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SLAcer.js/vendor/earcut.js
8424d63 Mar 18, 2016
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645 lines (513 sloc) 18 KB
'use strict';
//module.exports = earcut;
function earcut(data, holeIndices, dim) {
dim = dim || 2;
var hasHoles = holeIndices && holeIndices.length,
outerLen = hasHoles ? holeIndices[0] * dim : data.length,
outerNode = linkedList(data, 0, outerLen, dim, true),
triangles = [];
if (!outerNode) return triangles;
var minX, minY, maxX, maxY, x, y, size;
if (hasHoles) outerNode = eliminateHoles(data, holeIndices, outerNode, dim);
// if the shape is not too simple, we'll use z-order curve hash later; calculate polygon bbox
if (data.length > 80 * dim) {
minX = maxX = data[0];
minY = maxY = data[1];
for (var i = dim; i < outerLen; i += dim) {
x = data[i];
y = data[i + 1];
if (x < minX) minX = x;
if (y < minY) minY = y;
if (x > maxX) maxX = x;
if (y > maxY) maxY = y;
}
// minX, minY and size are later used to transform coords into integers for z-order calculation
size = Math.max(maxX - minX, maxY - minY);
}
earcutLinked(outerNode, triangles, dim, minX, minY, size);
return triangles;
}
// create a circular doubly linked list from polygon points in the specified winding order
function linkedList(data, start, end, dim, clockwise) {
var i, last;
if (clockwise === (signedArea(data, start, end, dim) > 0)) {
for (i = start; i < end; i += dim) last = insertNode(i, data[i], data[i + 1], last);
} else {
for (i = end - dim; i >= start; i -= dim) last = insertNode(i, data[i], data[i + 1], last);
}
if (last && equals(last, last.next)) {
removeNode(last);
last = last.next;
}
return last;
}
// eliminate colinear or duplicate points
function filterPoints(start, end) {
if (!start) return start;
if (!end) end = start;
var p = start,
again;
do {
again = false;
if (!p.steiner && (equals(p, p.next) || area(p.prev, p, p.next) === 0)) {
removeNode(p);
p = end = p.prev;
if (p === p.next) return null;
again = true;
} else {
p = p.next;
}
} while (again || p !== end);
return end;
}
// main ear slicing loop which triangulates a polygon (given as a linked list)
function earcutLinked(ear, triangles, dim, minX, minY, size, pass) {
if (!ear) return;
// interlink polygon nodes in z-order
if (!pass && size) indexCurve(ear, minX, minY, size);
var stop = ear,
prev, next;
// iterate through ears, slicing them one by one
while (ear.prev !== ear.next) {
prev = ear.prev;
next = ear.next;
if (size ? isEarHashed(ear, minX, minY, size) : isEar(ear)) {
// cut off the triangle
triangles.push(prev.i / dim);
triangles.push(ear.i / dim);
triangles.push(next.i / dim);
removeNode(ear);
// skipping the next vertice leads to less sliver triangles
ear = next.next;
stop = next.next;
continue;
}
ear = next;
// if we looped through the whole remaining polygon and can't find any more ears
if (ear === stop) {
// try filtering points and slicing again
if (!pass) {
earcutLinked(filterPoints(ear), triangles, dim, minX, minY, size, 1);
// if this didn't work, try curing all small self-intersections locally
} else if (pass === 1) {
ear = cureLocalIntersections(ear, triangles, dim);
earcutLinked(ear, triangles, dim, minX, minY, size, 2);
// as a last resort, try splitting the remaining polygon into two
} else if (pass === 2) {
splitEarcut(ear, triangles, dim, minX, minY, size);
}
break;
}
}
}
// check whether a polygon node forms a valid ear with adjacent nodes
function isEar(ear) {
var a = ear.prev,
b = ear,
c = ear.next;
if (area(a, b, c) >= 0) return false; // reflex, can't be an ear
