1 /* 2 Copyright 2008-2025 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 A general line is given by two points or three coordinates. 1073 * By setting additional properties 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 A (line) segment defined by two points. 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 A segment with an arrow head. 1527 * This element is just a wrapper for element 1528 * {@link Line} with {@link Line#straightFirst} 1529 * and {@link Line#straightLast} properties set to false and {@link Line#lastArrow} set to true. 1530 * @pseudo 1531 * @name Arrow 1532 * @augments JXG.Line 1533 * @constructor 1534 * @type JXG.Line 1535 * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown. 1536 * @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 1537 * coordinates of a point. In the latter case the point will be constructed automatically as a fixed invisible point. 1538 * @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 1539 * of the equation <tt>a*x+b*y+c*z = 0</tt>. 1540 * @see Line 1541 * @example 1542 * // Create an arrow providing two points. 1543 * var p1 = board.create('point', [4.5, 2.0]); 1544 * var p2 = board.create('point', [1.0, 1.0]); 1545 * var l1 = board.create('arrow', [p1, p2]); 1546 * </pre><div class="jxgbox" id="JXG1d26bd22-7d6d-4018-b164-4c8bc8d22ccf" style="width: 300px; height: 300px;"></div> 1547 * <script type="text/javascript"> 1548 * var alex1_board = JXG.JSXGraph.initBoard('JXG1d26bd22-7d6d-4018-b164-4c8bc8d22ccf', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}); 1549 * var alex1_p1 = alex1_board.create('point', [4.5, 2.0]); 1550 * var alex1_p2 = alex1_board.create('point', [1.0, 1.0]); 1551 * var alex1_l1 = alex1_board.create('arrow', [alex1_p1, alex1_p2]); 1552 * </script><pre> 1553 */ 1554 JXG.createArrow = function (board, parents, attributes) { 1555 var el, attr; 1556 1557 attributes.straightFirst = false; 1558 attributes.straightLast = false; 1559 attr = Type.copyAttributes(attributes, board.options, "arrow"); 1560 el = board.create("line", parents, attr); 1561 //el.setArrow(false, true); 1562 el.type = Const.OBJECT_TYPE_VECTOR; 1563 el.elType = "arrow"; 1564 1565 return el; 1566 }; 1567 1568 JXG.registerElement("arrow", JXG.createArrow); 1569 1570 /** 1571 * @class Axis is a line with optional ticks and labels. 1572 * It's strictly spoken just a wrapper for element {@link Line} with {@link Line#straightFirst} 1573 * and {@link Line#straightLast} properties set to true. Additionally {@link Line#lastArrow} is set to true and default {@link Ticks} will be created. 1574 * @pseudo 1575 * @name Axis 1576 * @augments JXG.Line 1577 * @constructor 1578 * @type JXG.Line 1579 * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown. 1580 * @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 1581 * coordinates of a point. In the latter case, the point will be constructed automatically as a fixed invisible point. 1582 * @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 1583 * of the equation <tt>a*x+b*y+c*z = 0</tt>. 1584 * @example 1585 * // Create an axis providing two coords pairs. 1586 * var l1 = board.create('axis', [[0.0, 1.0], [1.0, 1.3]]); 1587 * </pre><div class="jxgbox" id="JXG4f414733-624c-42e4-855c-11f5530383ae" style="width: 300px; height: 300px;"></div> 1588 * <script type="text/javascript"> 1589 * var axex1_board = JXG.JSXGraph.initBoard('JXG4f414733-624c-42e4-855c-11f5530383ae', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}); 1590 * var axex1_l1 = axex1_board.create('axis', [[0.0, 1.0], [1.0, 1.3]]); 1591 * </script><pre> 1592 * @example 1593 * // Create ticks labels as fractions 1594 * board.create('axis', [[0,1], [1,1]], { 1595 * ticks: { 1596 * label: { 1597 * toFraction: true, 1598 * useMathjax: false, 1599 * anchorX: 'middle', 1600 * offset: [0, -10] 1601 * } 1602 * } 1603 * }); 1604 * 1605 * 1606 * </pre><div id="JXG34174cc4-0050-4ab4-af69-e91365d0666f" class="jxgbox" style="width: 300px; height: 300px;"></div> 1607 * <script src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml.js" id="MathJax-script"></script> 1608 * <script type="text/javascript"> 1609 * (function() { 1610 * var board = JXG.JSXGraph.initBoard('JXG34174cc4-0050-4ab4-af69-e91365d0666f', 1611 * {boundingbox: [-1.2, 2.3, 1.2, -2.3], axis: true, showcopyright: false, shownavigation: false}); 1612 * board.create('axis', [[0,1], [1,1]], { 1613 * ticks: { 1614 * label: { 1615 * toFraction: true, 1616 * useMathjax: false, 1617 * anchorX: 'middle', 1618 * offset: [0, -10] 1619 * } 1620 * } 1621 * }); 1622 * 1623 * 1624 * })(); 1625 * 1626 * </script><pre> 1627 * 1628 */ 1629 JXG.createAxis = function (board, parents, attributes) { 1630 var axis, attr, 1631 ancestor, ticksDist; 1632 1633 // Create line 1634 attr = Type.copyAttributes(attributes, board.options, "axis"); 1635 try { 1636 axis = board.create("line", parents, attr); 1637 } catch (err) { 1638 throw new Error( 1639 "JSXGraph: Can't create axis with parent types '" + 1640 typeof parents[0] + 1641 "' and '" + 1642 typeof parents[1] + 1643 "'." + 1644 "\nPossible parent types: [point,point], [[x1,y1],[x2,y2]]" 1645 ); 1646 } 1647 1648 axis.type = Const.OBJECT_TYPE_AXIS; 1649 axis.isDraggable = false; 1650 axis.point1.isDraggable = false; 1651 axis.point2.isDraggable = false; 1652 1653 // Save usrCoords of points 1654 axis._point1UsrCoordsOrg = axis.point1.coords.usrCoords.slice(); 1655 axis._point2UsrCoordsOrg = axis.point2.coords.usrCoords.slice(); 1656 1657 for (ancestor in axis.ancestors) { 1658 if (axis.ancestors.hasOwnProperty(ancestor)) { 1659 axis.ancestors[ancestor].type = Const.OBJECT_TYPE_AXISPOINT; 1660 } 1661 } 1662 1663 // Create ticks 1664 // attrTicks = attr.ticks; 1665 if (Type.exists(attr.ticks.ticksdistance)) { 1666 ticksDist = attr.ticks.ticksdistance; 1667 } else if (Type.isArray(attr.ticks.ticks)) { 1668 ticksDist = attr.ticks.ticks; 1669 } else { 1670 ticksDist = 1.0; 1671 } 1672 1673 /** 1674 * The ticks attached to the axis. 1675 * @memberOf Axis.prototype 1676 * @name defaultTicks 1677 * @type JXG.Ticks 1678 */ 1679 