StackGenVis: Alignment of Data, Algorithms, and Models for Stacking Ensemble Learning Using Performance Metrics
https://doi.org/10.1109/TVCG.2020.3030352
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685 lines
54 KiB
685 lines
54 KiB
(function(f){if(typeof exports==="object"&&typeof module!=="undefined"){module.exports=f()}else if(typeof define==="function"&&define.amd){define([],f)}else{var g;if(typeof window!=="undefined"){g=window}else if(typeof global!=="undefined"){g=global}else if(typeof self!=="undefined"){g=self}else{g=this}g.earcut = f()}})(function(){var define,module,exports;return (function(){function r(e,n,t){function o(i,f){if(!n[i]){if(!e[i]){var c="function"==typeof require&&require;if(!f&&c)return c(i,!0);if(u)return u(i,!0);var a=new Error("Cannot find module '"+i+"'");throw a.code="MODULE_NOT_FOUND",a}var p=n[i]={exports:{}};e[i][0].call(p.exports,function(r){var n=e[i][1][r];return o(n||r)},p,p.exports,r,e,n,t)}return n[i].exports}for(var u="function"==typeof require&&require,i=0;i<t.length;i++)o(t[i]);return o}return r})()({1:[function(require,module,exports){
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'use strict';
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module.exports = earcut;
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module.exports.default = earcut;
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function earcut(data, holeIndices, dim) {
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dim = dim || 2;
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var hasHoles = holeIndices && holeIndices.length,
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outerLen = hasHoles ? holeIndices[0] * dim : data.length,
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outerNode = linkedList(data, 0, outerLen, dim, true),
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triangles = [];
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if (!outerNode || outerNode.next === outerNode.prev) return triangles;
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var minX, minY, maxX, maxY, x, y, invSize;
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if (hasHoles) outerNode = eliminateHoles(data, holeIndices, outerNode, dim);
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// if the shape is not too simple, we'll use z-order curve hash later; calculate polygon bbox
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if (data.length > 80 * dim) {
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minX = maxX = data[0];
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minY = maxY = data[1];
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for (var i = dim; i < outerLen; i += dim) {
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x = data[i];
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y = data[i + 1];
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if (x < minX) minX = x;
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if (y < minY) minY = y;
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if (x > maxX) maxX = x;
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if (y > maxY) maxY = y;
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}
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// minX, minY and invSize are later used to transform coords into integers for z-order calculation
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invSize = Math.max(maxX - minX, maxY - minY);
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invSize = invSize !== 0 ? 1 / invSize : 0;
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}
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earcutLinked(outerNode, triangles, dim, minX, minY, invSize);
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return triangles;
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}
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// create a circular doubly linked list from polygon points in the specified winding order
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function linkedList(data, start, end, dim, clockwise) {
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var i, last;
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if (clockwise === (signedArea(data, start, end, dim) > 0)) {
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for (i = start; i < end; i += dim) last = insertNode(i, data[i], data[i + 1], last);
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} else {
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for (i = end - dim; i >= start; i -= dim) last = insertNode(i, data[i], data[i + 1], last);
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}
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if (last && equals(last, last.next)) {
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removeNode(last);
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last = last.next;
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}
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return last;
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}
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// eliminate colinear or duplicate points
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function filterPoints(start, end) {
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if (!start) return start;
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if (!end) end = start;
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var p = start,
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again;
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do {
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again = false;
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if (!p.steiner && (equals(p, p.next) || area(p.prev, p, p.next) === 0)) {
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removeNode(p);
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p = end = p.prev;
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if (p === p.next) break;
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again = true;
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} else {
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p = p.next;
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}
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} while (again || p !== end);
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return end;
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}
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// main ear slicing loop which triangulates a polygon (given as a linked list)
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function earcutLinked(ear, triangles, dim, minX, minY, invSize, pass) {
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if (!ear) return;
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// interlink polygon nodes in z-order
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if (!pass && invSize) indexCurve(ear, minX, minY, invSize);
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var stop = ear,
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prev, next;
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// iterate through ears, slicing them one by one
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while (ear.prev !== ear.next) {
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prev = ear.prev;
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next = ear.next;
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if (invSize ? isEarHashed(ear, minX, minY, invSize) : isEar(ear)) {
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// cut off the triangle
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triangles.push(prev.i / dim);
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triangles.push(ear.i / dim);
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triangles.push(next.i / dim);
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removeNode(ear);
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// skipping the next vertex leads to less sliver triangles
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ear = next.next;
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stop = next.next;
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continue;
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}
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ear = next;
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// if we looped through the whole remaining polygon and can't find any more ears
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if (ear === stop) {
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// try filtering points and slicing again
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if (!pass) {
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earcutLinked(filterPoints(ear), triangles, dim, minX, minY, invSize, 1);
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// if this didn't work, try curing all small self-intersections locally
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} else if (pass === 1) {
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ear = cureLocalIntersections(filterPoints(ear), triangles, dim);
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earcutLinked(ear, triangles, dim, minX, minY, invSize, 2);
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// as a last resort, try splitting the remaining polygon into two
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} else if (pass === 2) {
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splitEarcut(ear, triangles, dim, minX, minY, invSize);
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}
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break;
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}
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}
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}
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// check whether a polygon node forms a valid ear with adjacent nodes
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function isEar(ear) {
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var a = ear.prev,
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b = ear,
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c = ear.next;
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if (area(a, b, c) >= 0) return false; // reflex, can't be an ear
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// now make sure we don't have other points inside the potential ear
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var p = ear.next.next;
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while (p !== ear.prev) {
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if (pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, p.x, p.y) &&
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area(p.prev, p, p.next) >= 0) return false;
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p = p.next;
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}
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return true;
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}
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function isEarHashed(ear, minX, minY, invSize) {
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var a = ear.prev,
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b = ear,
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c = ear.next;
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if (area(a, b, c) >= 0) return false; // reflex, can't be an ear
