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604 lines
20 KiB
JavaScript
604 lines
20 KiB
JavaScript
!function(e){if("object"==typeof exports&&"undefined"!=typeof module)module.exports=e();else if("function"==typeof define&&define.amd)define([],e);else{var f;"undefined"!=typeof window?f=window:"undefined"!=typeof global?f=global:"undefined"!=typeof self&&(f=self),f.decomp=e()}}(function(){var define,module,exports;return (function e(t,n,r){function s(o,u){if(!n[o]){if(!t[o]){var a=typeof require=="function"&&require;if(!u&&a)return a(o,!0);if(i)return i(o,!0);throw new Error("Cannot find module '"+o+"'")}var f=n[o]={exports:{}};t[o][0].call(f.exports,function(e){var n=t[o][1][e];return s(n?n:e)},f,f.exports,e,t,n,r)}return n[o].exports}var i=typeof require=="function"&&require;for(var o=0;o<r.length;o++)s(r[o]);return s})({1:[function(_dereq_,module,exports){
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module.exports = {
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decomp: polygonDecomp,
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quickDecomp: polygonQuickDecomp,
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isSimple: polygonIsSimple,
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removeCollinearPoints: polygonRemoveCollinearPoints,
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makeCCW: polygonMakeCCW
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};
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/**
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* Compute the intersection between two lines.
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* @static
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* @method lineInt
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* @param {Array} l1 Line vector 1
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* @param {Array} l2 Line vector 2
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* @param {Number} precision Precision to use when checking if the lines are parallel
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* @return {Array} The intersection point.
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*/
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function lineInt(l1,l2,precision){
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precision = precision || 0;
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var i = [0,0]; // point
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var a1, b1, c1, a2, b2, c2, det; // scalars
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a1 = l1[1][1] - l1[0][1];
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b1 = l1[0][0] - l1[1][0];
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c1 = a1 * l1[0][0] + b1 * l1[0][1];
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a2 = l2[1][1] - l2[0][1];
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b2 = l2[0][0] - l2[1][0];
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c2 = a2 * l2[0][0] + b2 * l2[0][1];
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det = a1 * b2 - a2*b1;
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if (!scalar_eq(det, 0, precision)) { // lines are not parallel
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i[0] = (b2 * c1 - b1 * c2) / det;
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i[1] = (a1 * c2 - a2 * c1) / det;
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}
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return i;
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}
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/**
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* Checks if two line segments intersects.
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* @method segmentsIntersect
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* @param {Array} p1 The start vertex of the first line segment.
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* @param {Array} p2 The end vertex of the first line segment.
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* @param {Array} q1 The start vertex of the second line segment.
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* @param {Array} q2 The end vertex of the second line segment.
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* @return {Boolean} True if the two line segments intersect
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*/
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function lineSegmentsIntersect(p1, p2, q1, q2){
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var dx = p2[0] - p1[0];
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var dy = p2[1] - p1[1];
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var da = q2[0] - q1[0];
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var db = q2[1] - q1[1];
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// segments are parallel
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if((da*dy - db*dx) === 0){
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return false;
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}
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var s = (dx * (q1[1] - p1[1]) + dy * (p1[0] - q1[0])) / (da * dy - db * dx);
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var t = (da * (p1[1] - q1[1]) + db * (q1[0] - p1[0])) / (db * dx - da * dy);
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return (s>=0 && s<=1 && t>=0 && t<=1);
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}
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/**
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* Get the area of a triangle spanned by the three given points. Note that the area will be negative if the points are not given in counter-clockwise order.