axis.defaultTicks = board.create("ticks", [axis, ticksDist], attr.ticks); 1680 axis.defaultTicks.dump = false; 1681 axis.elType = "axis"; 1682 axis.subs = { 1683 ticks: axis.defaultTicks 1684 }; 1685 axis.inherits.push(axis.defaultTicks); 1686 1687 axis.update = function () { 1688 var bbox, 1689 position, i, 1690 direction, horizontal, vertical, 1691 ticksAutoPos, ticksAutoPosThres, dist, 1692 anchor, left, right, 1693 distUsr, 1694 newPosP1, newPosP2, 1695 locationOrg, 1696 visLabel, anchr, off; 1697 1698 if (!this.needsUpdate) { 1699 return this; 1700 } 1701 1702 bbox = this.board.getBoundingBox(); 1703 position = this.evalVisProp('position'); 1704 direction = this.Direction(); 1705 horizontal = this.isHorizontal(); 1706 vertical = this.isVertical(); 1707 ticksAutoPos = this.evalVisProp('ticksautopos'); 1708 ticksAutoPosThres = this.evalVisProp('ticksautoposthreshold'); 1709 1710 if (horizontal) { 1711 ticksAutoPosThres = Type.parseNumber(ticksAutoPosThres, Math.abs(bbox[1] - bbox[3]), 1 / this.board.unitX) * this.board.unitX; 1712 } else if (vertical) { 1713 ticksAutoPosThres = Type.parseNumber(ticksAutoPosThres, Math.abs(bbox[1] - bbox[3]), 1 / this.board.unitY) * this.board.unitY; 1714 } else { 1715 ticksAutoPosThres = Type.parseNumber(ticksAutoPosThres, 1, 1); 1716 } 1717 1718 anchor = this.evalVisProp('anchor'); 1719 left = anchor.indexOf('left') > -1; 1720 right = anchor.indexOf('right') > -1; 1721 1722 distUsr = this.evalVisProp('anchordist'); 1723 if (horizontal) { 1724 distUsr = Type.parseNumber(distUsr, Math.abs(bbox[1] - bbox[3]), 1 / this.board.unitX); 1725 } else if (vertical) { 1726 distUsr = Type.parseNumber(distUsr, Math.abs(bbox[0] - bbox[2]), 1 / this.board.unitY); 1727 } else { 1728 distUsr = 0; 1729 } 1730 1731 locationOrg = this.board.getPointLoc(this._point1UsrCoordsOrg, distUsr); 1732 1733 // Set position of axis 1734 newPosP1 = this.point1.coords.usrCoords.slice(); 1735 newPosP2 = this.point2.coords.usrCoords.slice(); 1736 1737 if (position === 'static' || (!vertical && !horizontal)) { 1738 // Do nothing 1739 1740 } else if (position === 'fixed') { 1741 if (horizontal) { // direction[1] === 0 1742 if ((direction[0] > 0 && right) || (direction[0] < 0 && left)) { 1743 newPosP1[2] = bbox[3] + distUsr; 1744 newPosP2[2] = bbox[3] + distUsr; 1745 } else if ((direction[0] > 0 && left) || (direction[0] < 0 && right)) { 1746 newPosP1[2] = bbox[1] - distUsr; 1747 newPosP2[2] = bbox[1] - distUsr; 1748 1749 } else { 1750 newPosP1 = this._point1UsrCoordsOrg.slice(); 1751 newPosP2 = this._point2UsrCoordsOrg.slice(); 1752 } 1753 } 1754 if (vertical) { // direction[0] === 0 1755 if ((direction[1] > 0 && left) || (direction[1] < 0 && right)) { 1756 newPosP1[1] = bbox[0] + distUsr; 1757 newPosP2[1] = bbox[0] + distUsr; 1758 1759 } else if ((direction[1] > 0 && right) || (direction[1] < 0 && left)) { 1760 newPosP1[1] = bbox[2] - distUsr; 1761 newPosP2[1] = bbox[2] - distUsr; 1762 1763 } else { 1764 newPosP1 = this._point1UsrCoordsOrg.slice(); 1765 newPosP2 = this._point2UsrCoordsOrg.slice(); 1766 } 1767 } 1768 1769 } else if (position === 'sticky') { 1770 if (horizontal) { // direction[1] === 0 1771 if (locationOrg[1] < 0 && ((direction[0] > 0 && right) || (direction[0] < 0 && left))) { 1772 newPosP1[2] = bbox[3] + distUsr; 1773 newPosP2[2] = bbox[3] + distUsr; 1774 1775 } else if (locationOrg[1] > 0 && ((direction[0] > 0 && left) || (direction[0] < 0 && right))) { 1776 newPosP1[2] = bbox[1] - distUsr; 1777 newPosP2[2] = bbox[1] - distUsr; 1778 1779 } else { 1780 newPosP1 = this._point1UsrCoordsOrg.slice(); 1781 newPosP2 = this._point2UsrCoordsOrg.slice(); 1782 } 1783 } 1784 if (vertical) { // direction[0] === 0 1785 if (locationOrg[0] < 0 && ((direction[1] > 0 && left) || (direction[1] < 0 && right))) { 1786 newPosP1[1] = bbox[0] + distUsr; 1787 newPosP2[1] = bbox[0] + distUsr; 1788 1789 } else if (locationOrg[0] > 0 && ((direction[1] > 0 && right) || (direction[1] < 0 && left))) { 1790 newPosP1[1] = bbox[2] - distUsr; 1791 newPosP2[1] = bbox[2] - distUsr; 1792 1793 } else { 1794 newPosP1 = this._point1UsrCoordsOrg.slice(); 1795 newPosP2 = this._point2UsrCoordsOrg.slice(); 1796 } 1797 } 1798 } 1799 1800 this.point1.setPositionDirectly(JXG.COORDS_BY_USER, newPosP1); 1801 this.point2.setPositionDirectly(JXG.COORDS_BY_USER, newPosP2); 1802 1803 // Set position of tick labels 1804 if (Type.exists(this.defaultTicks)) { 1805 visLabel = this.defaultTicks.visProp.label; 1806 if (ticksAutoPos && (horizontal || vertical)) { 1807 1808 if (!Type.exists(visLabel._anchorx_org)) { 1809 visLabel._anchorx_org = Type.def(visLabel.anchorx, this.board.options.text.anchorX); 1810 } 1811 if (!Type.exists(visLabel._anchory_org)) { 1812 visLabel._anchory_org = Type.def(visLabel.anchory, this.board.options.text.anchorY); 1813 } 1814 if (!Type.exists(visLabel._offset_org)) { 1815 visLabel._offset_org = visLabel.offset.slice(); 1816 } 1817 1818 off = visLabel.offset; 1819 if (horizontal) { 1820 dist = axis.point1.coords.scrCoords[2] - (this.board.canvasHeight * 0.5); 1821 1822 anchr = visLabel.anchory; 1823 1824 // The last position of the labels is stored in visLabel._side 1825 if (dist < 0 && Math.abs(dist) > ticksAutoPosThres) { 1826 // Put labels on top of the line 1827 if (visLabel._side === 'bottom') { 1828 // Switch position 1829 if (visLabel.anchory === 'top') { 1830 anchr = 'bottom'; 1831 } 1832 off[1] *= -1; 1833 visLabel._side = 'top'; 1834 } 1835 1836 } else if (dist > 0 && Math.abs(dist) > ticksAutoPosThres) { 1837 // Put labels below the line 1838 if (visLabel._side === 'top') { 1839 // Switch position 1840 if (visLabel.anchory === 'bottom') { 1841 anchr = 'top'; 1842 } 1843 off[1] *= -1; 1844 visLabel._side = 'bottom'; 1845 } 1846 1847 } else { 1848 // Put to original position 1849 anchr = visLabel._anchory_org; 1850 off = visLabel._offset_org.slice(); 1851 1852 if (anchr === 'top') { 1853 visLabel._side = 'bottom'; 1854 } else if (anchr === 'bottom') { 1855 visLabel._side = 'top'; 1856 } else if (off[1] < 0) { 1857 visLabel._side = 'bottom'; 1858 } else { 1859 visLabel._side = 