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// triangle bbox; min & max are calculated like this for speed
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var minTX = a.x < b.x ? (a.x < c.x ? a.x : c.x) : (b.x < c.x ? b.x : c.x),
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minTY = a.y < b.y ? (a.y < c.y ? a.y : c.y) : (b.y < c.y ? b.y : c.y),
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maxTX = a.x > b.x ? (a.x > c.x ? a.x : c.x) : (b.x > c.x ? b.x : c.x),
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maxTY = a.y > b.y ? (a.y > c.y ? a.y : c.y) : (b.y > c.y ? b.y : c.y);
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// z-order range for the current triangle bbox;
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var minZ = zOrder(minTX, minTY, minX, minY, invSize),
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maxZ = zOrder(maxTX, maxTY, minX, minY, invSize);
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var p = ear.prevZ,
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n = ear.nextZ;
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// look for points inside the triangle in both directions
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while (p && p.z >= minZ && n && n.z <= maxZ) {
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if (p !== ear.prev && p !== ear.next &&
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pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, p.x, p.y) &&
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area(p.prev, p, p.next) >= 0) return false;
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p = p.prevZ;
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if (n !== ear.prev && n !== ear.next &&
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pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, n.x, n.y) &&
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area(n.prev, n, n.next) >= 0) return false;
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n = n.nextZ;
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}
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// look for remaining points in decreasing z-order
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while (p && p.z >= minZ) {
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if (p !== ear.prev && p !== ear.next &&
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pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, p.x, p.y) &&
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area(p.prev, p, p.next) >= 0) return false;
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p = p.prevZ;
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}
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// look for remaining points in increasing z-order
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while (n && n.z <= maxZ) {
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if (n !== ear.prev && n !== ear.next &&
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pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, n.x, n.y) &&
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area(n.prev, n, n.next) >= 0) return false;
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n = n.nextZ;
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}
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return true;
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}
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// go through all polygon nodes and cure small local self-intersections
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function cureLocalIntersections(start, triangles, dim) {
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var p = start;
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do {
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var a = p.prev,
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b = p.next.next;
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if (!equals(a, b) && intersects(a, p, p.next, b) && locallyInside(a, b) && locallyInside(b, a)) {
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triangles.push(a.i / dim);
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triangles.push(p.i / dim);
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triangles.push(b.i / dim);
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// remove two nodes involved
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removeNode(p);
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removeNode(p.next);
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p = start = b;
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}
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p = p.next;
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} while (p !== start);
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return filterPoints(p);
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}
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// try splitting polygon into two and triangulate them independently
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function splitEarcut(start, triangles, dim, minX, minY, invSize) {
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// look for a valid diagonal that divides the polygon into two
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var a = start;
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do {
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var b = a.next.next;
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while (b !== a.prev) {
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if (a.i !== b.i && isValidDiagonal(a, b)) {
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// split the polygon in two by the diagonal
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var c = splitPolygon(a, b);
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// filter colinear points around the cuts
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a = filterPoints(a, a.next);
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c = filterPoints(c, c.next);
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// run earcut on each half
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earcutLinked(a, triangles, dim, minX, minY, invSize);
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earcutLinked(c, triangles, dim, minX, minY, invSize);
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return;
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}
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b = b.next;
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}
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a = a.next;
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} while (a !== start);
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}
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// link every hole into the outer loop, producing a single-ring polygon without holes
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function eliminateHoles(data, holeIndices, outerNode, dim) {
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var queue = [],
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i, len, start, end, list;
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for (i = 0, len = holeIndices.length; i < len; i++) {
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start = holeIndices[i] * dim;
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end = i < len - 1 ? holeIndices[i + 1] * dim : data.length;
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list = linkedList(data, start, end, dim, false);
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if (list === list.next) list.steiner = true;
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queue.push(getLeftmost(list));
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}
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queue.sort(compareX);
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// process holes from left to right
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for (i = 0; i < queue.length; i++) {
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eliminateHole(queue[i], outerNode);
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outerNode = filterPoints(outerNode, outerNode.next);
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}
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return outerNode;
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}
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function compareX(a, b) {
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return a.x - b.x;
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}
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// find a bridge between vertices that connects hole with an outer ring and and link it
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function eliminateHole(hole, outerNode) {
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outerNode = findHoleBridge(hole, outerNode);
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if (outerNode) {
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var b = splitPolygon(outerNode, hole);
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// filter collinear points around the cuts
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filterPoints(outerNode, outerNode.next);
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filterPoints(b, b.next);
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}
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}
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// David Eberly's algorithm for finding a bridge between hole and outer polygon
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function findHoleBridge(hole, outerNode) {
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var p = outerNode,
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hx = hole.x,
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hy = hole.y,
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qx = -Infinity,
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m;
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// find a segment intersected by a ray from the hole's leftmost point to the left;
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// segment's endpoint with lesser x will be potential connection point
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do {
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if (hy <= p.y && hy >= p.next.y && p.next.y !== p.y) {
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var x = p.x + (hy - p.y) * (p.next.x - p.x) / (p.next.y - p.y);
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if (x <= hx && x > qx) {
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qx = x;
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if (x === hx) {
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if (hy === p.y) return p;
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if (hy === p.next.y) return p.next;
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}
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m = p.x < p.next.x ? p : p.next;
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}
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}
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p = p.next;
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} while (p !== outerNode);
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if (!m) return null;
