351 lines
14 KiB
JavaScript
351 lines
14 KiB
JavaScript
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// Copyright (c) 2011, Chris Umbel, James Coglan
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// Polygon class - depends on Vector, Plane, Polygon.Vertex and LinkedList.
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var Sylvester = require('./sylvester');
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function Polygon() {}
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Polygon.prototype = {
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// Returns the vertex at the given position on the vertex list, numbered from 1.
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v: function(i) {
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return this.vertices.at(i - 1).data;
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},
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// Returns the node in the vertices linked list that refers to the given vertex.
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nodeFor: function(vertex) {
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return this.vertices.withData(vertex);
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},
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// Returns a new polygon with the same vertices as the receiver. The vertices
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// will not be duplicates, they refer to the same objects as the vertices in this
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// polygon, but the linked list and nodes used to point to them are separate and
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// can be manipulated independently of this one.
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dup: function() {
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return Polygon.create(this.vertices, this.plane);
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},
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// Translates the polygon by the given vector and returns the polygon.
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translate: function(vector) {
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var P = vector.elements || vector;
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this.vertices.each(function(node) {
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var E = node.data.elements;
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node.data.setElements([E[0] + P[0], E[1] + P[1], E[2] + (P[2] || 0)]);
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});
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this.plane = this.plane.translate(vector);
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this.updateTrianglePlanes(function(plane) { return plane.translate(vector); });
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return this;
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},
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// Rotates the polygon about the given line and returns the polygon.
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rotate: function(t, line) {
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var R = Matrix.Rotation(t, line.direction);
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this.vertices.each(function(node) {
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node.data.setElements(node.data.rotate(R, line).elements);
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});
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this.plane = this.plane.rotate(R, line);
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this.updateTrianglePlanes(function(plane) { return plane.rotate(R, line); });
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return this;
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},
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// Scales the polygon relative to the given point and returns the polygon.
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scale: function(k, point) {
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var P = point.elements || point;
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this.vertices.each(function(node) {
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var E = node.data.elements;
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node.data.setElements([
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P[0] + k * (E[0] - P[0]),
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P[1] + k * (E[1] - P[1]),
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(P[2] || 0) + k * (E[2] - (P[2] || 0))
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]);
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});
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var anchor = this.vertices.first.data;
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this.plane.anchor.setElements(anchor);
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this.updateTrianglePlanes(function(plane) { return Plane.create(anchor, plane.normal); });
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return this;
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},
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// Updates the plane properties of all the cached triangles belonging to
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// the polygon according to the given function. For example, suppose you
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// just rotated the polygon, you should call:
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//
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// poly.updateTrianglePlanes(function(plane) { return plane.rotate(t, line); });
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//
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// This method is called automatically by Polygon.translate, Polygon.rotate
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// and Polygon.scale transformation methods.
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updateTrianglePlanes: function(fn) {
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var i;
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if (this.cached.triangles !== null) {
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i = this.cached.triangles.length;
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while (i--) {
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this.cached.triangles[i].plane = fn(this.cached.triangles[i].plane);
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}
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}
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if (this.cached.surfaceIntegralElements !== null) {
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i = this.cached.surfaceIntegralElements.length;
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while (i--) {
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this.cached.surfaceIntegralElements[i].plane = fn(this.cached.surfaceIntegralElements[i].plane);
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}
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}
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},
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// Returns true iff the polygon is a triangle
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isTriangle: function() {
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return this.vertices.length == 3;
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},
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// Returns a collection of triangles used for calculating area and center of mass.
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// Some of the triangles will not lie inside the polygon - this collection is essentially
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// a series of itervals in a surface integral, so some are 'negative'. If you want the
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// polygon broken into constituent triangles, use toTriangles(). This method is used
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// because it's much faster than toTriangles().
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// The triangles generated share vertices with the original polygon, so they transform
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// with the polygon. They are cached after first calculation and should remain in sync
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// with changes to the parent polygon.
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trianglesForSurfaceIntegral: function() {
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if (this.cached.surfaceIntegralElements !== null) { return this.cached.surfaceIntegralElements; }
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var triangles = [];
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var firstVertex = this.vertices.first.data;
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var plane = this.plane;
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this.vertices.each(function(node, i) {
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if (i < 2) { return; }
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var points = [firstVertex, node.prev.data, node.data];
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// If the vertices lie on a straigh line, give the polygon's own plane. If the
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// element has no area, it doesn't matter which way its normal faces.
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triangles.push(Polygon.create(points, Plane.fromPoints(points) || plane));
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});
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return this.setCache('surfaceIntegralElements', triangles);
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},
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// Returns the area of the polygon. Requires that the polygon
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// be converted to triangles, so use with caution.