'top'; 1860 } 1861 } 1862 1863 for (i = 0; i < axis.defaultTicks.labels.length; i++) { 1864 this.defaultTicks.labels[i].visProp.anchory = anchr; 1865 } 1866 visLabel.anchory = anchr; 1867 1868 } else if (vertical) { 1869 dist = axis.point1.coords.scrCoords[1] - (this.board.canvasWidth * 0.5); 1870 1871 if (dist < 0 && Math.abs(dist) > ticksAutoPosThres) { 1872 // Put labels to the left of the line 1873 if (visLabel._side === 'right') { 1874 // Switch position 1875 if (visLabel.anchorx === 'left') { 1876 anchr = 'right'; 1877 } 1878 off[0] *= -1; 1879 visLabel._side = 'left'; 1880 } 1881 1882 } else if (dist > 0 && Math.abs(dist) > ticksAutoPosThres) { 1883 // Put labels to the right of the line 1884 if (visLabel._side === 'left') { 1885 // Switch position 1886 if (visLabel.anchorx === 'right') { 1887 anchr = 'left'; 1888 } 1889 off[0] *= -1; 1890 visLabel._side = 'right'; 1891 } 1892 1893 } else { 1894 // Put to original position 1895 anchr = visLabel._anchorx_org; 1896 off = visLabel._offset_org.slice(); 1897 1898 if (anchr === 'left') { 1899 visLabel._side = 'right'; 1900 } else if (anchr === 'right') { 1901 visLabel._side = 'left'; 1902 } else if (off[0] < 0) { 1903 visLabel._side = 'left'; 1904 } else { 1905 visLabel._side = 'right'; 1906 } 1907 } 1908 1909 for (i = 0; i < axis.defaultTicks.labels.length; i++) { 1910 this.defaultTicks.labels[i].visProp.anchorx = anchr; 1911 } 1912 visLabel.anchorx = anchr; 1913 } 1914 visLabel.offset = off; 1915 1916 } else { 1917 delete visLabel._anchorx_org; 1918 delete visLabel._anchory_org; 1919 delete visLabel._offset_org; 1920 } 1921 this.defaultTicks.needsUpdate = true; 1922 } 1923 1924 JXG.Line.prototype.update.call(this); 1925 1926 return this; 1927 }; 1928 1929 return axis; 1930 }; 1931 1932 JXG.registerElement("axis", JXG.createAxis); 1933 1934 /** 1935 * @class The tangent line at a point on a line, circle, conic, turtle, or curve. 1936 * A tangent line is always constructed 1937 * by a point on a line, circle, or curve and describes the tangent in the point on that line, circle, or curve. 1938 * <p> 1939 * If the point is not on the object (line, circle, conic, curve, turtle) the output depends on the type of the object. 1940 * For conics and circles, the polar line will be constructed. For function graphs, 1941 * the tangent of the vertical projection of the point to the function graph is constructed. For all other objects, the tangent 1942 * in the orthogonal projection of the point to the object will be constructed. 1943 * @pseudo 1944 * @name Tangent 1945 * @augments JXG.Line 1946 * @constructor 1947 * @type JXG.Line 1948 * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown. 1949 * @param {Glider} g A glider on a line, circle, or curve. 1950 * @param {JXG.GeometryElement} [c] Optional element for which the tangent is constructed 1951 * @example 1952 * // Create a tangent providing a glider on a function graph 1953 * var c1 = board.create('curve', [function(t){return t},function(t){return t*t*t;}]); 1954 * var g1 = board.create('glider', [0.6, 1.2, c1]); 1955 * var t1 = board.create('tangent', [g1]); 1956 * </pre><div class="jxgbox" id="JXG7b7233a0-f363-47dd-9df5-4018d0d17a98" style="width: 400px; height: 400px;"></div> 1957 * <script type="text/javascript"> 1958 * var tlex1_board = JXG.JSXGraph.initBoard('JXG7b7233a0-f363-47dd-9df5-4018d0d17a98', {boundingbox: [-6, 6, 6, -6], axis: true, showcopyright: false, shownavigation: false}); 1959 * var tlex1_c1 = tlex1_board.create('curve', [function(t){return t},function(t){return t*t*t;}]); 1960 * var tlex1_g1 = tlex1_board.create('glider', [0.6, 1.2, tlex1_c1]); 1961 * var tlex1_t1 = tlex1_board.create('tangent', [tlex1_g1]); 1962 * </script><pre> 1963 */ 1964 JXG.createTangent = function (board, parents, attributes) { 1965 var p, c, j, el, tangent, attr, 1966 getCurveTangentDir, 1967 res, isTransformed, 1968 slides = []; 1969 1970 if (parents.length === 1) { 1971 // One argument: glider on line, circle or curve 1972 p = parents[0]; 1973 c = p.slideObject; 1974 1975 } else if (parents.length === 2) { 1976 // Two arguments: (point,line|curve|circle|conic) or (line|curve|circle|conic,point). 1977 // In fact, for circles and conics it is the polar 1978 if (Type.isPoint(parents[0])) { 1979 p = parents[0]; 1980 c = parents[1]; 1981 } else if (Type.isPoint(parents[1])) { 1982 c = parents[0]; 1983 p = parents[1]; 1984 } else { 1985 throw new Error( 1986 "JSXGraph: Can't create tangent with parent types '" + 1987 typeof parents[0] + 1988 "' and '" + 1989 typeof parents[1] + 1990 "'." + 1991 "\nPossible parent types: [glider|point], [point,line|curve|circle|conic]" 1992 ); 1993 } 1994 } else { 1995 throw new Error( 1996 "JSXGraph: Can't create tangent with parent types '" + 1997 typeof parents[0] + 1998 "' and '" + 1999 typeof parents[1] + 2000 "'." + 2001 "\nPossible parent types: [glider|point], [point,line|curve|circle|conic]" 2002 ); 2003 } 2004 2005 attr = Type.copyAttributes(attributes, board.options, 'tangent'); 2006 if (c.elementClass === Const.OBJECT_CLASS_LINE) { 2007 tangent = board.create("line", [c.point1, c.point2], attr); 2008 tangent.glider = p; 2009 } else if ( 2010 c.elementClass === Const.OBJECT_CLASS_CURVE && 2011 c.type !== Const.OBJECT_TYPE_CONIC 2012 ) { 2013 res = c.getTransformationSource(); 2014 isTransformed = res[0]; 2015 if (isTransformed) { 2016 // Curve is result of a transformation 2017 // We recursively collect all curves from which 2018 // the curve is transformed. 2019 slides.push(c); 2020 while (res[0] && Type.exists(res[1]._transformationSource)) { 2021 slides.push(res[1]); 2022 res = res[1].getTransformationSource(); 2023 } 2024 } 2025 2026 if (c.evalVisProp('curvetype') !== "plot" || isTransformed) { 2027 // Functiongraph or parametric curve or 2028 // transformed curve thereof. 