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if (hx === qx) return m; // hole touches outer segment; pick leftmost endpoint
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// look for points inside the triangle of hole point, segment intersection and endpoint;
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// if there are no points found, we have a valid connection;
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// otherwise choose the point of the minimum angle with the ray as connection point
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var stop = m,
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mx = m.x,
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my = m.y,
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tanMin = Infinity,
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tan;
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p = m;
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do {
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if (hx >= p.x && p.x >= mx && hx !== p.x &&
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pointInTriangle(hy < my ? hx : qx, hy, mx, my, hy < my ? qx : hx, hy, p.x, p.y)) {
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tan = Math.abs(hy - p.y) / (hx - p.x); // tangential
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if (locallyInside(p, hole) &&
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(tan < tanMin || (tan === tanMin && (p.x > m.x || (p.x === m.x && sectorContainsSector(m, p)))))) {
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m = p;
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tanMin = tan;
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}
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}
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p = p.next;
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} while (p !== stop);
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return m;
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}
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// whether sector in vertex m contains sector in vertex p in the same coordinates
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function sectorContainsSector(m, p) {
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return area(m.prev, m, p.prev) < 0 && area(p.next, m, m.next) < 0;
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}
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// interlink polygon nodes in z-order
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function indexCurve(start, minX, minY, invSize) {
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var p = start;
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do {
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if (p.z === null) p.z = zOrder(p.x, p.y, minX, minY, invSize);
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p.prevZ = p.prev;
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p.nextZ = p.next;
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p = p.next;
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} while (p !== start);
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p.prevZ.nextZ = null;
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p.prevZ = null;
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sortLinked(p);
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}
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// Simon Tatham's linked list merge sort algorithm
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// http://www.chiark.greenend.org.uk/~sgtatham/algorithms/listsort.html
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function sortLinked(list) {
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var i, p, q, e, tail, numMerges, pSize, qSize,
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inSize = 1;
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do {
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p = list;
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list = null;
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tail = null;
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numMerges = 0;
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while (p) {
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numMerges++;
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q = p;
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pSize = 0;
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for (i = 0; i < inSize; i++) {
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pSize++;
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q = q.nextZ;
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if (!q) break;
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}
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qSize = inSize;
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while (pSize > 0 || (qSize > 0 && q)) {
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if (pSize !== 0 && (qSize === 0 || !q || p.z <= q.z)) {
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e = p;
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p = p.nextZ;
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pSize--;
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} else {
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e = q;
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q = q.nextZ;
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qSize--;
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}
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if (tail) tail.nextZ = e;
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else list = e;
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e.prevZ = tail;
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tail = e;
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}
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p = q;
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}
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tail.nextZ = null;
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inSize *= 2;
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} while (numMerges > 1);
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return list;
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}
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// z-order of a point given coords and inverse of the longer side of data bbox
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function zOrder(x, y, minX, minY, invSize) {
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// coords are transformed into non-negative 15-bit integer range
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x = 32767 * (x - minX) * invSize;
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y = 32767 * (y - minY) * invSize;
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x = (x | (x << 8)) & 0x00FF00FF;
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x = (x | (x << 4)) & 0x0F0F0F0F;
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x = (x | (x << 2)) & 0x33333333;
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x = (x | (x << 1)) & 0x55555555;
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y = (y | (y << 8)) & 0x00FF00FF;
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y = (y | (y << 4)) & 0x0F0F0F0F;
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y = (y | (y << 2)) & 0x33333333;
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y = (y | (y << 1)) & 0x55555555;
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return x | (y << 1);
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}
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// find the leftmost node of a polygon ring
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function getLeftmost(start) {
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var p = start,
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leftmost = start;
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do {
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if (p.x < leftmost.x || (p.x === leftmost.x && p.y < leftmost.y)) leftmost = p;
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p = p.next;
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} while (p !== start);
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return leftmost;
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}
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// check if a point lies within a convex triangle
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function pointInTriangle(ax, ay, bx, by, cx, cy, px, py) {
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return (cx - px) * (ay - py) - (ax - px) * (cy - py) >= 0 &&
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(ax - px) * (by - py) - (bx - px) * (ay - py) >= 0 &&
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(bx - px) * (cy - py) - (cx - px) * (by - py) >= 0;
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}
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// check if a diagonal between two polygon nodes is valid (lies in polygon interior)
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function isValidDiagonal(a, b) {
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return a.next.i !== b.i && a.prev.i !== b.i && !intersectsPolygon(a, b) && // dones't intersect other edges
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(locallyInside(a, b) && locallyInside(b, a) && middleInside(a, b) && // locally visible
|
|
(area(a.prev, a, b.prev) || area(a, b.prev, b)) || // does not create opposite-facing sectors
|
|
equals(a, b) && area(a.prev, a, a.next) > 0 && area(b.prev, b, b.next) > 0); // special zero-length case
|
|
}
|
|
|
|
// signed area of a triangle
|
|
function area(p, q, r) {
|
|
return (q.y - p.y) * (r.x - q.x) - (q.x - p.x) * (r.y - q.y);
|
|
}
|
|
|
|
// check if two points are equal
|
|
function equals(p1, p2) {
|
|
return p1.x === p2.x && p1.y === p2.y;
|
|
}
|
|
|
|
// check if two segments intersect
|
|
function intersects(p1, q1, p2, q2) {
|
|
var o1 = sign(area(p1, q1, p2));
|
|
var o2 = sign(area(p1, q1, q2));
|
|
var o3 = sign(area(p2, q2, p1));
|
|
var o4 = sign(area(p2, q2, q1));
|
|
|
|
if (o1 !== o2 && o3 !== o4) return true; // general case
|
|
|
|
if (o1 === 0 && onSegment(p1, p2, q1)) return true; // p1, q1 and p2 are collinear and p2 lies on p1q1
|
|
if (o2 === 0 && onSegment(p1, q2, q1)) return true; // p1, q1 and q2 are collinear and q2 lies on p1q1
|
|
if (o3 === 0 && onSegment(p2, p1, q2)) return true; // p2, q2 and p1 are collinear and p1 lies on p2q2
|
|
if (o4 === 0 && onSegment(p2, q1, q2)) return true; // p2, q2 and q1 are collinear and q1 lies on p2q2
|
|
|
|
return false;
|
|
}
|
|
|
|
// for collinear points p, q, r, check if point q lies on segment pr
|
|
function onSegment(p, q, r) {
|
|
return q.x <= Math.max(p.x, r.x) && q.x >= Math.min(p.x, r.x) && q.y <= Math.max(p.y, r.y) && q.y >= Math.min(p.y, r.y);
|
|
}
|
|
|
|
function sign(num) {
|
|
return num > 0 ? 1 : num < 0 ? -1 : 0;
|
|
}
|
|
|
|
// check if a polygon diagonal intersects any polygon segments
|
|
function intersectsPolygon(a, b) {
|
|
var p = a;
|
|
do {
|
|
if (p.i !== a.i && p.next.i !== a.i && p.i !== b.i && p.next.i !== b.i &&
|
|
intersects(p, p.next, a, b)) return true;
|
|
p = p.next;
|
|
} while (p !== a);
|
|
|
|
return false;
|
|
}
|
|
|
|
// check if a polygon diagonal is locally inside the polygon
|
|
function locallyInside(a, b) {
|
|
return area(a.prev, a, a.next) < 0 ?