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* @static
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* @method area
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* @param {Array} a
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* @param {Array} b
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* @param {Array} c
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* @return {Number}
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*/
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function triangleArea(a,b,c){
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return (((b[0] - a[0])*(c[1] - a[1]))-((c[0] - a[0])*(b[1] - a[1])));
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}
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function isLeft(a,b,c){
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return triangleArea(a,b,c) > 0;
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}
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function isLeftOn(a,b,c) {
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return triangleArea(a, b, c) >= 0;
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}
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function isRight(a,b,c) {
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return triangleArea(a, b, c) < 0;
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}
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function isRightOn(a,b,c) {
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return triangleArea(a, b, c) <= 0;
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}
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var tmpPoint1 = [],
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tmpPoint2 = [];
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/**
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* Check if three points are collinear
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* @method collinear
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* @param {Array} a
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* @param {Array} b
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* @param {Array} c
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* @param {Number} [thresholdAngle=0] Threshold angle to use when comparing the vectors. The function will return true if the angle between the resulting vectors is less than this value. Use zero for max precision.
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* @return {Boolean}
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*/
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function collinear(a,b,c,thresholdAngle) {
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if(!thresholdAngle){
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return triangleArea(a, b, c) === 0;
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} else {
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var ab = tmpPoint1,
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bc = tmpPoint2;
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ab[0] = b[0]-a[0];
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ab[1] = b[1]-a[1];
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bc[0] = c[0]-b[0];
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bc[1] = c[1]-b[1];
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var dot = ab[0]*bc[0] + ab[1]*bc[1],
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magA = Math.sqrt(ab[0]*ab[0] + ab[1]*ab[1]),
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magB = Math.sqrt(bc[0]*bc[0] + bc[1]*bc[1]),
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angle = Math.acos(dot/(magA*magB));
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return angle < thresholdAngle;
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}
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}
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function sqdist(a,b){
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var dx = b[0] - a[0];
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var dy = b[1] - a[1];
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return dx * dx + dy * dy;
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}
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/**
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* Get a vertex at position i. It does not matter if i is out of bounds, this function will just cycle.
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* @method at
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* @param {Number} i
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* @return {Array}
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*/
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function polygonAt(polygon, i){
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var s = polygon.length;
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return polygon[i < 0 ? i % s + s : i % s];
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}
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/**
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* Clear the polygon data
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* @method clear
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* @return {Array}
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*/
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function polygonClear(polygon){
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polygon.length = 0;
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}
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/**
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* Append points "from" to "to"-1 from an other polygon "poly" onto this one.
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* @method append
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* @param {Polygon} poly The polygon to get points from.
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* @param {Number} from The vertex index in "poly".
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* @param {Number} to The end vertex index in "poly". Note that this vertex is NOT included when appending.
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* @return {Array}
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*/
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function polygonAppend(polygon, poly, from, to){
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for(var i=from; i<to; i++){
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polygon.push(poly[i]);
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}
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}
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/**
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* Make sure that the polygon vertices are ordered counter-clockwise.
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* @method makeCCW
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*/
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function polygonMakeCCW(polygon){
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var br = 0,
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v = polygon;
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// find bottom right point
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for (var i = 1; i < polygon.length; ++i) {
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if (v[i][1] < v[br][1] || (v[i][1] === v[br][1] && v[i][0] > v[br][0])) {
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br = i;
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}
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}
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// reverse poly if clockwise
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if (!isLeft(polygonAt(polygon, br - 1), polygonAt(polygon, br), polygonAt(polygon, br + 1))) {
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polygonReverse(polygon);
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}
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}
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/**
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* Reverse the vertices in the polygon
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* @method reverse
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*/
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function polygonReverse(polygon){
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var tmp = [];
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var N = polygon.length;
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for(var i=0; i!==N; i++){
