@flatten-js/core

<!DOCTYPE html> <html lang="en"> <head> <meta charset="utf-8"> <meta name="viewport" content="width=device-width,initial-scale=1"> <title>classes/arc.js - Documentation</title> <script src="scripts/prettify/prettify.js"></script> <script src="scripts/prettify/lang-css.js"></script>  <link type="text/css" rel="stylesheet" href="https://code.ionicframework.com/ionicons/2.0.1/css/ionicons.min.css"> <link type="text/css" rel="stylesheet" href="styles/prettify-tomorrow.css"> <link type="text/css" rel="stylesheet" href="styles/jsdoc-default.css"> </head> <body> <input type="checkbox" id="nav-trigger" class="nav-trigger" /> <label for="nav-trigger" class="navicon-button x"> <div class="navicon"></div> </label> <label for="nav-trigger" class="overlay"></label> <nav> <li class="nav-link nav-home-link"><a href="index.html">Home</a></li><li class="nav-heading">Classes</li><li class="nav-heading">C<a href="Arc.html">Arc</a></li><li class="nav-item">F<a href="Arc.html#clone">clone</a></li><li 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href="Vector.html#projectionOn">projectionOn</a></li><li class="nav-item">F<a href="Vector.html#toJSON">toJSON</a></li><li class="nav-heading">C<a href="CircularLinkedList.html">CircularLinkedList</a></li><li class="nav-item">F<a href="CircularLinkedList.html#append">append</a></li><li class="nav-item">F<a href="CircularLinkedList.html#insert">insert</a></li><li class="nav-item">F<a href="CircularLinkedList.html#remove">remove</a></li><li class="nav-heading">C<a href="DE9IM.html">DE9IM</a></li><li class="nav-item">F<a href="DE9IM.html#toString">toString</a></li><li class="nav-heading">C<a href="LinkedList.html">LinkedList</a></li><li class="nav-item">F<a href="LinkedList.html#toArray">toArray</a></li><li class="nav-item">F<a href="LinkedList.html#append">append</a></li><li class="nav-item">F<a href="LinkedList.html#insert">insert</a></li><li class="nav-item">F<a href="LinkedList.html#remove">remove</a></li><li class="nav-item">F<a href="LinkedList.html#isEmpty">isEmpty</a></li><li 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href="module-BooleanOperations.html#.intersect">intersect</a></li><li class="nav-item">F<a href="module-BooleanOperations.html#.innerClip">innerClip</a></li><li class="nav-item">F<a href="module-BooleanOperations.html#.outerClip">outerClip</a></li><li class="nav-item">F<a href="module-BooleanOperations.html#.calculateIntersections">calculateIntersections</a></li><li class="nav-heading">M<a href="module-RayShoot.html">RayShoot</a></li><li class="nav-item">F<a href="module-RayShoot.html#.ray_shoot">ray_shoot</a></li><li class="nav-heading">M<a href="module-Relation.html">Relation</a></li><li class="nav-item">F<a href="module-Relation.html#.equal">equal</a></li><li class="nav-item">F<a href="module-Relation.html#.intersect">intersect</a></li><li class="nav-item">F<a href="module-Relation.html#.touch">touch</a></li><li class="nav-item">F<a href="module-Relation.html#.disjoint">disjoint</a></li><li class="nav-item">F<a href="module-Relation.html#.inside">inside</a></li><li class="nav-item">F<a href="module-Relation.html#.covered">covered</a></li><li class="nav-item">F<a href="module-Relation.html#.contain">contain</a></li><li class="nav-item">F<a href="module-Relation.html#.cover">cover</a></li><li class="nav-item">F<a href="module-Relation.html#.relate">relate</a></li><li class="nav-heading"><a href="global.html">Globals</a></li><li class="nav-item">F<a href="global.html#inverse">inverse</a></li><li class="nav-item">M<a href="global.html#arc">arc</a></li><li class="nav-item">M<a href="global.html#box">box</a></li><li class="nav-item">M<a href="global.html#circle">circle</a></li><li class="nav-item">M<a href="global.html#line">line</a></li><li class="nav-item">M<a href="global.html#matrix">matrix</a></li><li class="nav-item">M<a href="global.html#multiline">multiline</a></li><li class="nav-item">M<a href="global.html#point">point</a></li><li