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area: function() {
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if (this.isTriangle()) {
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// Area is half the modulus of the cross product of two sides
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var A = this.vertices.first, B = A.next, C = B.next;
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A = A.data.elements; B = B.data.elements; C = C.data.elements;
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return 0.5 * Vector.create([
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(A[1] - B[1]) * (C[2] - B[2]) - (A[2] - B[2]) * (C[1] - B[1]),
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(A[2] - B[2]) * (C[0] - B[0]) - (A[0] - B[0]) * (C[2] - B[2]),
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(A[0] - B[0]) * (C[1] - B[1]) - (A[1] - B[1]) * (C[0] - B[0])
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]).modulus();
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} else {
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var trigs = this.trianglesForSurfaceIntegral(), area = 0;
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var i = trigs.length;
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while (i--) {
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area += trigs[i].area() * trigs[i].plane.normal.dot(this.plane.normal);
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}
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return area;
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}
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},
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// Returns the centroid of the polygon. Requires division into
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// triangles - use with caution
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centroid: function() {
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if (this.isTriangle()) {
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var A = this.v(1).elements, B = this.v(2).elements, C = this.v(3).elements;
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return Vector.create([(A[0] + B[0] + C[0])/3, (A[1] + B[1] + C[1])/3, (A[2] + B[2] + C[2])/3]);
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} else {
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var A, M = 0, V = Vector.Zero(3), P, C, trigs = this.trianglesForSurfaceIntegral();
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var i = trigs.length;
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while (i--) {
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A = trigs[i].area() * trigs[i].plane.normal.dot(this.plane.normal);
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M += A;
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P = V.elements;
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C = trigs[i].centroid().elements;
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V.setElements([P[0] + C[0] * A, P[1] + C[1] * A, P[2] + C[2] * A]);
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}
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return V.x(1/M);
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}
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},
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// Returns the polygon's projection on the given plane as another polygon
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projectionOn: function(plane) {
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var points = [];
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this.vertices.each(function(node) { points.push(plane.pointClosestTo(node.data)); });
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return Polygon.create(points);
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},
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// Removes the given vertex from the polygon as long as it's not triangular.
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removeVertex: function(vertex) {
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if (this.isTriangle()) { return; }
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var node = this.nodeFor(vertex);
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if (node === null) { return null; }
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this.clearCache();
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// Previous and next entries in the main vertex list
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var prev = node.prev, next = node.next;
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var prevWasConvex = prev.data.isConvex(this);
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var nextWasConvex = next.data.isConvex(this);
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if (node.data.isConvex(this)) {
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this.convexVertices.remove(this.convexVertices.withData(node.data));
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} else {
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this.reflexVertices.remove(this.reflexVertices.withData(node.data));
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}
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this.vertices.remove(node);
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// Deal with previous vertex's change of class
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if (prevWasConvex != prev.data.isConvex(this)) {
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if (prevWasConvex) {
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this.convexVertices.remove(this.convexVertices.withData(prev.data));
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this.reflexVertices.append(new LinkedList.Node(prev.data));
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} else {
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this.reflexVertices.remove(this.reflexVertices.withData(prev.data));
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this.convexVertices.append(new LinkedList.Node(prev.data));
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}
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}
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// Deal with next vertex's change of class
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if (nextWasConvex != next.data.isConvex(this)) {
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if (nextWasConvex) {
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this.convexVertices.remove(this.convexVertices.withData(next.data));
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this.reflexVertices.append(new LinkedList.Node(next.data));
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} else {
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this.reflexVertices.remove(this.reflexVertices.withData(next.data));
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this.convexVertices.append(new LinkedList.Node(next.data));
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}
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}
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return this;
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},
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// Returns true iff the point is strictly inside the polygon
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contains: function(point) {
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return this.containsByWindingNumber(point);
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},
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// Returns true iff the given point is strictly inside the polygon using the winding number method
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containsByWindingNumber: function(point) {
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var P = point.elements || point;
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if (!this.plane.contains(P)) { return false; }
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if (this.hasEdgeContaining(P)) { return false; }
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var V, W, A, B, theta = 0, dt, loops = 0, self = this;
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this.vertices.each(function(node) {
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V = node.data.elements;
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W = node.next.data.elements;
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A = Vector.create([V[0] - P[0], V[1] - P[1], V[2] - (P[2] || 0)]);
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B = Vector.create([W[0] - P[0], W[1] - P[1], W[2] - (P[2] || 0)]);
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dt = A.angleFrom(B);
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if (dt === null || dt === 0) { return; }
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theta += (A.cross(B).isParallelTo(self.plane.normal) ? 1 : -1) * dt;
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if (theta >= 2 * Math.PI - Sylvester.precision) { loops++; theta -= 2 * Math.PI; }
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if (theta <= -2 * Math.PI + Sylvester.precision) { loops--; theta += 2 * Math.PI; }
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});
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return loops != 0;
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},
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// Returns true if the given point lies on an edge of the polygon
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// May cause problems with 'hole-joining' edges