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tmp.push(polygon.pop());
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}
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for(var i=0; i!==N; i++){
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polygon[i] = tmp[i];
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}
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}
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/**
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* Check if a point in the polygon is a reflex point
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* @method isReflex
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* @param {Number} i
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* @return {Boolean}
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*/
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function polygonIsReflex(polygon, i){
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return isRight(polygonAt(polygon, i - 1), polygonAt(polygon, i), polygonAt(polygon, i + 1));
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}
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var tmpLine1=[],
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tmpLine2=[];
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/**
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* Check if two vertices in the polygon can see each other
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* @method canSee
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* @param {Number} a Vertex index 1
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* @param {Number} b Vertex index 2
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* @return {Boolean}
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*/
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function polygonCanSee(polygon, a,b) {
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var p, dist, l1=tmpLine1, l2=tmpLine2;
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if (isLeftOn(polygonAt(polygon, a + 1), polygonAt(polygon, a), polygonAt(polygon, b)) && isRightOn(polygonAt(polygon, a - 1), polygonAt(polygon, a), polygonAt(polygon, b))) {
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return false;
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}
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dist = sqdist(polygonAt(polygon, a), polygonAt(polygon, b));
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for (var i = 0; i !== polygon.length; ++i) { // for each edge
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if ((i + 1) % polygon.length === a || i === a){ // ignore incident edges
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continue;
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}
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if (isLeftOn(polygonAt(polygon, a), polygonAt(polygon, b), polygonAt(polygon, i + 1)) && isRightOn(polygonAt(polygon, a), polygonAt(polygon, b), polygonAt(polygon, i))) { // if diag intersects an edge
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l1[0] = polygonAt(polygon, a);
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l1[1] = polygonAt(polygon, b);
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l2[0] = polygonAt(polygon, i);
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l2[1] = polygonAt(polygon, i + 1);
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p = lineInt(l1,l2);
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if (sqdist(polygonAt(polygon, a), p) < dist) { // if edge is blocking visibility to b
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return false;
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}
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}
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}
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return true;
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}
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/**
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* Copy the polygon from vertex i to vertex j.
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* @method copy
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* @param {Number} i
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* @param {Number} j
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* @param {Polygon} [targetPoly] Optional target polygon to save in.
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* @return {Polygon} The resulting copy.
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*/
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function polygonCopy(polygon, i,j,targetPoly){
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var p = targetPoly || [];
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polygonClear(p);
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if (i < j) {
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// Insert all vertices from i to j
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for(var k=i; k<=j; k++){
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p.push(polygon[k]);
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}
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} else {
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// Insert vertices 0 to j
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for(var k=0; k<=j; k++){
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p.push(polygon[k]);
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}
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// Insert vertices i to end
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for(var k=i; k<polygon.length; k++){
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p.push(polygon[k]);
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}
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}
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return p;
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}
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/**
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* Decomposes the polygon into convex pieces. Returns a list of edges [[p1,p2],[p2,p3],...] that cuts the polygon.
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* Note that this algorithm has complexity O(N^4) and will be very slow for polygons with many vertices.
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* @method getCutEdges
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* @return {Array}
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*/
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function polygonGetCutEdges(polygon) {
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var min=[], tmp1=[], tmp2=[], tmpPoly = [];
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var nDiags = Number.MAX_VALUE;
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for (var i = 0; i < polygon.length; ++i) {
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if (polygonIsReflex(polygon, i)) {
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for (var j = 0; j < polygon.length; ++j) {
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if (polygonCanSee(polygon, i, j)) {
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tmp1 = polygonGetCutEdges(polygonCopy(polygon, i, j, tmpPoly));
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tmp2 = polygonGetCutEdges(polygonCopy(polygon, j, i, tmpPoly));
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for(var k=0; k<tmp2.length; k++){
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tmp1.push(tmp2[k]);
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}
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if (tmp1.length < nDiags) {
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min = tmp1;
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nDiags = tmp1.length;
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min.push([polygonAt(polygon, i), polygonAt(polygon, j)]);
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}
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}
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}
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}
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}
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return min;
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}
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/**
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* Decomposes the polygon into one or more convex sub-Polygons.
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* @method decomp
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* @return {Array} An array or Polygon objects.