|
|
area(a, b, a.next) >= 0 && area(a, a.prev, b) >= 0 :
|
|
area(a, b, a.prev) < 0 || area(a, a.next, b) < 0;
|
|
}
|
|
|
|
// check if the middle point of a polygon diagonal is inside the polygon
|
|
function middleInside(a, b) {
|
|
var p = a,
|
|
inside = false,
|
|
px = (a.x + b.x) / 2,
|
|
py = (a.y + b.y) / 2;
|
|
do {
|
|
if (((p.y > py) !== (p.next.y > py)) && p.next.y !== p.y &&
|
|
(px < (p.next.x - p.x) * (py - p.y) / (p.next.y - p.y) + p.x))
|
|
inside = !inside;
|
|
p = p.next;
|
|
} while (p !== a);
|
|
|
|
return inside;
|
|
}
|
|
|
|
// link two polygon vertices with a bridge; if the vertices belong to the same ring, it splits polygon into two;
|
|
// if one belongs to the outer ring and another to a hole, it merges it into a single ring
|
|
function splitPolygon(a, b) {
|
|
var a2 = new Node(a.i, a.x, a.y),
|
|
b2 = new Node(b.i, b.x, b.y),
|
|
an = a.next,
|
|
bp = b.prev;
|
|
|
|
a.next = b;
|
|
b.prev = a;
|
|
|
|
a2.next = an;
|
|
an.prev = a2;
|
|
|
|
b2.next = a2;
|
|
a2.prev = b2;
|
|
|
|
bp.next = b2;
|
|
b2.prev = bp;
|
|
|
|
return b2;
|
|
}
|
|
|
|
// create a node and optionally link it with previous one (in a circular doubly linked list)
|
|
function insertNode(i, x, y, last) {
|
|
var p = new Node(i, x, y);
|
|
|
|
if (!last) {
|
|
p.prev = p;
|
|
p.next = p;
|
|
|
|
} else {
|
|
p.next = last.next;
|
|
p.prev = last;
|
|
last.next.prev = p;
|
|
last.next = p;
|
|
}
|
|
return p;
|
|
}
|
|
|
|
function removeNode(p) {
|
|
p.next.prev = p.prev;
|
|
p.prev.next = p.next;
|
|
|
|
if (p.prevZ) p.prevZ.nextZ = p.nextZ;
|
|
if (p.nextZ) p.nextZ.prevZ = p.prevZ;
|
|
}
|
|
|
|
function Node(i, x, y) {
|
|
// vertex index in coordinates array
|
|
this.i = i;
|
|
|
|
// vertex coordinates
|
|
this.x = x;
|
|
this.y = y;
|
|
|
|
// previous and next vertex nodes in a polygon ring
|
|
this.prev = null;
|
|
this.next = null;
|
|
|
|
// z-order curve value
|
|
this.z = null;
|
|
|
|
// previous and next nodes in z-order
|
|
this.prevZ = null;
|
|
this.nextZ = null;
|
|
|
|
// indicates whether this is a steiner point
|
|
this.steiner = false;
|
|
}
|
|
|
|
// return a percentage difference between the polygon area and its triangulation area;
|
|
// used to verify correctness of triangulation
|
|
earcut.deviation = function (data, holeIndices, dim, triangles) {
|
|
var hasHoles = holeIndices && holeIndices.length;
|
|
var outerLen = hasHoles ? holeIndices[0] * dim : data.length;
|
|
|
|
var polygonArea = Math.abs(signedArea(data, 0, outerLen, dim));
|
|
if (hasHoles) {
|
|
for (var i = 0, len = holeIndices.length; i < len; i++) {
|
|
var start = holeIndices[i] * dim;
|
|
var end = i < len - 1 ? holeIndices[i + 1] * dim : data.length;
|
|
polygonArea -= Math.abs(signedArea(data, start, end, dim));
|
|
}
|
|
}
|
|
|
|
var trianglesArea = 0;
|
|
for (i = 0; i < triangles.length; i += 3) {
|
|
var a = triangles[i] * dim;
|
|
var b = triangles[i + 1] * dim;
|
|
var c = triangles[i + 2] * dim;
|
|
trianglesArea += Math.abs(
|
|
(data[a] - data[c]) * (data[b + 1] - data[a + 1]) -
|
|
(data[a] - data[b]) * (data[c + 1] - data[a + 1]));
|
|
}
|
|
|
|
return polygonArea === 0 && trianglesArea === 0 ? 0 :
|
|
Math.abs((trianglesArea - polygonArea) / polygonArea);
|
|
};
|
|
|
|
function signedArea(data, start, end, dim) {
|
|
var sum = 0;
|
|
for (var i = start, j = end - dim; i < end; i += dim) {
|
|
sum += (data[j] - data[i]) * (data[i + 1] + data[j + 1]);
|
|
j = i;
|
|
}
|
|
return sum;
|
|
}
|
|
|
|
// turn a polygon in a multi-dimensional array form (e.g. as in GeoJSON) into a form Earcut accepts
|
|
earcut.flatten = function (data) {
|
|
var dim = data[0][0].length,
|
|
result = {vertices: [], holes: [], dimensions: dim},
|
|
holeIndex = 0;
|
|
|
|
for (var i = 0; i < data.length; i++) {
|
|
for (var j = 0; j < data[i].length; j++) {
|
|
for (var d = 0; d < dim; d++) result.vertices.push(data[i][j][d]);
|
|
}
|
|
if (i > 0) {
|
|
holeIndex += data[i - 1].length;
|
|
result.holes.push(holeIndex);
|
|
}
|
|
}
|
|
return result;
|
|
};
|
|
|
|
},{}]},{},[1])(1)
|
|
});
|
|
|
|
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holeIndices[0] * dim : data.length,\n        outerNode = linkedList(data, 0, outerLen, dim, true),\n        triangles = [];\n\n    if (!outerNode || outerNode.next === outerNode.prev) return triangles;\n\n    var minX, minY, maxX, maxY, x, y, invSize;\n\n    if (hasHoles) outerNode = eliminateHoles(data, holeIndices, outerNode, dim);\n\n    // if the shape is not too simple, we'll use z-order curve hash later; calculate polygon bbox\n    if (data.length > 80 * dim) {\n        minX = maxX = data[0];\n        minY = maxY = data[1];\n\n        for (var i = dim; i < outerLen; i += dim) {\n            x = data[i];\n            y = data[i + 1];\n            if (x < minX) minX = x;\n            if (y < minY) minY = y;\n            if (x > maxX) maxX = x;\n            if (y > maxY) maxY = y;\n        }\n\n        // minX, minY and invSize are later used to transform coords into integers for z-order calculation\n        invSize = Math.max(maxX - minX, maxY - minY);\n        invSize = invSize !