1 /* 2 Copyright 2008-2016 3 Matthias Ehmann, 4 Michael Gerhaeuser, 5 Carsten Miller, 6 Bianca Valentin, 7 Alfred Wassermann, 8 Peter Wilfahrt 9 10 This file is part of JSXGraph. 11 12 JSXGraph is free software dual licensed under the GNU LGPL or MIT License. 13 14 You can redistribute it and/or modify it under the terms of the 15 16 * GNU Lesser General Public License as published by 17 the Free Software Foundation, either version 3 of the License, or 18 (at your option) any later version 19 OR 20 * MIT License: https://github.com/jsxgraph/jsxgraph/blob/master/LICENSE.MIT 21 22 JSXGraph is distributed in the hope that it will be useful, 23 but WITHOUT ANY WARRANTY; without even the implied warranty of 24 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 25 GNU Lesser General Public License for more details. 26 27 You should have received a copy of the GNU Lesser General Public License and 28 the MIT License along with JSXGraph. If not, see <http://www.gnu.org/licenses/> 29 and <http://opensource.org/licenses/MIT/>. 30 */ 31 32 33 /*global JXG: true, define: true*/ 34 /*jslint nomen: true, plusplus: true*/ 35 36 /* depends: 37 jxg 38 math/geometry 39 math/math 40 base/coords 41 base/circle 42 utils/type 43 base/constants 44 elements: 45 curve 46 midpoint 47 circumcenter 48 */ 49 50 /** 51 * @fileoverview In this file the geometry object Arc is defined. Arc stores all 52 * style and functional properties that are required to draw an arc on a board. 53 */ 54 55 define([ 56 'jxg', 'math/geometry', 'math/math', 'base/coords', 'base/circle', 'utils/type', 'base/constants', 57 'base/curve', 'element/composition' 58 ], function (JXG, Geometry, Mat, Coords, Circle, Type, Const, Curve, Compositions) { 59 60 "use strict"; 61 62 /** 63 * @class An arc is a segment of the circumference of a circle. It is defined by a center, one point that 64 * defines the radius, and a third point that defines the angle of the arc. 65 * @pseudo 66 * @name Arc 67 * @augments Curve 68 * @constructor 69 * @type JXG.Curve 70 * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown. 71 * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 The result will be an arc of a circle around p1 through p2. The arc is drawn 72 * counter-clockwise from p2 to p3. 73 * @example 74 * // Create an arc out of three free points 75 * var p1 = board.create('point', [2.0, 2.0]); 76 * var p2 = board.create('point', [1.0, 0.5]); 77 * var p3 = board.create('point', [3.5, 1.0]); 78 * 79 * var a = board.create('arc', [p1, p2, p3]); 80 * </pre><div class="jxgbox"id="114ef584-4a5e-4686-8392-c97501befb5b" style="width: 300px; height: 300px;"></div> 81 * <script type="text/javascript"> 82 * (function () { 83 * var board = JXG.JSXGraph.initBoard('114ef584-4a5e-4686-8392-c97501befb5b', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}), 84 * p1 = board.create('point', [2.0, 2.0]), 85 * p2 = board.create('point', [1.0, 0.5]), 86 * p3 = board.create('point', [3.5, 1.0]), 87 * 88 * a = board.create('arc', [p1, p2, p3]); 89 * })(); 90 * </script><pre> 91 */ 92 JXG.createArc = function (board, parents, attributes) { 93 var el, attr, i, points; 94 95 // This method is used to create circumcirclearcs, too. If a circumcirclearc is created we get a fourth 96 // point, that's why we need to check that case, too. 97 points = Type.providePoints(board, parents, attributes, 'point'); 98 if (points === false || points.length < 3) { 99 throw new Error("JSXGraph: Can't create Arc with parent types '" + 100 (typeof parents[0]) + "' and '" + (typeof parents[1]) + "' and '" + 101 (typeof parents[2]) + "'." + 102 "\nPossible parent types: [point,point,point]"); 103 } 104 105 attr = Type.copyAttributes(attributes, board.options, 'arc'); 106 el = board.create('curve', [[0], [0]], attr); 107 108 el.elType = 'arc'; 109 el.setParents(points); 110 111 /** 112 * documented in JXG.GeometryElement 113 * @ignore 114 */ 115 el.type = Const.OBJECT_TYPE_ARC; 116 117 /** 118 * Center of the arc. 119 * @memberOf Arc.prototype 120 * @name center 121 * @type JXG.Point 122 */ 123 el.center = points[0]; 124 125 /** 126 * Point defining the arc's radius. 