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*/
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function polygonDecomp(polygon){
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var edges = polygonGetCutEdges(polygon);
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if(edges.length > 0){
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return polygonSlice(polygon, edges);
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} else {
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return [polygon];
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}
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}
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/**
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* Slices the polygon given one or more cut edges. If given one, this function will return two polygons (false on failure). If many, an array of polygons.
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* @method slice
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* @param {Array} cutEdges A list of edges, as returned by .getCutEdges()
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* @return {Array}
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*/
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function polygonSlice(polygon, cutEdges){
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if(cutEdges.length === 0){
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return [polygon];
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}
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if(cutEdges instanceof Array && cutEdges.length && cutEdges[0] instanceof Array && cutEdges[0].length===2 && cutEdges[0][0] instanceof Array){
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var polys = [polygon];
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for(var i=0; i<cutEdges.length; i++){
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var cutEdge = cutEdges[i];
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// Cut all polys
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for(var j=0; j<polys.length; j++){
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var poly = polys[j];
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var result = polygonSlice(poly, cutEdge);
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if(result){
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// Found poly! Cut and quit
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polys.splice(j,1);
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polys.push(result[0],result[1]);
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break;
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}
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}
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}
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return polys;
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} else {
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// Was given one edge
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var cutEdge = cutEdges;
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var i = polygon.indexOf(cutEdge[0]);
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var j = polygon.indexOf(cutEdge[1]);
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if(i !== -1 && j !== -1){
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return [polygonCopy(polygon, i,j),
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polygonCopy(polygon, j,i)];
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} else {
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return false;
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}
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}
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}
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/**
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* Checks that the line segments of this polygon do not intersect each other.
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* @method isSimple
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* @param {Array} path An array of vertices e.g. [[0,0],[0,1],...]
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* @return {Boolean}
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* @todo Should it check all segments with all others?
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*/
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function polygonIsSimple(polygon){
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var path = polygon, i;
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// Check
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for(i=0; i<path.length-1; i++){
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for(var j=0; j<i-1; j++){
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if(lineSegmentsIntersect(path[i], path[i+1], path[j], path[j+1] )){
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return false;
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}
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}
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}
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// Check the segment between the last and the first point to all others
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for(i=1; i<path.length-2; i++){
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if(lineSegmentsIntersect(path[0], path[path.length-1], path[i], path[i+1] )){
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return false;
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}
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}
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return true;
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}
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function getIntersectionPoint(p1, p2, q1, q2, delta){
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delta = delta || 0;
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var a1 = p2[1] - p1[1];
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var b1 = p1[0] - p2[0];
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var c1 = (a1 * p1[0]) + (b1 * p1[1]);
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var a2 = q2[1] - q1[1];
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var b2 = q1[0] - q2[0];
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var c2 = (a2 * q1[0]) + (b2 * q1[1]);
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var det = (a1 * b2) - (a2 * b1);
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if(!scalar_eq(det,0,delta)){
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return [((b2 * c1) - (b1 * c2)) / det, ((a1 * c2) - (a2 * c1)) / det];
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} else {
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return [0,0];
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}
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}
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/**
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* Quickly decompose the Polygon into convex sub-polygons.
