.createTangentTo = function (board, parents, attributes) { 2948 var el, attr, 2949 conic, pointFrom, num, 2950 intersect, polar; 2951 2952 conic = board.select(parents[0]); 2953 pointFrom = Type.providePoints(board, parents[1], attributes, 'point')[0]; 2954 num = Type.def(parents[2], 0); 2955 2956 if ( 2957 (conic.type !== Const.OBJECT_TYPE_CIRCLE && conic.type !== Const.OBJECT_TYPE_CONIC) || 2958 (pointFrom.elementClass !== Const.OBJECT_CLASS_POINT) 2959 ) { 2960 throw new Error( 2961 "JSXGraph: Can't create tangentto with parent types '" + 2962 typeof parents[0] + 2963 "' and '" + 2964 typeof parents[1] + 2965 "' and '" + 2966 typeof parents[2] + 2967 "'." + 2968 "\nPossible parent types: [circle|conic,point,number]" 2969 ); 2970 } 2971 2972 attr = Type.copyAttributes(attributes, board.options, 'tangentto'); 2973 // A direct analytic geometry approach would be in 2974 // Richter-Gebert: Perspectives on projective geometry, 11.3 2975 polar = board.create('polar', [conic, pointFrom], attr.polar); 2976 intersect = board.create('intersection', [polar, conic, num], attr.point); 2977 2978 el = board.create('tangent', [conic, intersect], attr); 2979 2980 /** 2981 * The intersection point of the conic/circle with the polar line of the tangentto construction. 2982 * @memberOf TangentTo.prototype 2983 * @name point 2984 * @type JXG.Point 2985 */ 2986 el.point = intersect; 2987 2988 /** 2989 * The polar line of the tangentto construction. 2990 * @memberOf TangentTo.prototype 2991 * @name polar 2992 * @type JXG.Line 2993 */ 2994 el.polar = polar; 2995 2996 el.elType = 'tangentto'; 2997 2998 return el; 2999 }; 3000 3001 /** 3002 * Register the element type tangent at JSXGraph 3003 * @private 3004 */ 3005 JXG.registerElement("tangent", JXG.createTangent); 3006 JXG.registerElement("normal", JXG.createNormal); 3007 JXG.registerElement('tangentto', JXG.createTangentTo); 3008 JXG.registerElement("polar", JXG.createTangent); 3009 JXG.registerElement("radicalaxis", JXG.createRadicalAxis); 3010 JXG.registerElement("polarline", JXG.createPolarLine); 3011 3012 export default JXG.Line; 3013 // export default { 3014 // Line: JXG.Line, 3015 // createLine: JXG.createLine, 3016 // createTangent: JXG.createTangent, 3017 // createPolar: JXG.createTangent, 3018 // createSegment: JXG.createSegment, 3019 // createAxis: JXG.createAxis, 3020 // createArrow: JXG.createArrow, 3021 // createRadicalAxis: JXG.createRadicalAxis, 3022 // createPolarLine: JXG.createPolarLine 3023 // }; 3024