127 * @memberOf Arc.prototype 128 * @name radiuspoint 129 * @type JXG.Point 130 */ 131 el.radiuspoint = points[1]; 132 el.point2 = el.radiuspoint; 133 134 /** 135 * The point defining the arc's angle. 136 * @memberOf Arc.prototype 137 * @name anglepoint 138 * @type JXG.Point 139 */ 140 el.anglepoint = points[2]; 141 el.point3 = el.anglepoint; 142 143 // Add arc as child to defining points 144 el.center.addChild(el); 145 el.radiuspoint.addChild(el); 146 el.anglepoint.addChild(el); 147 148 // should be documented in options 149 el.useDirection = attr.usedirection; 150 151 // documented in JXG.Curve 152 el.updateDataArray = function () { 153 var ar, phi, v, det, p0c, p1c, p2c, 154 sgn = 1, 155 A = this.radiuspoint, 156 B = this.center, 157 C = this.anglepoint; 158 159 phi = Geometry.rad(A, B, C); 160 if ((this.visProp.selection === 'minor' && phi > Math.PI) || 161 (this.visProp.selection === 'major' && phi < Math.PI)) { 162 sgn = -1; 163 } 164 165 // This is true for circumCircleArcs. In that case there is 166 // a fourth parent element: [center, point1, point3, point2] 167 if (this.useDirection) { 168 p0c = points[1].coords.usrCoords; 169 p1c = points[3].coords.usrCoords; 170 p2c = points[2].coords.usrCoords; 171 det = (p0c[1] - p2c[1]) * (p0c[2] - p1c[2]) - (p0c[2] - p2c[2]) * (p0c[1] - p1c[1]); 172 173 if (det < 0) { 174 this.radiuspoint = points[1]; 175 this.anglepoint = points[2]; 176 } else { 177 this.radiuspoint = points[2]; 178 this.anglepoint = points[1]; 179 } 180 } 181 182 A = A.coords.usrCoords; 183 B = B.coords.usrCoords; 184 C = C.coords.usrCoords; 185 186 ar = Geometry.bezierArc(A, B, C, false, sgn); 187 188 this.dataX = ar[0]; 189 this.dataY = ar[1]; 190 191 this.bezierDegree = 3; 192 193 this.updateStdform(); 194 this.updateQuadraticform(); 195 }; 196 197 /** 198 * Determines the arc's current radius. I.e. the distance between {@link Arc#center} and {@link Arc#radiuspoint}. 199 * @memberOf Arc.prototype 200 * @name Radius 201 * @function 202 * @returns {Number} The arc's radius 203 */ 204 el.Radius = function () { 205 return this.radiuspoint.Dist(this.center); 206 }; 207 208 /** 209 * @deprecated Use {@link Arc#Radius} 210 * @memberOf Arc.prototype 211 * @name getRadius 212 * @function 213 * @returns {Number} 214 */ 215 el.getRadius = function () { 216 JXG.deprecated('Arc.getRadius()', 'Arc.Radius()'); 217 return this.Radius(); 218 }; 219 220 /** 221 * Returns the length of the arc. 222 * @memberOf Arc.prototype 223 * @name Value 224 * @function 225 * @returns {Number} The arc length 226 */ 227 el.Value = function () { 228 return this.Radius() * Geometry.rad(this.radiuspoint, this.center, this.anglepoint); 229 }; 230 231 // documented in geometry element 232 el.hasPoint = function (x, y) { 233 var dist, checkPoint, 234 has, angle, alpha, beta, 235 invMat, c, 236 prec = this.board.options.precision.hasPoint / this.board.unitX, 237 r = this.Radius(); 238 239 checkPoint = new Coords(Const.COORDS_BY_SCREEN, [x, y], this.board); 240 241 if (this.transformations.length > 0) { 242 // Transform the mouse/touch coordinates 243 // back to the original position of the curve. 244 this.updateTransformMatrix(); 245 invMat = Mat.inverse(this.transformMat); 246 c = Mat.matVecMult(invMat, checkPoint.usrCoords); 247 checkPoint = new Coords(Const.COORDS_BY_USER, c, this.board); 248 } 249 250 dist = this.center.coords.distance(Const.COORDS_BY_USER, checkPoint); 251 has = (Math.abs(dist - r) < prec); 252 253 /** 254 * At that point we know that the user has touched the circle line. 255 */ 256 if (has) { 257 angle = Geometry.rad(this.radiuspoint, this.center, checkPoint.usrCoords.slice(1)); 258 alpha = 0.0; 259 beta = Geometry.rad(this.radiuspoint, this.center, this.anglepoint); 260 261 if ((this.visProp.selection === 'minor' && beta > Math.PI) || 262 (this.visProp.selection === 'major' && beta < Math.PI)) { 263 alpha = beta; 264 beta = 2 * Math.PI; 265 } 266 if (angle < alpha || angle > beta) { 267 has = false; 268 } 269 } 270 271 return has; 272 }; 273 274 /** 275 * Checks whether (x,y) is within the sector defined by the arc. 276 * @memberOf Arc.prototype 277 * @name hasPointSector 278 * @function 279 * @param {Number} x Coordinate in x direction, screen coordinates. 