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* @method quickDecomp
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* @param {Array} result
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* @param {Array} [reflexVertices]
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* @param {Array} [steinerPoints]
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* @param {Number} [delta]
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* @param {Number} [maxlevel]
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* @param {Number} [level]
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* @return {Array}
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*/
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function polygonQuickDecomp(polygon, result,reflexVertices,steinerPoints,delta,maxlevel,level){
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maxlevel = maxlevel || 100;
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level = level || 0;
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delta = delta || 25;
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result = typeof(result)!=="undefined" ? result : [];
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reflexVertices = reflexVertices || [];
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steinerPoints = steinerPoints || [];
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var upperInt=[0,0], lowerInt=[0,0], p=[0,0]; // Points
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var upperDist=0, lowerDist=0, d=0, closestDist=0; // scalars
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var upperIndex=0, lowerIndex=0, closestIndex=0; // Integers
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var lowerPoly=[], upperPoly=[]; // polygons
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var poly = polygon,
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v = polygon;
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if(v.length < 3){
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return result;
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}
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level++;
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if(level > maxlevel){
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console.warn("quickDecomp: max level ("+maxlevel+") reached.");
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return result;
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}
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for (var i = 0; i < polygon.length; ++i) {
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if (polygonIsReflex(poly, i)) {
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reflexVertices.push(poly[i]);
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upperDist = lowerDist = Number.MAX_VALUE;
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for (var j = 0; j < polygon.length; ++j) {
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if (isLeft(polygonAt(poly, i - 1), polygonAt(poly, i), polygonAt(poly, j)) && isRightOn(polygonAt(poly, i - 1), polygonAt(poly, i), polygonAt(poly, j - 1))) { // if line intersects with an edge
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p = getIntersectionPoint(polygonAt(poly, i - 1), polygonAt(poly, i), polygonAt(poly, j), polygonAt(poly, j - 1)); // find the point of intersection
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if (isRight(polygonAt(poly, i + 1), polygonAt(poly, i), p)) { // make sure it's inside the poly
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d = sqdist(poly[i], p);
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if (d < lowerDist) { // keep only the closest intersection
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lowerDist = d;
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lowerInt = p;
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lowerIndex = j;
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}
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}
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}
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if (isLeft(polygonAt(poly, i + 1), polygonAt(poly, i), polygonAt(poly, j + 1)) && isRightOn(polygonAt(poly, i + 1), polygonAt(poly, i), polygonAt(poly, j))) {
|
|