== 0 ? 1 / invSize : 0;\n    }\n\n    earcutLinked(outerNode, triangles, dim, minX, minY, invSize);\n\n    return triangles;\n}\n\n// create a circular doubly linked list from polygon points in the specified winding order\nfunction linkedList(data, start, end, dim, clockwise) {\n    var i, last;\n\n    if (clockwise === (signedArea(data, start, end, dim) > 0)) {\n        for (i = start; i < end; i += dim) last = insertNode(i, data[i], data[i + 1], last);\n    } else {\n        for (i = end - dim; i >= start; i -= dim) last = insertNode(i, data[i], data[i + 1], last);\n    }\n\n    if (last && equals(last, last.next)) {\n        removeNode(last);\n        last = last.next;\n    }\n\n    return last;\n}\n\n// eliminate colinear or duplicate points\nfunction filterPoints(start, end) {\n    if (!start) return start;\n    if (!end) end = start;\n\n    var p = start,\n        again;\n    do {\n        again = false;\n\n        if (!p.steiner && (equals(p, p.next) || area(p.prev, p, p.next) === 0)) {\n            removeNode(p);\n            p = end = p.prev;\n            if (p === p.next) break;\n            again = true;\n\n        } else {\n            p = p.next;\n        }\n    } while (again || p !== end);\n\n    return end;\n}\n\n// main ear slicing loop which triangulates a polygon (given as a linked list)\nfunction earcutLinked(ear, triangles, dim, minX, minY, invSize, pass) {\n    if (!ear) return;\n\n    // interlink polygon nodes in z-order\n    if (!pass && invSize) indexCurve(ear, minX, minY, invSize);\n\n    var stop = ear,\n        prev, next;\n\n    // iterate through ears, slicing them one by one\n    while (ear.prev !== ear.next) {\n        prev = ear.prev;\n        next = ear.next;\n\n        if (invSize ? isEarHashed(ear, minX, minY, invSize) : isEar(ear)) {\n            // cut off the triangle\n            triangles.push(prev.i / dim);\n            triangles.push(ear.i / dim);\n            triangles.push(next.i / dim);\n\n            removeNode(ear);\n\n            // skipping the next vertex leads to less sliver triangles\n            ear = next.next;\n            stop = next.next;\n\n            continue;\n        }\n\n        ear = next;\n\n        // if we looped through the whole remaining polygon and can't find any more ears\n        if (ear === stop) {\n            // try filtering points and slicing again\n            if (!pass) {\n                earcutLinked(filterPoints(ear), triangles, dim, minX, minY, invSize, 1);\n\n            // if this didn't work, try curing all small self-intersections locally\n            } else if (pass === 1) {\n                ear = cureLocalIntersections(filterPoints(ear), triangles, dim);\n                earcutLinked(ear, triangles, dim, minX, minY, invSize, 2);\n\n            // as a last resort, try splitting the remaining polygon into two\n            } else if (pass === 2) {\n                splitEarcut(ear, triangles, dim, minX, minY, invSize);\n            }\n\n            break;\n        }\n    }\n}\n\n// check whether a polygon node forms a valid ear with adjacent nodes\nfunction isEar(ear) {\n    var a = ear.prev,\n        b = ear,\n        c = ear.next;\n\n    if (area(a, b, c) >= 0) return false; // reflex, can't be an ear\n\n    // now make sure we don't have other points inside the potential ear\n    var p = ear.next.next;\n\n    while (p !== ear.prev) {\n        if (pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, p.x, p.y) &&\n            area(p.prev, p, p.next) >= 0) return false;\n        p = p.next;\n    }\n\n    return true;\n}\n\nfunction isEarHashed(ear, minX, minY, invSize) {\n    var a = ear.prev,\n        b = ear,\n        c = ear.next;\n\n    if (area(a, b, c) >= 0) return false; // reflex, can't be an ear\n\n    // triangle bbox; min & max are calculated like this for speed\n    var minTX = a.x < b.x ? (a.x < c.x ? a.x : c.x) : (b.x < c.x ? b.x : c.x),\n        minTY = a.y < b.y ? (a.y < c.y ? a.y : c.y) : (b.y < c.y ? b.y : c.y),\n        maxTX = a.x > b.x ? (a.x > c.x ? a.x : c.x) : (b.x > c.x ? b.x : c.x),\n        maxTY = a.y > b.y ? (a.y > c.y ? a.y : c.y) : (b.y > c.y ? b.y : c.y);\n\n    // z-order range for the current triangle bbox;\n    var minZ = zOrder(minTX, minTY, minX, minY, invSize),\n        maxZ = zOrder(maxTX, maxTY, minX, minY, invSize);\n\n    var p = ear.prevZ,\n        n = ear.nextZ;\n\n    // look for points inside the triangle in both directions\n    while (p && p.z >= minZ && n && n.z <= maxZ) {\n        if (p !== ear.prev && p !== ear.next &&\n            pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, p.x, p.y) &&\n            area(p.prev, p, p.next) >= 0) return false;\n        p = p.prevZ;\n\n        if (n !== ear.prev && n !== ear.next &&\n            pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, n.x, n.y) &&\n            area(n.prev, n, n.next) >= 0) return false;\n        n = n.nextZ;\n    }\n\n    // look for remaining points in decreasing z-order\n    while (p && p.z >= minZ) {\n        if (p !