280 * @param {Number} y Coordinate in y direction, screen coordinates. 281 * @returns {Boolean} True if (x,y) is within the sector defined by the arc, False otherwise. 282 */ 283 el.hasPointSector = function (x, y) { 284 var angle, alpha, beta, 285 checkPoint = new Coords(Const.COORDS_BY_SCREEN, [x, y], this.board), 286 r = this.Radius(), 287 dist = this.center.coords.distance(Const.COORDS_BY_USER, checkPoint), 288 has = (dist < r); 289 290 if (has) { 291 angle = Geometry.rad(this.radiuspoint, this.center, checkPoint.usrCoords.slice(1)); 292 alpha = 0; 293 beta = Geometry.rad(this.radiuspoint, this.center, this.anglepoint); 294 295 if ((this.visProp.selection === 'minor' && beta > Math.PI) || 296 (this.visProp.selection === 'major' && beta < Math.PI)) { 297 alpha = beta; 298 beta = 2 * Math.PI; 299 } 300 if (angle < alpha || angle > beta) { 301 has = false; 302 } 303 } 304 305 return has; 306 }; 307 308 // documented in geometry element 309 el.getTextAnchor = function () { 310 return this.center.coords; 311 }; 312 313 // documented in geometry element 314 el.getLabelAnchor = function () { 315 var coords, vecx, vecy, len, 316 angle = Geometry.rad(this.radiuspoint, this.center, this.anglepoint), 317 dx = 10 / this.board.unitX, 318 dy = 10 / this.board.unitY, 319 p2c = this.point2.coords.usrCoords, 320 pmc = this.center.coords.usrCoords, 321 bxminusax = p2c[1] - pmc[1], 322 byminusay = p2c[2] - pmc[2]; 323 324 // If this is uncommented, the angle label can not be dragged 325 //if (Type.exists(this.label)) { 326 // this.label.relativeCoords = new Coords(Const.COORDS_BY_SCREEN, [0, 0], this.board); 327 //} 328 329 if ((this.visProp.selection === 'minor' && angle > Math.PI) || 330 (this.visProp.selection === 'major' && angle < Math.PI)) { 331 angle = -(2 * Math.PI - angle); 332 } 333 334 coords = new Coords(Const.COORDS_BY_USER, [ 335 pmc[1] + Math.cos(angle * 0.5) * bxminusax - Math.sin(angle * 0.5) * byminusay, 336 pmc[2] + Math.sin(angle * 0.5) * bxminusax + Math.cos(angle * 0.5) * byminusay 337 ], this.board); 338 339 vecx = coords.usrCoords[1] - pmc[1]; 340 vecy = coords.usrCoords[2] - pmc[2]; 341 342 len = Math.sqrt(vecx * vecx + vecy * vecy); 343 vecx = vecx * (len + dx) / len; 344 vecy = vecy * (len + dy) / len; 345 346 return new Coords(Const.COORDS_BY_USER, [pmc[1] + vecx, pmc[2] + vecy], this.board); 347 }; 348 349 // documentation in jxg.circle 350 el.updateQuadraticform = Circle.Circle.prototype.updateQuadraticform; 351 352 // documentation in jxg.circle 353 el.updateStdform = Circle.Circle.prototype.updateStdform; 354 355 el.methodMap = JXG.deepCopy(el.methodMap, { 356 getRadius: 'getRadius', 357 radius: 'Radius', 358 center: 'center', 359 radiuspoint: 'radiuspoint', 360 anglepoint: 'anglepoint', 361 Value: 'Value' 362 }); 363 364 el.prepareUpdate().update(); 365 return el; 366 }; 367 368 JXG.registerElement('arc', JXG.createArc); 369 370 /** 371 * @class A semicircle is a special arc defined by two points. The arc hits both points. 372 * @pseudo 373 * @name Semicircle 374 * @augments Arc 375 * @constructor 376 * @type Arc 377 * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown. 378 * @param {JXG.Point_JXG.Point} p1,p2 The result will be a composition of an arc drawn clockwise from <tt>p1</tt> and 379 * <tt>p2</tt> and the midpoint of <tt>p1</tt> and <tt>p2</tt>. 