2029 tangent = board.create( 2030 "line", 2031 [ 2032 function () { 2033 var g = c.X, 2034 f = c.Y, 2035 df, dg, 2036 li, i, c_org, invMat, po, 2037 t; 2038 2039 if (p.type === Const.OBJECT_TYPE_GLIDER) { 2040 t = p.position; 2041 } else if (c.evalVisProp('curvetype') === 'functiongraph') { 2042 t = p.X(); 2043 } else { 2044 t = Geometry.projectPointToCurve(p, c, board)[1]; 2045 } 2046 2047 // po are the coordinates of the point 2048 // on the "original" curve. That is the curve or 2049 // the original curve which is transformed (maybe multiple times) 2050 // to this curve. 2051 // t is the position of the point on the "original" curve 2052 po = p.Coords(true); 2053 if (isTransformed) { 2054 c_org = slides[slides.length - 1]._transformationSource; 2055 g = c_org.X; 2056 f = c_org.Y; 2057 for (i = 0; i < slides.length; i++) { 2058 slides[i].updateTransformMatrix(); 2059 invMat = Mat.inverse(slides[i].transformMat); 2060 po = Mat.matVecMult(invMat, po); 2061 } 2062 2063 if (p.type !== Const.OBJECT_TYPE_GLIDER) { 2064 po[1] /= po[0]; 2065 po[2] /= po[0]; 2066 po[0] /= po[0]; 2067 t = Geometry.projectCoordsToCurve(po[1], po[2], 0, c_org, board)[1]; 2068 } 2069 } 2070 2071 // li are the coordinates of the line on the "original" curve 2072 df = Numerics.D(f)(t); 2073 dg = Numerics.D(g)(t); 2074 li = [ 2075 -po[1] * df + po[2] * dg, 2076 po[0] * df, 2077 -po[0] * dg 2078 ]; 2079 2080 if (isTransformed) { 2081 // Transform the line to the transformed curve 2082 for (i = slides.length - 1; i >= 0; i--) { 2083 invMat = Mat.transpose(Mat.inverse(slides[i].transformMat)); 2084 li = Mat.matVecMult(invMat, li); 2085 } 2086 } 2087 2088 return li; 2089 } 2090 ], 2091 attr 2092 ); 2093 2094 p.addChild(tangent); 2095 // this is required for the geogebra reader to display a slope 2096 tangent.glider = p; 2097 } else { 2098 // curveType 'plot': discrete data 2099 /** 2100 * @ignore 2101 * 2102 * In case of bezierDegree == 1: 2103 * Find two points p1, p2 enclosing the glider. 2104 * Then the equation of the line segment is: 0 = y*(x1-x2) + x*(y2-y1) + y1*x2-x1*y2, 2105 * which is the cross product of p1 and p2. 2106 * 2107 * In case of bezierDegree === 3: 2108 * The slope dy / dx of the tangent is determined. Then the 2109 * tangent is computed as cross product between 2110 * the glider p and [1, p.X() + dx, p.Y() + dy] 2111 * 2112 */ 2113 getCurveTangentDir = function (position, c, num) { 2114 var i = Math.floor(position), 2115 p1, p2, t, A, B, C, D, dx, dy, d, 2116 points, le; 2117 2118 if (c.bezierDegree === 1) { 2119 if (i === c.numberPoints - 1) { 2120 i--; 2121 } 2122 } else if (c.bezierDegree === 3) { 2123 // i is start of the Bezier segment 2124 // t is the position in the Bezier segment 2125 if (c.elType === 'sector') { 2126 points = c.points.slice(3, c.numberPoints - 3); 2127 le = points.length; 2128 } else { 2129 points = c.points; 2130 le = points.length; 2131 } 2132 i = Math.floor((position * (le - 1)) / 3) * 3; 2133 t = (position * (le - 1) - i) / 3; 2134 if (i >= le - 1) { 2135 i = le - 4; 2136 t = 1; 2137 } 2138 } else { 2139 return 0; 2140 } 2141 2142 if (i < 0) { 2143 return 1; 2144 } 2145 2146 // The curve points are transformed (if there is a transformation) 2147 // c.X(i) is not transformed. 2148 if (c.bezierDegree === 1) { 2149 p1 = c.points[i].usrCoords; 2150 p2 = c.points[i + 1].usrCoords; 2151 } else { 2152 A = points[i].usrCoords; 2153 B = points[i + 1].usrCoords; 2154 C = points[i + 2].usrCoords; 2155 D = points[i + 3].usrCoords; 2156 dx = (1 - t) * (1 - t) * (B[1] - A[1]) + 2157 2 * (1 - t) * t * (C[1] - B[1]) + 2158 t * t * (D[1] - C[1]); 2159 dy = (1 - t) * (1 - t) * (B[2] - A[2]) + 2160 2 * (1 - t) * t * (C[2] - B[2]) + 2161 t * t * (D[2] - C[2]); 2162 d = Mat.hypot(dx, dy); 2163 dx /= d; 2164 dy /= d; 2165 p1 = p.coords.usrCoords; 2166 p2 = [1, p1[1] + dx, p1[2] + dy]; 2167 } 2168 2169 switch (num) { 2170 case 0: 2171 return p1[2] * p2[1] - p1[1] * p2[2]; 2172 case 1: 2173 return p2[2] - p1[2]; 2174 case 2: 2175 return p1[1] - p2[1]; 2176 default: 2177 return [ 2178 p1[2] * p2[1] - p1[1] * p2[2], 2179 p2[2] - p1[2], 2180 p1[1] - p2[1] 2181 ]; 2182 } 2183 }; 2184 2185 tangent = board.create( 2186 "line", 2187 [ 2188 function () { 2189 var t; 2190 2191 if (p.type === Const.OBJECT_TYPE_GLIDER) { 2192 t = p.position; 2193 } else { 2194 t = Geometry.projectPointToCurve(p, c, board)[1]; 2195 } 2196 2197 return getCurveTangentDir(t, c); 2198 } 2199 ], 2200 attr 2201 ); 2202 2203 p.addChild(tangent); 2204 // this is required for the geogebra reader to display a slope 2205 tangent.glider = p; 2206 } 2207 } else if (c.type === Const.OBJECT_TYPE_TURTLE) { 2208 tangent = board.create( 2209 "line", 2210 [ 2211 function () { 2212 var i, t; 2213 if (p.type === Const.OBJECT_TYPE_GLIDER) { 2214 t = p.position; 2215 } else { 2216 t = Geometry.projectPointToTurtle(p, c, board)[1]; 2217 } 2218 2219 i = Math.floor(t); 2220 2221 // run through all curves of this turtle 2222 for (j = 0; j < c.objects.length; j++) { 2223 el = c.objects[j]; 2224 2225 if (el.type === Const.OBJECT_TYPE_CURVE) { 2226 if (i < el.numberPoints) { 2227 break; 2228 } 2229 2230 i -= el.numberPoints; 2231 } 2232 } 2233 2234 if (i === el.numberPoints - 1) { 2235 i--; 2236 } 2237 2238 if (i < 0) { 2239 return [1, 0, 0]; 2240 } 2241 2242 return [ 2243 el.Y(i) * el.X(i + 1) - el.X(i) * el.Y(i + 1), 2244 el.Y(i + 1) - el.Y(i), 2245 el.X(i) - el.X(i + 1) 2246 ]; 2247 } 2248 ], 2249 attr 2250 ); 2251 p.addChild(tangent); 2252 2253 // this is required for the geogebra reader to display a slope 2254 tangent.glider = p; 2255 } else if ( 2256 c.elementClass === Const.OBJECT_CLASS_CIRCLE || 2257 c.type === Const.OBJECT_TYPE_CONIC 2258 ) { 2259 // If p is not on c, the tangent is the polar. 2260 // This construction should work on conics, too. p has to lie on c. 2261 tangent = board.create( 2262 "line", 2263 [ 2264 function () { 2265 return Mat.matVecMult(c.quadraticform, p.coords.usrCoords); 2266 } 2267 ], 2268 attr 2269 ); 2270 2271 p.addChild(tangent); 2272 // this is required for the geogebra reader to display a slope 2273 tangent.glider = p; 2274 } 2275 2276 if (!Type.exists(tangent)) { 2277 throw new Error("JSXGraph: Couldn't create tangent with the given parents."); 2278 } 2279 2280 tangent.elType = "tangent"; 2281 tangent.type = Const.OBJECT_TYPE_TANGENT; 2282 tangent.setParents(parents); 2283 2284 return tangent; 2285 }; 2286 2287 /** 2288 * @class A normal is the line perpendicular to a line or to a tangent of a circle or curve. 