== ear.prev && p !== ear.next &&\n            pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, p.x, p.y) &&\n            area(p.prev, p, p.next) >= 0) return false;\n        p = p.prevZ;\n    }\n\n    // look for remaining points in increasing z-order\n    while (n && n.z <= maxZ) {\n        if (n !== ear.prev && n !== ear.next &&\n            pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, n.x, n.y) &&\n            area(n.prev, n, n.next) >= 0) return false;\n        n = n.nextZ;\n    }\n\n    return true;\n}\n\n// go through all polygon nodes and cure small local self-intersections\nfunction cureLocalIntersections(start, triangles, dim) {\n    var p = start;\n    do {\n        var a = p.prev,\n            b = p.next.next;\n\n        if (!equals(a, b) && intersects(a, p, p.next, b) && locallyInside(a, b) && locallyInside(b, a)) {\n\n            triangles.push(a.i / dim);\n            triangles.push(p.i / dim);\n            triangles.push(b.i / dim);\n\n            // remove two nodes involved\n            removeNode(p);\n            removeNode(p.next);\n\n            p = start = b;\n        }\n        p = p.next;\n    } while (p !== start);\n\n    return filterPoints(p);\n}\n\n// try splitting polygon into two and triangulate them independently\nfunction splitEarcut(start, triangles, dim, minX, minY, invSize) {\n    // look for a valid diagonal that divides the polygon into two\n    var a = start;\n    do {\n        var b = a.next.next;\n        while (b !== a.prev) {\n            if (a.i !== b.i && isValidDiagonal(a, b)) {\n                // split the polygon in two by the diagonal\n                var c = splitPolygon(a, b);\n\n                // filter colinear points around the cuts\n                a = filterPoints(a, a.next);\n                c = filterPoints(c, c.next);\n\n                // run earcut on each half\n                earcutLinked(a, triangles, dim, minX, minY, invSize);\n                earcutLinked(c, triangles, dim, minX, minY, invSize);\n                return;\n            }\n            b = b.next;\n        }\n        a = a.next;\n    } while (a !== start);\n}\n\n// link every hole into the outer loop, producing a single-ring polygon without holes\nfunction eliminateHoles(data, holeIndices, outerNode, dim) {\n    var queue = [],\n        i, len, start, end, list;\n\n    for (i = 0, len = holeIndices.length; i < len; i++) {\n        start = holeIndices[i] * dim;\n        end = i < len - 1 ? holeIndices[i + 1] * dim : data.length;\n        list = linkedList(data, start, end, dim, false);\n        if (list === list.next) list.steiner = true;\n        queue.push(getLeftmost(list));\n    }\n\n    queue.sort(compareX);\n\n    // process holes from left to right\n    for (i = 0; i < queue.length; i++) {\n        eliminateHole(queue[i], outerNode);\n        outerNode = filterPoints(outerNode, outerNode.next);\n    }\n\n    return outerNode;\n}\n\nfunction compareX(a, b) {\n    return a.x - b.x;\n}\n\n// find a bridge between vertices that connects hole with an outer ring and and link it\nfunction eliminateHole(hole, outerNode) {\n    outerNode = findHoleBridge(hole, outerNode);\n    if (outerNode) {\n        var b = splitPolygon(outerNode, hole);\n\n        // filter collinear points around the cuts\n        filterPoints(outerNode, outerNode.next);\n        filterPoints(b, b.next);\n    }\n}\n\n// David Eberly's algorithm for finding a bridge between hole and outer polygon\nfunction findHoleBridge(hole, outerNode) {\n    var p = outerNode,\n        hx = hole.x,\n        hy = hole.y,\n        qx = -Infinity,\n        m;\n\n    // find a segment intersected by a ray from the hole's leftmost point to the left;\n    // segment's endpoint with lesser x will be potential connection point\n    do {\n        if (hy <= p.y && hy >= p.next.y && p.next.y !== p.y) {\n            var x = p.x + (hy - p.y) * (p.next.x - p.x) / (p.next.y - p.y);\n            if (x <= hx && x > qx) {\n                qx = x;\n                if (x === hx) {\n                    if (hy === p.y) return p;\n                    if (hy === p.next.y) return p.next;\n                }\n                m = p.x < p.next.x ? p : p.next;\n            }\n        }\n        p = p.next;\n    } while (p !== outerNode);\n\n    if (!m) return null;\n\n    if (hx === qx) return m; // hole touches outer segment; pick leftmost endpoint\n\n    // look for points inside the triangle of hole point, segment intersection and endpoint;\n    // if there are no points found, we have a valid connection;\n    // otherwise choose the point of the minimum angle with the ray as connection point\n\n    var stop = m,\n        mx = m.x,\n        my = m.y,\n        tanMin = Infinity,\n        tan;\n\n    p = m;\n\n    do {\n        if (hx >= p.x && p.x >= mx && hx !