380 * @example 381 * // Create an arc out of three free points 382 * var p1 = board.create('point', [4.5, 2.0]); 383 * var p2 = board.create('point', [1.0, 0.5]); 384 * 385 * var a = board.create('semicircle', [p1, p2]); 386 * </pre><div class="jxgbox"id="5385d349-75d7-4078-b732-9ae808db1b0e" style="width: 300px; height: 300px;"></div> 387 * <script type="text/javascript"> 388 * (function () { 389 * var board = JXG.JSXGraph.initBoard('5385d349-75d7-4078-b732-9ae808db1b0e', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}), 390 * p1 = board.create('point', [4.5, 2.0]), 391 * p2 = board.create('point', [1.0, 0.5]), 392 * 393 * sc = board.create('semicircle', [p1, p2]); 394 * })(); 395 * </script><pre> 396 */ 397 JXG.createSemicircle = function (board, parents, attributes) { 398 var el, mp, attr, points; 399 400 // we need 2 points 401 points = Type.providePoints(board, parents, attributes, 'point'); 402 if (points === false || points.length !== 2) { 403 throw new Error("JSXGraph: Can't create Semicircle with parent types '" + 404 (typeof parents[0]) + "' and '" + (typeof parents[1]) + "'." + 405 "\nPossible parent types: [point,point]"); 406 } 407 408 attr = Type.copyAttributes(attributes, board.options, 'semicircle', 'midpoint'); 409 mp = board.create('midpoint', points, attr); 410 mp.dump = false; 411 412 attr = Type.copyAttributes(attributes, board.options, 'semicircle'); 413 el = board.create('arc', [mp, points[1], points[0]], attr); 414 el.elType = 'semicircle'; 415 el.setParents([points[0].id, points[1].id]); 416 el.subs = { 417 midpoint: mp 418 }; 419 420 /** 421 * The midpoint of the two defining points. 422 * @memberOf Semicircle.prototype 423 * @name midpoint 424 * @type Midpoint 425 */ 426 el.midpoint = el.center = mp; 427 428 return el; 429 }; 430 431 JXG.registerElement('semicircle', JXG.createSemicircle); 432 433 /** 434 * @class A circumcircle arc is an {@link Arc} defined by three points. All three points lie on the arc. 435 * @pseudo 436 * @name CircumcircleArc 437 * @augments Arc 438 * @constructor 439 * @type Arc 440 * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown. 441 * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 The result will be a composition of an arc of the circumcircle of 442 * <tt>p1</tt>, <tt>p2</tt>, and <tt>p3</tt> and the midpoint of the circumcircle of the three points. The arc is drawn 443 * counter-clockwise from <tt>p1</tt> over <tt>p2</tt> to <tt>p3</tt>. 444 * @example 445 * // Create a circum circle arc out of three free points 446 * var p1 = board.create('point', [2.0, 2.0]); 447 * var p2 = board.create('point', [1.0, 0.5]); 448 * var p3 = board.create('point', [3.5, 1.0]); 449 * 450 * var a = board.create('arc', [p1, p2, p3]); 451 * </pre><div class="jxgbox"id="87125fd4-823a-41c1-88ef-d1a1369504e3" style="width: 300px; height: 300px;"></div> 452 * <script type="text/javascript"> 453 * (function () { 454 * var board = JXG.JSXGraph.initBoard('87125fd4-823a-41c1-88ef-d1a1369504e3', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}), 455 * p1 = board.create('point', [2.0, 2.0]), 456 * p2 = board.create('point', [1.0, 0.5]), 457 * p3 = board.create('point', [3.5, 1.0]), 458 * 459 * cca = board.create('circumcirclearc', [p1, p2, p3]); 460 * })(); 461 * </script><pre> 462 */ 463 JXG.createCircumcircleArc = function (board, parents, attributes) { 464 var el, mp, attr, points; 465 466 // We need three points 467 points = Type.providePoints(board, parents, attributes, 'point'); 468 if (points === false || points.length !== 3) { 469 throw new Error("JSXGraph: create Circumcircle Arc with parent types '" + 470 (typeof parents[0]) + "' and '" + (typeof parents[1]) + "' and '" + (typeof parents[2]) + "'." + 471 "\nPossible parent types: [point,point,point]"); 472 } 473 474 attr = Type.copyAttributes(attributes, board.options, 'circumcirclearc', 'center'); 475 mp = board.create('circumcenter', points, attr); 476 mp.dump = false; 477 478 attr = Type.copyAttributes(attributes, board.options, 'circumcirclearc'); 479 attr.usedirection = true; 480 el = board.create('arc', [mp, points[0], points[2], points[1]], attr); 481 482 el.elType = 'circumcirclearc'; 483 el.setParents([points[0].id, points[1].id, points[2].id]); 484 el.subs = { 485 center: mp 486 }; 487 488 /** 489 * The midpoint