2289 * @pseudo 2290 * @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. 2291 * @constructor 2292 * @name Normal 2293 * @type JXG.Line 2294 * @augments JXG.Line 2295 * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown. 2296 * @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 2297 * to the tangent to the object in the given point. 2298 * @param {Glider} p Works like above, however the object is given by {@link JXG.CoordsElement#slideObject}. 2299 * @example 2300 * // Create a normal to a circle. 2301 * var p1 = board.create('point', [2.0, 2.0]); 2302 * var p2 = board.create('point', [3.0, 2.0]); 2303 * var c1 = board.create('circle', [p1, p2]); 2304 * 2305 * var norm1 = board.create('normal', [c1, p2]); 2306 * </pre><div class="jxgbox" id="JXG4154753d-3d29-40fb-a860-0b08aa4f3743" style="width: 400px; height: 400px;"></div> 2307 * <script type="text/javascript"> 2308 * var nlex1_board = JXG.JSXGraph.initBoard('JXG4154753d-3d29-40fb-a860-0b08aa4f3743', {boundingbox: [-1, 9, 9, -1], axis: true, showcopyright: false, shownavigation: false}); 2309 * var nlex1_p1 = nlex1_board.create('point', [2.0, 2.0]); 2310 * var nlex1_p2 = nlex1_board.create('point', [3.0, 2.0]); 2311 * var nlex1_c1 = nlex1_board.create('circle', [nlex1_p1, nlex1_p2]); 2312 * 2313 * // var nlex1_p3 = nlex1_board.create('point', [1.0, 2.0]); 2314 * var nlex1_norm1 = nlex1_board.create('normal', [nlex1_c1, nlex1_p2]); 2315 * </script><pre> 2316 */ 2317 JXG.createNormal = function (board, parents, attributes) { 2318 var p, c, l, i, attr, pp, attrp, 2319 getCurveNormalDir, 2320 res, isTransformed, 2321 slides = []; 2322 2323 for (i = 0; i < parents.length; ++i) { 2324 parents[i] = board.select(parents[i]); 2325 } 2326 // One arguments: glider on line, circle or curve 2327 if (parents.length === 1) { 2328 p = parents[0]; 2329 c = p.slideObject; 2330 // Two arguments: (point,line), (point,circle), (line,point) or (circle,point) 2331 } else if (parents.length === 2) { 2332 if (Type.isPointType(board, parents[0])) { 2333 p = Type.providePoints(board, [parents[0]], attributes, "point")[0]; 2334 c = parents[1]; 2335 } else if (Type.isPointType(board, parents[1])) { 2336 c = parents[0]; 2337 p = Type.providePoints(board, [parents[1]], attributes, "point")[0]; 2338 } else { 2339 throw new Error( 2340 "JSXGraph: Can't create normal with parent types '" + 2341 typeof parents[0] + 2342 "' and '" + 2343 typeof parents[1] + 2344 "'." + 2345 "\nPossible parent types: [point,line], [point,circle], [glider]" 2346 ); 2347 } 2348 } else { 2349 throw new Error( 2350 "JSXGraph: Can't create normal with parent types '" + 2351 typeof parents[0] + 2352 "' and '" + 2353 typeof parents[1] + 2354 "'." + 2355 "\nPossible parent types: [point,line], [point,circle], [glider]" 2356 ); 2357 } 2358 2359 attr = Type.copyAttributes(attributes, board.options, "normal"); 2360 if (c.elementClass === Const.OBJECT_CLASS_LINE) { 2361 // Private point 2362 attrp = Type.copyAttributes(attributes, board.options, "normal", "point"); 2363 pp = board.create( 2364 "point", 2365 [ 2366 function () { 2367 var p = Mat.crossProduct([1, 0, 0], c.stdform); 2368 return [p[0], -p[2], p[1]]; 2369 } 2370 ], 2371 attrp 2372 ); 2373 pp.isDraggable = true; 2374 2375 l = board.create("line", [p, pp], attr); 2376 2377 /** 2378 * A helper point used to create a normal to a {@link JXG.Line} object. For normals to circles or curves this 2379 * element is <tt>undefined</tt>. 2380 * @type JXG.Point 2381 * @name point 2382 * @memberOf Normal.prototype 2383 */ 2384 l.point = pp; 2385 l.subs = { 2386 point: pp 2387 }; 2388 l.inherits.push(pp); 2389 } else if (c.elementClass === Const.OBJECT_CLASS_CIRCLE) { 2390 l = board.create("line", [c.midpoint, p], attr); 2391 } else if (c.elementClass === Const.OBJECT_CLASS_CURVE) { 2392 res = c.getTransformationSource(); 2393 isTransformed = res[0]; 2394 if (isTransformed) { 2395 // Curve is result of a transformation 2396 // We recursively collect all curves from which 2397 // the curve is transformed. 2398 slides.push(c); 2399 while (res[0] && Type.exists(res[1]._transformationSource)) { 2400 slides.push(res[1]); 2401 res = res[1].getTransformationSource(); 2402 } 2403 } 2404 2405 if (c.evalVisProp('curvetype') !== "plot" || isTransformed) { 2406 // Functiongraph or parametric curve or 2407 // transformed curve thereof. 2408 l = board.create( 2409 "line", 2410 [ 2411 function () { 2412 var g = c.X, 2413 f = c.Y, 2414 df, dg, 2415 li, i, c_org, invMat, po, 2416 t; 2417 2418 if (p.type === Const.OBJECT_TYPE_GLIDER) { 2419 t = p.position; 2420 } else if (c.evalVisProp('curvetype') === 'functiongraph') { 2421 t = p.X(); 2422 } else { 2423 t = Geometry.projectPointToCurve(p, c, board)[1]; 2424 } 2425 2426 // po are the coordinates of the point 2427 // on the "original" curve. That is the curve or 2428 // the original curve which is transformed (maybe multiple times) 2429 // to this curve. 2430 // t is the position of the point on the "original" curve 2431 po = p.Coords(true); 2432 if (isTransformed) { 2433 c_org = slides[slides.length - 1]._transformationSource; 2434 g = c_org.X; 2435 f = c_org.Y; 2436 for (i = 0; i < slides.length; i++) { 2437 slides[i].updateTransformMatrix(); 2438 invMat = Mat.inverse(slides[i].transformMat); 2439 po = Mat.matVecMult(invMat, po); 2440 } 2441 2442 if (p.type !