p = getIntersectionPoint(polygonAt(poly, i + 1), polygonAt(poly, i), polygonAt(poly, j), polygonAt(poly, j + 1));
|
|
if (isLeft(polygonAt(poly, i - 1), polygonAt(poly, i), p)) {
|
|
d = sqdist(poly[i], p);
|
|
if (d < upperDist) {
|
|
upperDist = d;
|
|
upperInt = p;
|
|
upperIndex = j;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
// if there are no vertices to connect to, choose a point in the middle
|
|
if (lowerIndex === (upperIndex + 1) % polygon.length) {
|
|
//console.log("Case 1: Vertex("+i+"), lowerIndex("+lowerIndex+"), upperIndex("+upperIndex+"), poly.size("+polygon.length+")");
|
|
p[0] = (lowerInt[0] + upperInt[0]) / 2;
|
|
p[1] = (lowerInt[1] + upperInt[1]) / 2;
|
|
steinerPoints.push(p);
|
|
|
|
if (i < upperIndex) {
|
|
//lowerPoly.insert(lowerPoly.end(), poly.begin() + i, poly.begin() + upperIndex + 1);
|
|
polygonAppend(lowerPoly, poly, i, upperIndex+1);
|
|
lowerPoly.push(p);
|
|
upperPoly.push(p);
|
|
if (lowerIndex !== 0){
|
|
//upperPoly.insert(upperPoly.end(), poly.begin() + lowerIndex, poly.end());
|
|
polygonAppend(upperPoly, poly,lowerIndex,poly.length);
|
|
}
|
|
//upperPoly.insert(upperPoly.end(), poly.begin(), poly.begin() + i + 1);
|
|
polygonAppend(upperPoly, poly,0,i+1);
|
|
} else {
|
|
if (i !== 0){
|
|
//lowerPoly.insert(lowerPoly.end(), poly.begin() + i, poly.end());
|
|
polygonAppend(lowerPoly, poly,i,poly.length);
|
|
}
|
|
//lowerPoly.insert(lowerPoly.end(), poly.begin(), poly.begin() + upperIndex + 1);
|
|
polygonAppend(lowerPoly, poly,0,upperIndex+1);
|
|
lowerPoly.push(p);
|
|
upperPoly.push(p);
|
|
//upperPoly.insert(upperPoly.end(), poly.begin() + lowerIndex, poly.begin() + i + 1);
|
|
polygonAppend(upperPoly, poly,lowerIndex,i+1);
|
|
}
|
|
} else {
|
|
// connect to the closest point within the triangle
|
|
//console.log("Case 2: Vertex("+i+"), closestIndex("+closestIndex+"), poly.size("+polygon.length+")\n");
|
|
|
|
if (lowerIndex > upperIndex) {
|
|
upperIndex += polygon.length;
|
|
}
|
|
closestDist = Number.MAX_VALUE;
|
|
|
|
if(upperIndex < lowerIndex){
|
|
return result;
|
|
}
|
|
|
|
for (var j = lowerIndex; j <= upperIndex; ++j) {
|
|
if (isLeftOn(polygonAt(poly, i - 1), polygonAt(poly, i), polygonAt(poly, j)) && isRightOn(polygonAt(poly, i + 1), polygonAt(poly, i), polygonAt(poly, j))) {
|
|
d = sqdist(polygonAt(poly, i), polygonAt(poly, j));
|
|
if (d < closestDist) {
|
|
closestDist = d;
|
|
closestIndex = j % polygon.length;
|
|
}
|
|
}
|
|
}
|
|
|
|
if (i < closestIndex) {
|
|
polygonAppend(lowerPoly, poly,i,closestIndex+1);
|
|
if (closestIndex !== 0){
|
|
polygonAppend(upperPoly, poly,closestIndex,v.length);
|
|
}
|
|
polygonAppend(upperPoly, poly,0,i+1);
|
|
} else {
|
|
if (i !== 0){
|
|
polygonAppend(lowerPoly, poly,i,v.length);
|
|
}
|
|
polygonAppend(lowerPoly, poly,0,closestIndex+1);
|
|
polygonAppend(upperPoly, poly,closestIndex,i+1);
|
|
}
|
|
}
|
|
|
|
// solve smallest poly first
|
|
if (lowerPoly.length < upperPoly.length) {
|
|
polygonQuickDecomp(lowerPoly,result,reflexVertices,steinerPoints,delta,maxlevel,level);
|
|
polygonQuickDecomp(upperPoly,result,reflexVertices,steinerPoints,delta,maxlevel,level);
|
|
} else {
|
|
polygonQuickDecomp(upperPoly,result,reflexVertices,steinerPoints,delta,maxlevel,level);
|
|
polygonQuickDecomp(lowerPoly,result,reflexVertices,steinerPoints,delta,maxlevel,level);
|
|
}
|
|
|
|
return result;
|
|
}
|
|
}
|
|
result.push(polygon);
|
|
|
|
return result;
|
|
}
|
|
|
|
/**
|
|
* Remove collinear points in the polygon.
|
|
* @method removeCollinearPoints
|
|
* @param {Number} [precision] The threshold angle to use when determining whether two edges are collinear. Use zero for finest precision.
|
|
* @return {Number} The number of points removed
|
|
*/
|
|
function polygonRemoveCollinearPoints(polygon, precision){
|
|
var num = 0;
|
|
for(var i=polygon.length-1; polygon.length>3 && i>=0; --i){
|
|
if(collinear(polygonAt(polygon, i-1),polygonAt(polygon, i),polygonAt(polygon, i+1),precision)){
|
|
// Remove the middle point
|
|
polygon.splice(i%polygon.length,1);
|
|
num++;
|
|
}
|
|
}
|
|
return num;
|
|
}
|
|
|
|
/**
|
|
* Check if two scalars are equal
|
|
* @static
|
|
* @method eq
|
|
* @param {Number} a
|
|
* @param {Number} b
|
|
* @param {Number} [precision]
|
|
* @return {Boolean}
|
|
*/
|
|
function scalar_eq(a,b,precision){
|
|
precision = precision || 0;
|
|
return Math.abs(a-b) < precision;
|
|
}
|
|
|
|
},{}]},{},[1])
|
|
(1)
|
|
});
|