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hasEdgeContaining: function(point) {
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var P = (point.elements || point);
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var success = false;
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this.vertices.each(function(node) {
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if (Line.Segment.create(node.data, node.next.data).contains(P)) { success = true; }
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});
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return success;
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},
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// Returns an array of 3-vertex polygons that the original has been split into
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// Stores the first calculation for faster retrieval later on
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toTriangles: function() {
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if (this.cached.triangles !== null) { return this.cached.triangles; }
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return this.setCache('triangles', this.triangulateByEarClipping());
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},
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// Implementation of ear clipping algorithm
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// Found in 'Triangulation by ear clipping', by David Eberly
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// at http://www.geometrictools.com
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// This will not deal with overlapping sections - contruct your polygons sensibly
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triangulateByEarClipping: function() {
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var poly = this.dup(), triangles = [], success, convexNode, mainNode, trig;
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while (!poly.isTriangle()) {
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success = false;
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while (!success) {
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success = true;
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// Ear tips must be convex vertices - let's pick one at random
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convexNode = poly.convexVertices.randomNode();
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mainNode = poly.vertices.withData(convexNode.data);
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// For convex vertices, this order will always be anticlockwise
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trig = Polygon.create([mainNode.data, mainNode.next.data, mainNode.prev.data], this.plane);
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// Now test whether any reflex vertices lie within the ear
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poly.reflexVertices.each(function(node) {
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// Don't test points belonging to this triangle. node won't be
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// equal to convexNode as node is reflex and vertex is convex.
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if (node.data != mainNode.prev.data && node.data != mainNode.next.data) {
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if (trig.contains(node.data) || trig.hasEdgeContaining(node.data)) { success = false; }
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}
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});
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}
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triangles.push(trig);
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poly.removeVertex(mainNode.data);
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}
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// Need to do this to renumber the remaining vertices
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triangles.push(Polygon.create(poly.vertices, this.plane));
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return triangles;
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},
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// Sets the polygon's vertices
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setVertices: function(points, plane) {
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var pointSet = points.toArray ? points.toArray() : points;
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this.plane = (plane && plane.normal) ? plane.dup() : Plane.fromPoints(pointSet);
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if (this.plane === null) { return null; }
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this.vertices = new LinkedList.Circular();
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// Construct linked list of vertices. If each point is already a polygon
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// vertex, we reference it rather than creating a new vertex.
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var i = pointSet.length, newVertex;
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while (i--) {
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newVertex = pointSet[i].isConvex ? pointSet[i] : new Polygon.Vertex(pointSet[i]);
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this.vertices.prepend(new LinkedList.Node(newVertex));
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}
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this.clearCache();
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this.populateVertexTypeLists();
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return this;
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},
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// Constructs lists of convex and reflex vertices based on the main vertex list.
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populateVertexTypeLists: function() {
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this.convexVertices = new LinkedList.Circular();
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this.reflexVertices = new LinkedList.Circular();
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var self = this;
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this.vertices.each(function(node) {
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// Split vertices into convex / reflex groups
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// The LinkedList.Node class wraps each vertex so it can belong to many linked lists.
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self[node.data.type(self) + 'Vertices'].append(new LinkedList.Node(node.data));
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});
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},
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// Gives the polygon its own local set of vertex points, allowing it to be
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// transformed independently of polygons it may be sharing vertices with.
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copyVertices: function() {
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this.clearCache();
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this.vertices.each(function(node) {
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node.data = new Polygon.Vertex(node.data);
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});
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this.populateVertexTypeLists();
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},
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// Clear any cached properties
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clearCache: function() {
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this.cached = {
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triangles: null,
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surfaceIntegralElements: null
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};
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},
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// Set cached value and return the value
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setCache: function(key, value) {
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this.cached[key] = value;
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return value;
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},
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// Returns a string representation of the polygon's vertices.
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inspect: function() {
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var points = [];
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this.vertices.each(function(node) { points.push(node.data.inspect()); });
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return points.join(' -> ');
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}
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};
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// Constructor function
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Polygon.create = function(points, plane) {
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var P = new Polygon();
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return P.setVertices(points, plane);
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};
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module.exports = Polygon;
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