== Const.OBJECT_TYPE_GLIDER) { 2443 po[1] /= po[0]; 2444 po[2] /= po[0]; 2445 po[0] /= po[0]; 2446 t = Geometry.projectCoordsToCurve(po[1], po[2], 0, c_org, board)[1]; 2447 } 2448 } 2449 2450 df = Numerics.D(f)(t); 2451 dg = Numerics.D(g)(t); 2452 li = [ 2453 -po[1] * dg - po[2] * df, 2454 po[0] * dg, 2455 po[0] * df 2456 ]; 2457 2458 if (isTransformed) { 2459 // Transform the line to the transformed curve 2460 for (i = slides.length - 1; i >= 0; i--) { 2461 invMat = Mat.transpose(Mat.inverse(slides[i].transformMat)); 2462 li = Mat.matVecMult(invMat, li); 2463 } 2464 } 2465 2466 return li; 2467 } 2468 ], 2469 attr 2470 ); 2471 } else { 2472 // curveType 'plot': discrete data 2473 getCurveNormalDir = function (position, c, num) { 2474 var i = Math.floor(position), 2475 lbda, 2476 p1, p2, t, A, B, C, D, dx, dy, d, 2477 li, p_org, pp, 2478 points, le; 2479 2480 2481 if (c.bezierDegree === 1) { 2482 if (i === c.numberPoints - 1) { 2483 i--; 2484 } 2485 t = position; 2486 } else if (c.bezierDegree === 3) { 2487 // i is start of the Bezier segment 2488 // t is the position in the Bezier segment 2489 if (c.elType === 'sector') { 2490 points = c.points.slice(3, c.numberPoints - 3); 2491 le = points.length; 2492 } else { 2493 points = c.points; 2494 le = points.length; 2495 } 2496 i = Math.floor((position * (le - 1)) / 3) * 3; 2497 t = (position * (le - 1) - i) / 3; 2498 if (i >= le - 1) { 2499 i = le - 4; 2500 t = 1; 2501 } 2502 } else { 2503 return 0; 2504 } 2505 2506 if (i < 0) { 2507 return 1; 2508 } 2509 2510 lbda = t - i; 2511 if (c.bezierDegree === 1) { 2512 p1 = c.points[i].usrCoords; 2513 p2 = c.points[i + 1].usrCoords; 2514 p_org = [ 2515 p1[0] + lbda * (p2[0] - p1[0]), 2516 p1[1] + lbda * (p2[1] - p1[1]), 2517 p1[2] + lbda * (p2[2] - p1[2]) 2518 ]; 2519 li = Mat.crossProduct(p1, p2); 2520 pp = Mat.crossProduct([1, 0, 0], li); 2521 pp = [pp[0], -pp[2], pp[1]]; 2522 li = Mat.crossProduct(p_org, pp); 2523 2524 } else { 2525 A = points[i].usrCoords; 2526 B = points[i + 1].usrCoords; 2527 C = points[i + 2].usrCoords; 2528 D = points[i + 3].usrCoords; 2529 dx = 2530 (1 - t) * (1 - t) * (B[1] - A[1]) + 2531 2 * (1 - t) * t * (C[1] - B[1]) + 2532 t * t * (D[1] - C[1]); 2533 dy = 2534 (1 - t) * (1 - t) * (B[2] - A[2]) + 2535 2 * (1 - t) * t * (C[2] - B[2]) + 2536 t * t * (D[2] - C[2]); 2537 d = Mat.hypot(dx, dy); 2538 dx /= d; 2539 dy /= d; 2540 p1 = p.coords.usrCoords; 2541 p2 = [1, p1[1] - dy, p1[2] + dx]; 2542 2543 li = [ 2544 p1[2] * p2[1] - p1[1] * p2[2], 2545 p2[2] - p1[2], 2546 p1[1] - p2[1] 2547 ]; 2548 } 2549 2550 switch (num) { 2551 case 0: 2552 return li[0]; 2553 case 1: 2554 return li[1]; 2555 case 2: 2556 return li[2]; 2557 default: 2558 return li; 2559 } 2560 }; 2561 2562 l = board.create( 2563 "line", 2564 [ 2565 function () { 2566 var t; 2567 2568 if (p.type === Const.OBJECT_TYPE_GLIDER) { 2569 t = p.position; 2570 } else { 2571 t = Geometry.projectPointToCurve(p, c, board)[1]; 2572 } 2573 2574 return getCurveNormalDir(t, c); 2575 } 2576 ], 2577 attr 2578 ); 2579 p.addChild(l); 2580 l.glider = p; 2581 } 2582 } else if (c.type === Const.OBJECT_TYPE_TURTLE) { 2583 l = board.create( 2584 "line", 2585 [ 2586 function () { 2587 var el, 2588 j, 2589 i = Math.floor(p.position), 2590 lbda = p.position - i; 2591 2592 // run through all curves of this turtle 2593 for (j = 0; j < c.objects.length; j++) { 2594 el = c.objects[j]; 2595 2596 if (el.type === Const.OBJECT_TYPE_CURVE) { 2597 if (i < el.numberPoints) { 2598 break; 2599 } 2600 2601 i -= el.numberPoints; 2602 } 2603 } 2604 2605 if (i === el.numberPoints - 1) { 2606 i -= 1; 2607 lbda = 1; 2608 } 2609 2610 if (i < 0) { 2611 return 1; 2612 } 2613 2614 return ( 2615 (el.Y(i) + lbda * (el.Y(i + 1) - el.Y(i))) * (el.Y(i) - el.Y(i + 1)) - 2616 (el.X(i) + lbda * (el.X(i + 1) - el.X(i))) * (el.X(i + 1) - el.X(i)) 2617 ); 2618 }, 2619 function () { 2620 var el, 2621 j, 2622 i = Math.floor(p.position); 2623 2624 // run through all curves of this turtle 2625 for (j = 0; j < c.objects.length; j++) { 2626 el = c.objects[j]; 2627 if (el.type === Const.OBJECT_TYPE_CURVE) { 2628 if (i < el.numberPoints) { 2629 break; 2630 } 2631 2632 i -= el.numberPoints; 2633 } 2634 } 2635 2636 if (i === el.numberPoints - 1) { 2637 i -= 1; 2638 } 2639 2640 if (i < 0) { 2641 return 0; 2642 } 2643 2644 return el.X(i + 1) - el.X(i); 2645 }, 2646 function () { 2647 var el, 2648 j, 2649 i = Math.floor(p.position); 2650 2651 // run through all curves of this turtle 2652 for (j = 0; j < c.objects.length; j++) { 2653 el = c.objects[j]; 2654 if (el.type === Const.OBJECT_TYPE_CURVE) { 2655 if (i < el.numberPoints) { 2656 break; 2657 } 2658 2659 i -= el.numberPoints; 2660 } 2661 } 2662 2663 if (i === el.numberPoints - 1) { 2664 i -= 1; 2665 } 2666 2667 if (i < 0) { 2668 return 0; 2669 } 2670 2671 return el.Y(i + 1) - el.Y(i); 2672 } 2673 ], 2674 attr 2675 ); 2676 } else { 2677 throw new Error( 2678 "JSXGraph: Can't create normal with parent types '" + 2679 typeof parents[0] + 2680 "' and '" + 2681 typeof parents[1] + 2682 "'." + 2683 "\nPossible parent types: [point,line], [point,circle], [glider]" 2684 ); 2685 } 2686 2687 l.elType = "normal"; 2688 l.setParents(parents); 2689 2690 if (Type.exists(p._is_new)) { 2691 l.addChild(p); 2692 delete p._is_new; 2693 } else { 2694 p.addChild(l); 2695 } 2696 c.addChild(l); 2697 2698 return l; 2699 }; 2700 2701 /** 2702 * @class The radical axis is the line connecting the two interstion points of two circles with distinct centers. 2703 * The angular bisector of the polar lines of the circle centers with respect to the other circle is always the radical axis. 2704 * The radical axis passes through the intersection points when the circles intersect. 2705 * 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. 2706 * @pseudo 2707 * @name RadicalAxis 2708 * @augments JXG.Line 2709 * @constructor 2710 * @type JXG.Line 2711 * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown. 2712 * @param {JXG.Circle} circle one of the two respective circles. 2713 * @param {JXG.Circle} circle the other of the two respective circles. 