class="nav-item">M<a href="global.html#polygon">polygon</a></li><li class="nav-item">M<a href="global.html#segment">segment</a></li><li class="nav-item">M<a href="global.html#vector">vector</a></li><li class="nav-item">M<a href="global.html#CCW">CCW</a></li><li class="nav-item">M<a href="global.html#CW">CW</a></li><li class="nav-item">M<a href="global.html#ORIENTATION">ORIENTATION</a></li><li class="nav-item">M<a href="global.html#DP_TOL">DP_TOL</a></li><li class="nav-item">F<a href="global.html#setTolerance">setTolerance</a></li><li class="nav-item">F<a href="global.html#getTolerance">getTolerance</a></li><li class="nav-item">F<a href="global.html#EQ_0">EQ_0</a></li><li class="nav-item">F<a href="global.html#EQ">EQ</a></li><li class="nav-item">F<a href="global.html#GT">GT</a></li><li class="nav-item">F<a href="global.html#GE">GE</a></li><li class="nav-item">F<a href="global.html#LT">LT</a></li><li class="nav-item">F<a href="global.html#LE">LE</a></li> </nav> <div id="main"> <h1 class="page-title">classes/arc.js</h1> <section> <article> <pre class="prettyprint source linenums"><code>/** * Created by Alex Bol on 3/10/2017. */ "use strict"; import Flatten from '../flatten'; import * as Intersection from '../algorithms/intersection'; /** * Class representing a circular arc * @type {Arc} */ export class Arc { /** * * @param {Point} pc - arc center * @param {number} r - arc radius * @param {number} startAngle - start angle in radians from 0 to 2*PI * @param {number} endAngle - end angle in radians from 0 to 2*PI * @param {boolean} counterClockwise - arc direction, true - clockwise, false - counter clockwise */ constructor(...args) { /** * Arc center * @type {Point} */ this.pc = new Flatten.Point(); /** * Arc radius * @type {number} */ this.r = 1; /** * Arc start angle in radians * @type {number} */ this.startAngle = 0; /** * Arc end angle in radians * @type {number} */ this.endAngle = 2 * Math.PI; /** * Arc orientation * @type {boolean} */ this.counterClockwise = Flatten.CCW; if (args.length == 0) return; if (args.length == 1 && args[0] instanceof Object && args[0].name === "arc") { let {pc, r, startAngle, endAngle, counterClockwise} = args[0]; this.pc = new Flatten.Point(pc.x, pc.y); this.r = r; this.startAngle = startAngle; this.endAngle = endAngle; this.counterClockwise = counterClockwise; return; } else { let [pc, r, startAngle, endAngle, counterClockwise] = [...args]; if (pc && pc instanceof Flatten.Point) this.pc = pc.clone(); if (r !== undefined) this.r = r; if (startAngle !== undefined) this.startAngle = startAngle; if (endAngle !== undefined) this.endAngle = endAngle; if (counterClockwise !== undefined) this.counterClockwise = counterClockwise; return; } throw Flatten.Errors.ILLEGAL_PARAMETERS; } /** * Return new cloned instance of arc * @returns {Arc} */ clone() { return new Flatten.Arc(this.pc.clone(), this.r, this.startAngle, this.endAngle, this.counterClockwise); } /** * Get sweep angle in radians. Sweep angle is non-negative number from 0 to 2*PI * @returns {number} */ get sweep() { if (Flatten.Utils.EQ(this.startAngle, this.endAngle)) return 0.0; if (Flatten.Utils.EQ(Math.abs(this.startAngle - this.endAngle), Flatten.PIx2)) { return Flatten.PIx2; } let sweep; if (this.counterClockwise) { sweep = Flatten.Utils.GT(this.endAngle, this.startAngle) ? this.endAngle - this.startAngle : this.endAngle - this.startAngle + Flatten.PIx2; } else { sweep = Flatten.Utils.GT(this.startAngle, this.endAngle) ? this.startAngle - this.endAngle : this.startAngle - this.endAngle + Flatten.PIx2; } if (Flatten.Utils.GT(sweep, Flatten.PIx2)) { sweep -= Flatten.PIx2; } if (Flatten.Utils.LT(sweep, 0)) { sweep += Flatten.PIx2; } return sweep; } /** * Get start point of arc * @returns {Point} */ get start() { let p0 = new Flatten.Point(this.pc.x + this.r, this.pc.y); return p0.rotate(this.startAngle, this.pc); } /** * Get end point of arc * @returns {Point} */ get end() { let p0 = new Flatten.Point(this.pc.x + this.r, this.pc.y); return