of the circumcircle of the three points defining the circumcircle arc. 490 * @memberOf CircumcircleArc.prototype 491 * @name center 492 * @type Circumcenter 493 */ 494 el.center = mp; 495 496 return el; 497 }; 498 499 JXG.registerElement('circumcirclearc', JXG.createCircumcircleArc); 500 501 /** 502 * @class A minor arc is a segment of the circumference of a circle having measure less than or equal to 503 * 180 degrees (pi radians). It is defined by a center, one point that 504 * defines the radius, and a third point that defines the angle of the arc. 505 * @pseudo 506 * @name MinorArc 507 * @augments Curve 508 * @constructor 509 * @type JXG.Curve 510 * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown. 511 * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 . Minor arc is an arc of a circle around p1 having measure less than or equal to 512 * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3. 513 * @example 514 * // Create an arc out of three free points 515 * var p1 = board.create('point', [2.0, 2.0]); 516 * var p2 = board.create('point', [1.0, 0.5]); 517 * var p3 = board.create('point', [3.5, 1.0]); 518 * 519 * var a = board.create('arc', [p1, p2, p3]); 520 * </pre><div class="jxgbox"id="64ba7ca2-8728-45f3-96e5-3c7a4414de2f" style="width: 300px; height: 300px;"></div> 521 * <script type="text/javascript"> 522 * (function () { 523 * var board = JXG.JSXGraph.initBoard('64ba7ca2-8728-45f3-96e5-3c7a4414de2f', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}), 524 * p1 = board.create('point', [2.0, 2.0]), 525 * p2 = board.create('point', [1.0, 0.5]), 526 * p3 = board.create('point', [3.5, 1.0]), 527 * 528 * a = board.create('minorarc', [p1, p2, p3]); 529 * })(); 530 * </script><pre> 531 */ 532 533 JXG.createMinorArc = function (board, parents, attributes) { 534 attributes.selection = 'minor'; 535 return JXG.createArc(board, parents, attributes); 536 }; 537 538 JXG.registerElement('minorarc', JXG.createMinorArc); 539 540 /** 541 * @class A major arc is a segment of the circumference of a circle having measure greater than or equal to 542 * 180 degrees (pi radians). It is defined by a center, one point that 543 * defines the radius, and a third point that defines the angle of the arc. 544 * @pseudo 545 * @name MajorArc 546 * @augments Curve 547 * @constructor 548 * @type JXG.Curve 549 * @throws {Error} If the element cannot be constructed with the given parent objects an exception is thrown. 550 * @param {JXG.Point_JXG.Point_JXG.Point} p1,p2,p3 . Major arc is an arc of a circle around p1 having measure greater than or equal to 551 * 180 degrees (pi radians) and starts at p2. The radius is determined by p2, the angle by p3. 552 * @example 553 * // Create an arc out of three free points 554 * var p1 = board.create('point', [2.0, 2.0]); 555 * var p2 = board.create('point', [1.0, 0.5]); 556 * var p3 = board.create('point', [3.5, 1.0]); 557 * 558 * var a = board.create('minorarc', [p1, p2, p3]); 559 * </pre><div class="jxgbox"id="17a10d38-5629-40a4-b150-f41806edee9f" style="width: 300px; height: 300px;"></div> 560 * <script type="text/javascript"> 561 * (function () { 562 * var board = JXG.JSXGraph.initBoard('17a10d38-5629-40a4-b150-f41806edee9f', {boundingbox: [-1, 7, 7, -1], axis: true, showcopyright: false, shownavigation: false}), 563 * p1 = board.create('point', [2.0, 2.0]), 564 * p2 = board.create('point', [1.0, 0.5]), 565 * p3 = board.create('point', [3.5, 1.0]), 566 * 567 * a = board.create('majorarc', [p1, p2, p3]); 568 * })(); 569 * </script><pre> 570 */ 571 JXG.createMajorArc = function (board, parents, attributes) { 572 attributes.selection = 'major'; 573 return JXG.createArc(board, parents, attributes); 574 }; 575 576 JXG.registerElement('majorarc', JXG.createMajorArc); 577 578 return { 579 createArc: JXG.createArc, 580 createSemicircle: JXG.createSemicircle, 581 createCircumcircleArc: JXG.createCircumcircleArc, 582 createMinorArc: JXG.createMinorArc, 583 createMajorArc: JXG.createMajorArc 584 }; 585 }); 586