== p.x &&\n                pointInTriangle(hy < my ? hx : qx, hy, mx, my, hy < my ? qx : hx, hy, p.x, p.y)) {\n\n            tan = Math.abs(hy - p.y) / (hx - p.x); // tangential\n\n            if (locallyInside(p, hole) &&\n                (tan < tanMin || (tan === tanMin && (p.x > m.x || (p.x === m.x && sectorContainsSector(m, p)))))) {\n                m = p;\n                tanMin = tan;\n            }\n        }\n\n        p = p.next;\n    } while (p !== stop);\n\n    return m;\n}\n\n// whether sector in vertex m contains sector in vertex p in the same coordinates\nfunction sectorContainsSector(m, p) {\n    return area(m.prev, m, p.prev) < 0 && area(p.next, m, m.next) < 0;\n}\n\n// interlink polygon nodes in z-order\nfunction indexCurve(start, minX, minY, invSize) {\n    var p = start;\n    do {\n        if (p.z === null) p.z = zOrder(p.x, p.y, minX, minY, invSize);\n        p.prevZ = p.prev;\n        p.nextZ = p.next;\n        p = p.next;\n    } while (p !== start);\n\n    p.prevZ.nextZ = null;\n    p.prevZ = null;\n\n    sortLinked(p);\n}\n\n// Simon Tatham's linked list merge sort algorithm\n// http://www.chiark.greenend.org.uk/~sgtatham/algorithms/listsort.html\nfunction sortLinked(list) {\n    var i, p, q, e, tail, numMerges, pSize, qSize,\n        inSize = 1;\n\n    do {\n        p = list;\n        list = null;\n        tail = null;\n        numMerges = 0;\n\n        while (p) {\n            numMerges++;\n            q = p;\n            pSize = 0;\n            for (i = 0; i < inSize; i++) {\n                pSize++;\n                q = q.nextZ;\n                if (!q) break;\n            }\n            qSize = inSize;\n\n            while (pSize > 0 || (qSize > 0 && q)) {\n\n                if (pSize !== 0 && (qSize === 0 || !q || p.z <= q.z)) {\n                    e = p;\n                    p = p.nextZ;\n                    pSize--;\n                } else {\n                    e = q;\n                    q = q.nextZ;\n                    qSize--;\n                }\n\n                if (tail) tail.nextZ = e;\n                else list = e;\n\n                e.prevZ = tail;\n                tail = e;\n            }\n\n            p = q;\n        }\n\n        tail.nextZ = null;\n        inSize *= 2;\n\n    } while (numMerges > 1);\n\n    return list;\n}\n\n// z-order of a point given coords and inverse of the longer side of data bbox\nfunction zOrder(x, y, minX, minY, invSize) {\n    // coords are transformed into non-negative 15-bit integer range\n    x = 32767 * (x - minX) * invSize;\n    y = 32767 * (y - minY) * invSize;\n\n    x = (x | (x << 8)) & 0x00FF00FF;\n    x = (x | (x << 4)) & 0x0F0F0F0F;\n    x = (x | (x << 2)) & 0x33333333;\n    x = (x | (x << 1)) & 0x55555555;\n\n    y = (y | (y << 8)) & 0x00FF00FF;\n    y = (y | (y << 4)) & 0x0F0F0F0F;\n    y = (y | (y << 2)) & 0x33333333;\n    y = (y | (y << 1)) & 0x55555555;\n\n    return x | (y << 1);\n}\n\n// find the leftmost node of a polygon ring\nfunction getLeftmost(start) {\n    var p = start,\n        leftmost = start;\n    do {\n        if (p.x < leftmost.x || (p.x === leftmost.x && p.y < leftmost.y)) leftmost = p;\n        p = p.next;\n    } while (p !== start);\n\n    return leftmost;\n}\n\n// check if a point lies within a convex triangle\nfunction pointInTriangle(ax, ay, bx, by, cx, cy, px, py) {\n    return (cx - px) * (ay - py) - (ax - px) * (cy - py) >= 0 &&\n           (ax - px) * (by - py) - (bx - px) * (ay - py) >= 0 &&\n           (bx - px) * (cy - py) - (cx - px) * (by - py) >= 0;\n}\n\n// check if a diagonal between two polygon nodes is valid (lies in polygon interior)\nfunction isValidDiagonal(a, b) {\n    return a.next.i !== b.i && a.prev.i !== b.i && !intersectsPolygon(a, b) && // dones't intersect other edges\n           (locallyInside(a, b) && locallyInside(b, a) && middleInside(a, b) && // locally visible\n            (area(a.prev, a, b.prev) || area(a, b.prev, b)) || // does not create opposite-facing sectors\n            equals(a, b) && area(a.prev, a, a.next) > 0 && area(b.prev, b, b.next) > 0); // special zero-length case\n}\n\n// signed area of a triangle\nfunction area(p, q, r) {\n    return (q.y - p.y) * (r.x - q.x) - (q.x - p.x) * (r.y - q.y);\n}\n\n// check if two points are equal\nfunction equals(p1, p2) {\n    return p1.x === p2.x && p1.y === p2.y;\n}\n\n// check if two segments intersect\nfunction intersects(p1, q1, p2, q2) {\n    var o1 = sign(area(p1, q1, p2));\n    var o2 = sign(area(p1, q1, q2));\n    var o3 = sign(area(p2, q2, p1));\n    var o4 = sign(area(p2, q2, q1));\n\n    if (o1 !== o2 && o3 !== o4) return true; // general case\n\n    if (o1 === 0 && onSegment(p1, p2, q1)) return true; // p1, q1 and p2 are collinear and p2 lies on p1q1\n    if (o2 === 0 && onSegment(p1, q2, q1)) return true; // p1, q1 and q2 are collinear and q2 lies on p1q1\n    if (o3 === 0 && onSegment(p2, p1, q2)) return true; // p2, q2 and p1 are collinear and p1 lies on p2q2\n    if (o4 === 0 && onSegment(p2, q1, q2)) return true; // p2, q2 and q1 are collinear and q1 lies on p2q2\n\n    return false;\n}\n\n// for collinear points p, q, r, check if point q lies on segment pr\nfunction onSegment(p, q, r) {\n    return q.x <= Math.max(p.x, r.x) && q.x >= Math.min(p.x, r.x) && q.y <= Math.max(p.y, r.y) && q.y >= Math.min(p.y, r.y);\n}\n\nfunction sign(num) {\n    return num > 0 ? 