2714 * @example 2715 * // Create the radical axis line with respect to two circles 2716 * var board = JXG.JSXGraph.initBoard('7b7233a0-f363-47dd-9df5-5018d0d17a98', {boundingbox: [-1, 9, 9, -1], axis: true, showcopyright: false, shownavigation: false}); 2717 * var p1 = board.create('point', [2, 3]); 2718 * var p2 = board.create('point', [1, 4]); 2719 * var c1 = board.create('circle', [p1, p2]); 2720 * var p3 = board.create('point', [6, 5]); 2721 * var p4 = board.create('point', [8, 6]); 2722 * var c2 = board.create('circle', [p3, p4]); 2723 * var r1 = board.create('radicalaxis', [c1, c2]); 2724 * </pre><div class="jxgbox" id="JXG7b7233a0-f363-47dd-9df5-5018d0d17a98" class="jxgbox" style="width:400px; height:400px;"></div> 2725 * <script type='text/javascript'> 2726 * var rlex1_board = JXG.JSXGraph.initBoard('JXG7b7233a0-f363-47dd-9df5-5018d0d17a98', {boundingbox: [-1, 9, 9, -1], axis: true, showcopyright: false, shownavigation: false}); 2727 * var rlex1_p1 = rlex1_board.create('point', [2, 3]); 2728 * var rlex1_p2 = rlex1_board.create('point', [1, 4]); 2729 * var rlex1_c1 = rlex1_board.create('circle', [rlex1_p1, rlex1_p2]); 2730 * var rlex1_p3 = rlex1_board.create('point', [6, 5]); 2731 * var rlex1_p4 = rlex1_board.create('point', [8, 6]); 2732 * var rlex1_c2 = rlex1_board.create('circle', [rlex1_p3, rlex1_p4]); 2733 * var rlex1_r1 = rlex1_board.create('radicalaxis', [rlex1_c1, rlex1_c2]); 2734 * </script><pre> 2735 */ 2736 JXG.createRadicalAxis = function (board, parents, attributes) { 2737 var el, el1, el2; 2738 2739 if ( 2740 parents.length !== 2 || 2741 parents[0].elementClass !== Const.OBJECT_CLASS_CIRCLE || 2742 parents[1].elementClass !== Const.OBJECT_CLASS_CIRCLE 2743 ) { 2744 // Failure 2745 throw new Error( 2746 "JSXGraph: Can't create 'radical axis' with parent types '" + 2747 typeof parents[0] + 2748 "' and '" + 2749 typeof parents[1] + 2750 "'." + 2751 "\nPossible parent type: [circle,circle]" 2752 ); 2753 } 2754 2755 el1 = board.select(parents[0]); 2756 el2 = board.select(parents[1]); 2757 2758 el = board.create( 2759 "line", 2760 [ 2761 function () { 2762 var a = el1.stdform, 2763 b = el2.stdform; 2764 2765 return Mat.matVecMult(Mat.transpose([a.slice(0, 3), b.slice(0, 3)]), [ 2766 b[3], 2767 -a[3] 2768 ]); 2769 } 2770 ], 2771 attributes 2772 ); 2773 2774 el.elType = "radicalaxis"; 2775 el.setParents([el1.id, el2.id]); 2776 2777 el1.addChild(el); 2778 el2.addChild(el); 2779 2780 return el; 2781 }; 2782 2783 /** 2784 * @class The polar line of a point with respect to a conic or a circle. 2785 * @pseudo 2786 * @description The polar line is the unique reciprocal relationship of a point with respect to a conic. 2787 * The lines through the intersections of a conic and the polar line of a point 2788 * with respect to that conic and through that point are tangent to the conic. 2789 * A point on a conic has the polar line of that point with respect to that 2790 * conic as the tangent line to that conic at that point. 2791 * See {@link https://en.wikipedia.org/wiki/Pole_and_polar} for more information on pole and polar. 2792 * @name PolarLine 2793 * @augments JXG.Line 2794 * @constructor 2795 * @type JXG.Line 2796 * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown. 2797 * @param {JXG.Conic,JXG.Circle_JXG.Point} el1,el2 or 2798 * @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. 2799 * @example 2800 * // Create the polar line of a point with respect to a conic 2801 * var p1 = board.create('point', [-1, 2]); 2802 * var p2 = board.create('point', [ 1, 4]); 2803 * var p3 = board.create('point', [-1,-2]); 2804 * var p4 = board.create('point', [ 0, 0]); 2805 * var p5 = board.create('point', [ 4,-2]); 2806 * var c1 = board.create('conic',[p1,p2,p3,p4,p5]); 2807 * var p6 = board.create('point', [-1, 1]); 2808 * var l1 = board.create('polarline', [c1, p6]); 2809 * </pre><div class="jxgbox" id="JXG7b7233a0-f363-47dd-9df5-6018d0d17a98" class="jxgbox" style="width:400px; height:400px;"></div> 2810 * <script type='text/javascript'> 2811 * var plex1_board = JXG.JSXGraph.initBoard('JXG7b7233a0-f363-47dd-9df5-6018d0d17a98', {boundingbox: [-3, 5, 5, -3], axis: true, showcopyright: false, shownavigation: false}); 2812 * var plex1_p1 = plex1_board.create('point', [-1, 2]); 2813 * var plex1_p2 = plex1_board.create('point', [ 1, 4]); 2814 * var plex1_p3 = plex1_board.create('point', [-1,-2]); 2815 * var plex1_p4 = plex1_board.create('point', [ 0, 0]); 2816 * var plex1_p5 = plex1_board.create('point', [ 4,-2]); 2817 * var plex1_c1 = plex1_board.create('conic',[plex1_p1,plex1_p2,plex1_p3,plex1_p4,plex1_p5]); 2818 * var plex1_p6 = plex1_board.create('point', [-1, 1]); 2819 * var plex1_l1 = plex1_board.create('polarline', [plex1_c1, plex1_p6]); 2820 * </script><pre> 2821 * @example 2822 * // Create the polar line of a point with respect to a circle. 2823 * var p1 = board.create('point', [ 1, 1]); 2824 * var p2 = board.create('point', [ 2, 3]); 2825 * var c1 = board.create('circle',[p1,p2]); 2826 * var p3 = board.create('point', [ 6, 6]); 2827 * var l1 = board.create('polarline', [c1, p3]); 2828 * </pre><div class="jxgbox" id="JXG7b7233a0-f363-47dd-9df5-7018d0d17a98" class="jxgbox" style="width:400px; height:400px;"></div> 2829 * <script type='text/javascript'> 2830 * var plex2_board = JXG.JSXGraph.initBoard('JXG7b7233a0-f363-47dd-9df5-7018d0d17a98', {boundingbox: [-3, 7, 7, -3], axis: true, showcopyright: false, shownavigation: false}); 2831 * var plex2_p1 = plex2_board.create('point', [ 1, 1]); 2832 * var plex2_p2 = plex2_board.create('point', [ 2, 3]); 2833 * var plex2_c1 = plex2_board.create('circle',[plex2_p1,plex2_p2]); 2834 * var plex2_p3 = plex2_board.create('point', [ 6, 6]); 2835 * var plex2_l1 = plex2_board.create('polarline', [plex2_c1, plex2_p3]); 2836 * </script><pre> 2837 */ 2838 JXG.createPolarLine = function (board, parents, attributes) { 2839 var el, 2840 el1, 2841 el2, 2842 firstParentIsConic, 2843 secondParentIsConic, 2844 firstParentIsPoint, 2845 secondParentIsPoint; 2846 2847 if (parents.length > 1) { 2848 firstParentIsConic = 2849 parents[0].type === Const.OBJECT_TYPE_CONIC || 2850 parents[0].elementClass === Const.OBJECT_CLASS_CIRCLE; 2851 secondParentIsConic = 2852 parents[1].type === Const.OBJECT_TYPE_CONIC || 2853 parents[1].elementClass === Const.OBJECT_CLASS_CIRCLE; 2854 2855 firstParentIsPoint = Type.isPoint(parents[0]); 2856 secondParentIsPoint = Type.isPoint(parents[1]); 2857 } 2858 2859 if ( 2860 parents.length !== 2 || 2861 !