p0.rotate(this.endAngle, this.pc); } /** * Get center of arc * @returns {Point} */ get center() { return this.pc.clone(); } get vertices() { return [this.start.clone(), this.end.clone()]; } /** * Get arc length * @returns {number} */ get length() { return Math.abs(this.sweep * this.r); } /** * Get bounding box of the arc * @returns {Box} */ get box() { let func_arcs = this.breakToFunctional(); let box = func_arcs.reduce((acc, arc) => acc.merge(arc.start.box), new Flatten.Box()); box = box.merge(this.end.box); return box; } /** * Returns true if arc contains point, false otherwise * @param {Point} pt - point to test * @returns {boolean} */ contains(pt) { // first check if point on circle (pc,r) if (!Flatten.Utils.EQ(this.pc.distanceTo(pt)[0], this.r)) return false; // point on circle if (pt.equalTo(this.start)) return true; let angle = new Flatten.Vector(this.pc, pt).slope; let test_arc = new Flatten.Arc(this.pc, this.r, this.startAngle, angle, this.counterClockwise); return Flatten.Utils.LE(test_arc.length, this.length); } /** * When given point belongs to arc, return array of two arcs split by this point. If points is incident * to start or end point of the arc, return clone of the arc. If point does not belong to the arcs, return * empty array. * @param {Point} pt Query point * @returns {Arc[]} */ split(pt) { if (this.start.equalTo(pt)) return [null, this.clone()]; if (this.end.equalTo(pt)) return [this.clone(), null]; let angle = new Flatten.Vector(this.pc, pt).slope; return [ new Flatten.Arc(this.pc, this.r, this.startAngle, angle, this.counterClockwise), new Flatten.Arc(this.pc, this.r, angle, this.endAngle, this.counterClockwise) ] } /** * Return middle point of the arc * @returns {Point} */ middle() { let endAngle = this.counterClockwise ? this.startAngle + this.sweep / 2 : this.startAngle - this.sweep / 2; let arc = new Flatten.Arc(this.pc, this.r, this.startAngle, endAngle, this.counterClockwise); return arc.end; } /** * Returns chord height ("sagitta") of the arc * @returns {number} */ chordHeight() { return (1.0 - Math.cos(Math.abs(this.sweep / 2.0))) * this.r; } /** * Returns array of intersection points between arc and other shape * @param {Shape} shape Shape of the one of supported types * @returns {Points[]} */ intersect(shape) { if (shape instanceof Flatten.Point) { return this.contains(shape) ? [shape] : []; } if (shape instanceof Flatten.Line) { return Intersection.intersectLine2Arc(shape, this); } if (shape instanceof Flatten.Circle) { return Intersection.intersectArc2Circle(this, shape); } if (shape instanceof Flatten.Segment) { return Intersection.intersectSegment2Arc(shape, this); } if (shape instanceof Flatten.Box) { return Intersection.intersectArc2Box(this, shape); } if (shape instanceof Flatten.Arc) { return Intersection.intersectArc2Arc(this, shape); } if (shape instanceof Flatten.Polygon) { return Intersection.intersectArc2Polygon(this, shape); } } /** * Calculate distance and shortest segment from arc to shape and return array [distance, shortest segment] * @param {Shape} shape Shape of the one of supported types Point, Line, Circle, Segment, Arc, Polygon or Planar Set * @returns {number} distance from arc to shape * @returns {Segment} shortest segment between arc and shape (started at arc, ended at shape) */ distanceTo(shape) { if (shape instanceof Flatten.Point) { let [dist, shortest_segment] = Flatten.Distance.point2arc(shape, this); shortest_segment = shortest_segment.reverse(); return [dist, shortest_segment]; } if (shape instanceof Flatten.Circle) { let [dist, shortest_segment] = Flatten.Distance.arc2circle(this, shape); return [dist, shortest_segment]; } if (shape instanceof Flatten.Line) { let [dist, shortest_segment] = Flatten.Distance.arc2line(this, shape); return [dist, shortest_segment]; } if (shape instanceof Flatten.Segment) { let [dist, shortest_segment] = Flatten.Distance.segment2arc(shape, this); shortest_segment = shortest_segment.reverse(); return [dist, shortest_segment]; } if (shape instanceof Flatten.Arc) { let [dist, shortest_segment] = Flatten.Distance.arc2arc(this, shape); return [dist, shortest_segment]; } if (shape instanceof Flatten.Polygon) { let [dist, shortest_segment] = Flatten.Distance.shape2polygon(this, shape); return [dist, shortest_segment]; } if (shape instanceof Flatten.PlanarSet) { let [dist, shortest_segment] = Flatten.Distance.shape2planarSet(this, shape); return [dist, shortest_segment]; } } /** * Breaks arc in extreme point 0, pi/2, pi, 3*pi/2 and returns array of sub-arcs * @returns {Arcs[]} */ breakToFunctional() { let func_arcs_array = []; let angles = [0, Math.PI / 2, 2 * Math.PI / 2, 3 * Math.PI / 2]; let pts = [ this.pc.translate(this.r, 0), this.pc.translate(0, this.r), this.pc.translate(-this.r, 0), this.pc.translate(0, -this.r) ]; // If arc contains extreme point, // create test arc started at start point and ended at this extreme point let test_arcs = []; for (let i = 0; i < 4; i++) { if (pts[i].on(this)) { test_arcs.push(new Flatten.Arc(this.pc, this.r, this.startAngle, angles[i], this.counterClockwise)); } } if (test_arcs.length == 0) { // arc does contain any extreme point func_arcs_array.push(this.clone()); } else { // arc passes extreme point // sort these arcs by length test_arcs.sort((arc1, arc2) => arc1.length - arc2.length); for (let i = 0; i < test_arcs.length; i++) { let prev_arc = func_arcs_array.length > 0 ? func_arcs_array[func_arcs_array.length - 1] : undefined; let new_arc; if (prev_arc) { new_arc = new Flatten.Arc(this.pc, this.r, prev_arc.endAngle, test_arcs[i].endAngle, this.counterClockwise); } else { new_arc = new Flatten.Arc(this.pc, this.r, this.startAngle, test_arcs[i].endAngle, this.counterClockwise); } if (!Flatten.Utils.EQ_0(new_arc.length)) { func_arcs_array.push(new_arc.clone()); } } // add last sub arc let prev_arc = func_arcs_array.length > 0 ? func_arcs_array[func_arcs_array.length - 1] : undefined; let new_arc; if (prev_arc) { new_arc = new Flatten.Arc(this.pc, this.r, prev_arc.endAngle, this.endAngle, this.counterClockwise); } else { new_arc = new Flatten.Arc(this.pc, this.r, this.startAngle, this.endAngle, this.counterClockwise); } // It could be 2*PI when occasionally start = 0 and end = 2*PI but this is not valid for breakToFunctional if (!Flatten.Utils.EQ_0(new_arc.length) && !Flatten.Utils.EQ(new_arc.sweep, 2*Math.PI)) { func_arcs_array.push(new_arc.clone()); } } return func_arcs_array; } /** * Return tangent unit vector in the start point in the direction from start to end * @returns {Vector} */ tangentInStart() { let vec = new Flatten.Vector(this.pc, this.start); let angle = this.counterClockwise ? Math.PI / 2. : -Math.PI / 2.; let tangent = vec.rotate(angle).normalize(); return tangent; } /** * Return tangent unit vector in the end point in the direction from end to start * @returns {Vector} */ tangentInEnd() { let vec = new Flatten.Vector(this.pc, this.end); let angle = this.counterClockwise ? -Math.PI / 2. : Math.PI / 2.; let tangent = vec.rotate(angle).normalize(); return tangent; } /** * Returns new arc with swapped start and end angles and reversed direction * @returns {Arc} */ reverse() { return new Flatten.Arc(this.pc, this.r, this.endAngle, this.startAngle, !this.counterClockwise); } /** * Returns new arc translated by vector vec * @param {Vector} vec * @returns {Segment} */ translate(...args) { let arc = this.clone(); arc.pc = this.pc.translate(...args); return arc; } /** * Return new segment rotated by given angle around given point * If point omitted, rotate around origin (0,0) * Positive value of angle defines rotation counter clockwise, negative - clockwise * @param {number} angle - rotation angle in radians * @param {Point} center - center point, default is (0,0) * @returns {Arc} */ rotate(angle = 0, center = new Flatten.Point()) { let m = new Flatten.Matrix(); m = m.translate(center.x, center.y).rotate(angle).translate(-center.x, -center.y); return this.transform(m); } /**