1 : num < 0 ? -1 : 0;\n}\n\n// check if a polygon diagonal intersects any polygon segments\nfunction intersectsPolygon(a, b) {\n    var p = a;\n    do {\n        if (p.i !== a.i && p.next.i !== a.i && p.i !== b.i && p.next.i !== b.i &&\n                intersects(p, p.next, a, b)) return true;\n        p = p.next;\n    } while (p !== a);\n\n    return false;\n}\n\n// check if a polygon diagonal is locally inside the polygon\nfunction locallyInside(a, b) {\n    return area(a.prev, a, a.next) < 0 ?\n        area(a, b, a.next) >= 0 && area(a, a.prev, b) >= 0 :\n        area(a, b, a.prev) < 0 || area(a, a.next, b) < 0;\n}\n\n// check if the middle point of a polygon diagonal is inside the polygon\nfunction middleInside(a, b) {\n    var p = a,\n        inside = false,\n        px = (a.x + b.x) / 2,\n        py = (a.y + b.y) / 2;\n    do {\n        if (((p.y > py) !== (p.next.y > py)) && p.next.y !== p.y &&\n                (px < (p.next.x - p.x) * (py - p.y) / (p.next.y - p.y) + p.x))\n            inside = !inside;\n        p = p.next;\n    } while (p !== a);\n\n    return inside;\n}\n\n// link two polygon vertices with a bridge; if the vertices belong to the same ring, it splits polygon into two;\n// if one belongs to the outer ring and another to a hole, it merges it into a single ring\nfunction splitPolygon(a, b) {\n    var a2 = new Node(a.i, a.x, a.y),\n        b2 = new Node(b.i, b.x, b.y),\n        an = a.next,\n        bp = b.prev;\n\n    a.next = b;\n    b.prev = a;\n\n    a2.next = an;\n    an.prev = a2;\n\n    b2.next = a2;\n    a2.prev = b2;\n\n    bp.next = b2;\n    b2.prev = bp;\n\n    return b2;\n}\n\n// create a node and optionally link it with previous one (in a circular doubly linked list)\nfunction insertNode(i, x, y, last) {\n    var p = new Node(i, x, y);\n\n    if (!last) {\n        p.prev = p;\n        p.next = p;\n\n    } else {\n        p.next = last.next;\n        p.prev = last;\n        last.next.prev = p;\n        last.next = p;\n    }\n    return p;\n}\n\nfunction removeNode(p) {\n    p.next.prev = p.prev;\n    p.prev.next = p.next;\n\n    if (p.prevZ) p.prevZ.nextZ = p.nextZ;\n    if (p.nextZ) p.nextZ.prevZ = p.prevZ;\n}\n\nfunction Node(i, x, y) {\n    // vertex index in coordinates array\n    this.i = i;\n\n    // vertex coordinates\n    this.x = x;\n    this.y = y;\n\n    // previous and next vertex nodes in a polygon ring\n    this.prev = null;\n    this.next = null;\n\n    // z-order curve value\n    this.z = null;\n\n    // previous and next nodes in z-order\n    this.prevZ = null;\n    this.nextZ = null;\n\n    // indicates whether this is a steiner point\n    this.steiner = false;\n}\n\n// return a percentage difference between the polygon area and its triangulation area;\n// used to verify correctness of triangulation\nearcut.deviation = function (data, holeIndices, dim, triangles) {\n    var hasHoles = holeIndices && holeIndices.length;\n    var outerLen = hasHoles ? holeIndices[0] * dim : data.length;\n\n    var polygonArea = Math.abs(signedArea(data, 0, outerLen, dim));\n    if (hasHoles) {\n        for (var i = 0, len = holeIndices.length; i < len; i++) {\n            var start = holeIndices[i] * dim;\n            var end = i < len - 1 ? holeIndices[i + 1] * dim : data.length;\n            polygonArea -= Math.abs(signedArea(data, start, end, dim));\n        }\n    }\n\n    var trianglesArea = 0;\n    for (i = 0; i < triangles.length; i += 3) {\n        var a = triangles[i] * dim;\n        var b = triangles[i + 1] * dim;\n        var c = triangles[i + 2] * dim;\n        trianglesArea += Math.abs(\n            (data[a] - data[c]) * (data[b + 1] - data[a + 1]) -\n            (data[a] - data[b]) * (data[c + 1] - data[a + 1]));\n    }\n\n    return polygonArea === 0 && trianglesArea === 0 ? 0 :\n        Math.abs((trianglesArea - polygonArea) / polygonArea);\n};\n\nfunction signedArea(data, start, end, dim) {\n    var sum = 0;\n    for (var i = start, j = end - dim; i < end; i += dim) {\n        sum += (data[j] - data[i]) * (data[i + 1] + data[j + 1]);\n        j = i;\n    }\n    return sum;\n}\n\n// turn a polygon in a multi-dimensional array form (e.g. as in GeoJSON) into a form Earcut accepts\nearcut.flatten = function (data) {\n    var dim = data[0][0].length,\n        result = {vertices: [], holes: [], dimensions: dim},\n        holeIndex = 0;\n\n    for (var i = 0; i < data.length; i++) {\n        for (var j = 0; j < data[i].length; j++) {\n            for (var d = 0; d < dim; d++) result.vertices.push(data[i][j][d]);\n        }\n        if (i > 0) {\n            holeIndex += data[i - 1].length;\n            result.holes.push(holeIndex);\n        }\n    }\n    return result;\n};\n"]}
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