( 2862 (firstParentIsConic && secondParentIsPoint) || 2863 (firstParentIsPoint && secondParentIsConic) 2864 ) 2865 ) { 2866 // Failure 2867 throw new Error( 2868 "JSXGraph: Can't create 'polar line' with parent types '" + 2869 typeof parents[0] + 2870 "' and '" + 2871 typeof parents[1] + 2872 "'." + 2873 "\nPossible parent type: [conic|circle,point], [point,conic|circle]" 2874 ); 2875 } 2876 2877 if (secondParentIsPoint) { 2878 el1 = board.select(parents[0]); 2879 el2 = board.select(parents[1]); 2880 } else { 2881 el1 = board.select(parents[1]); 2882 el2 = board.select(parents[0]); 2883 } 2884 2885 // Polar lines have been already provided in the tangent element. 2886 el = board.create("tangent", [el1, el2], attributes); 2887 2888 el.elType = "polarline"; 2889 return el; 2890 }; 2891 2892 /** 2893 * 2894 * @class One of the two tangent lines to a conic or a circle through an external point. 2895 * @pseudo 2896 * @description Construct the tangent line through a point to a conic or a circle. There will be either two, one or no 2897 * such tangent, depending if the point is outside of the conic, on the conic, or inside of the conic. 2898 * Similar to the intersection of a line with a circle, the specific tangent can be chosen with a third (optional) parameter 2899 * <i>number</i>. 2900 * <p> 2901 * Attention: from a technical point of view, the point from which the tangent to the conic/circle is constructed is not an element of 2902 * the tangent line. 2903 * @name TangentTo 2904 * @augments JXG.Line 2905 * @constructor 2906 * @type JXG.Line 2907 * @throws {Exception} If the element cannot be constructed with the given parent objects an exception is thrown. 2908 * @param {JXG.Conic,JXG.Circle_JXG.Point_Number} conic,point,[number=0] The result will be the tangent line through 2909 * the point with respect to the conic or circle. 2910 * 2911 * @example 2912 * var c = board.create('circle', [[3, 0], [3, 4]]); 2913 * var p = board.create('point', [0, 6]); 2914 * var t0 = board.create('tangentto', [c, p, 0], { color: 'black', polar: {visible: true}, point: {visible: true} }); 2915 * var t1 = board.create('tangentto', [c, p, 1], { color: 'black' }); 2916 * 2917 * </pre><div id="JXGd4b359c7-3a29-44c3-a19d-d51b42a00c8b" class="jxgbox" style="width: 300px; height: 300px;"></div> 2918 * <script type="text/javascript"> 2919 * (function() { 2920 * var board = JXG.JSXGraph.initBoard('JXGd4b359c7-3a29-44c3-a19d-d51b42a00c8b', 2921 * {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false}); 2922 * var c = board.create('circle', [[3, 0], [3, 4]]); 2923 * var p = board.create('point', [0, 6]); 2924 * var t0 = board.create('tangentto', [c, p, 0], { color: 'black', polar: {visible: true}, point: {visible: true} }); 2925 * var t1 = board.create('tangentto', [c, p, 1], { color: 'black' }); 2926 * 2927 * })(); 2928 * 2929 * </script><pre> 2930 * 2931 * @example 2932 * var p = board.create('point', [0, 6]); 2933 * var ell = board.create('ellipse', [[-5, 1], [-2, -1], [-3, 2]]); 2934 * var t0 = board.create('tangentto', [ell, p, 0]); 2935 * var t1 = board.create('tangentto', [ell, p, 1]); 2936 * 2937 * </pre><div id="JXG6e625663-1c3e-4e08-a9df-574972a374e8" class="jxgbox" style="width: 300px; height: 300px;"></div> 2938 * <script type="text/javascript"> 2939 * (function() { 2940 * var board = JXG.JSXGraph.initBoard('JXG6e625663-1c3e-4e08-a9df-574972a374e8', 2941 * {boundingbox: [-8, 8, 8,-8], axis: true, showcopyright: false, shownavigation: false}); 2942 * var p = board.create('point', [0, 6]); 2943 * var ell = board.create('ellipse', [[-5, 1], [-2, -1], [-3, 2]]); 2944 * var t0 = board.create('tangentto', [ell, p, 0]); 2945 * var t1 = board.create('tangentto', [ell, p, 1]); 2946 * 2947 * })(); 2948 * 2949 * </script><pre> 2950 * 2951 */ 2952 JXG.createTangentTo = function (board, parents, attributes) { 2953 var el, attr, 2954 conic, pointFrom, num, 2955 intersect, polar; 2956 2957 conic = board.select(parents[0]); 2958 pointFrom = Type.providePoints(board, parents[1], attributes, 'point')[0]; 2959 num = Type.def(parents[2], 0); 2960 2961 if ( 2962 (conic.type !== Const.OBJECT_TYPE_CIRCLE && conic.type !== Const.OBJECT_TYPE_CONIC) || 2963 (pointFrom.elementClass !== Const.OBJECT_CLASS_POINT) 2964 ) { 2965 throw new Error( 2966 "JSXGraph: Can't create tangentto with parent types '" + 2967 typeof parents[0] + 2968 "' and '" + 2969 typeof parents[1] + 2970 "' and '" + 2971 typeof parents[2] + 2972 "'." + 2973 "\nPossible parent types: [circle|conic,point,number]" 2974 ); 2975 } 2976 2977 attr = Type.copyAttributes(attributes, board.options, 'tangentto'); 2978 // A direct analytic geometry approach would be in 2979 // Richter-Gebert: Perspectives on projective geometry, 11.3 2980 polar = board.create('polar', [conic, pointFrom], attr.polar); 2981 intersect = board.create('intersection', [polar, conic, num], attr.point); 2982 2983 el = board.create('tangent', [conic, intersect], attr); 2984 2985 /** 2986 * The intersection point of the conic/circle with the polar line of the tangentto construction. 2987 * @memberOf TangentTo.prototype 2988 * @name point 2989 * @type JXG.Point 2990 */ 2991 el.point = intersect; 2992 2993 /** 2994 * The polar line of the tangentto construction. 2995 * @memberOf TangentTo.prototype 2996 * @name polar 2997 * @type JXG.Line 2998 */ 2999 el.polar = polar; 3000 3001 el.elType = 'tangentto'; 3002 3003 return el; 3004 }; 3005 3006 /** 3007 * Register the element type tangent at JSXGraph 3008 * @private 3009 */ 3010 JXG.registerElement("tangent", JXG.createTangent); 3011 JXG.registerElement("normal", JXG.createNormal); 3012 JXG.registerElement('tangentto', JXG.createTangentTo); 3013 JXG.registerElement("polar", JXG.createTangent); 3014 JXG.registerElement("radicalaxis", JXG.createRadicalAxis); 3015 JXG.registerElement("polarline", JXG.createPolarLine); 3016 3017 export default JXG.Line; 3018 // export default { 3019 // Line: JXG.Line, 3020 // createLine: JXG.createLine, 3021 // createTangent: JXG.createTangent, 3022 // createPolar: JXG.createTangent, 3023 // createSegment: JXG.createSegment, 3024 // createAxis: JXG.createAxis, 3025 // createArrow: JXG.createArrow, 3026 // createRadicalAxis: JXG.createRadicalAxis, 3027 // createPolarLine: JXG.createPolarLine 3028 // }; 3029