// now make sure we don't have other points inside the potential ear
var p = ear.next.next;
while (p !== ear.prev) {
if (pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, p.x, p.y) &&
area(p.prev, p, p.next) >= 0) return false;
p = p.next;
}
return true;
}
function isEarHashed(ear, minX, minY, size) {
var a = ear.prev,
b = ear,
c = ear.next;
if (area(a, b, c) >= 0) return false; // reflex, can't be an ear
// triangle bbox; min & max are calculated like this for speed
var minTX = a.x < b.x ? (a.x < c.x ? a.x : c.x) : (b.x < c.x ? b.x : c.x),
minTY = a.y < b.y ? (a.y < c.y ? a.y : c.y) : (b.y < c.y ? b.y : c.y),
maxTX = a.x > b.x ? (a.x > c.x ? a.x : c.x) : (b.x > c.x ? b.x : c.x),
maxTY = a.y > b.y ? (a.y > c.y ? a.y : c.y) : (b.y > c.y ? b.y : c.y);
// z-order range for the current triangle bbox;
var minZ = zOrder(minTX, minTY, minX, minY, size),
maxZ = zOrder(maxTX, maxTY, minX, minY, size);
// first look for points inside the triangle in increasing z-order
var p = ear.nextZ;
while (p && p.z <= maxZ) {
if (p !== ear.prev && p !== ear.next &&
pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, p.x, p.y) &&
area(p.prev, p, p.next) >= 0) return false;
p = p.nextZ;
}
// then look for points in decreasing z-order
p = ear.prevZ;
while (p && p.z >= minZ) {
if (p !== ear.prev && p !== ear.next &&
pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, p.x, p.y) &&
area(p.prev, p, p.next) >= 0) return false;
p = p.prevZ;
}
return true;
}
// go through all polygon nodes and cure small local self-intersections
function cureLocalIntersections(start, triangles, dim) {
var p = start;
do {
var a = p.prev,
b = p.next.next;
if (!equals(a, b) && intersects(a, p, p.next, b) && locallyInside(a, b) && locallyInside(b, a)) {
triangles.push(a.i / dim);
triangles.push(p.i / dim);
triangles.push(b.i / dim);
// remove two nodes involved
removeNode(p);
removeNode(p.next);
p = start = b;
}
p = p.next;
} while (p !== start);
return p;
}
// try splitting polygon into two and triangulate them independently
function splitEarcut(start, triangles, dim, minX, minY, size) {
// look for a valid diagonal that divides the polygon into two
var a = start;
do {
var b = a.next.next;
while (b !== a.prev) {
if (a.i !== b.i && isValidDiagonal(a, b)) {
// split the polygon in two by the diagonal
var c = splitPolygon(a, b);
// filter colinear points around the cuts
a = filterPoints(a, a.next);
c = filterPoints(c, c.next);
// run earcut on each half
earcutLinked(a, triangles, dim, minX, minY, size);
earcutLinked(c, triangles, dim, minX, minY, size);
return;
}
b = b.next;
}
a = a.next;
} while (a !== start);
}
// link every hole into the outer loop, producing a single-ring polygon without holes
function eliminateHoles(data, holeIndices, outerNode, dim) {
var queue = [],
i, len, start, end, list;
for (i = 0, len = holeIndices.length; i < len; i++) {
start = holeIndices[i] * dim;
end = i < len - 1 ? holeIndices[i + 1] * dim : data.length;
list = linkedList(data, start, end, dim, false);
if (list === list.next) list.steiner = true;
queue.push(getLeftmost(list));
}
queue.sort(compareX);
// process holes from left to right
for (i = 0; i < queue.length; i++) {
eliminateHole(queue[i], outerNode);
outerNode = filterPoints(outerNode, outerNode.next);
}
return outerNode;
}
function compareX(a, b) {
return a.x - b.x;
}
// find a bridge between vertices that connects hole with an outer ring and and link it
function eliminateHole(hole, outerNode) {
outerNode = findHoleBridge(hole, outerNode);
if (outerNode) {
var b = splitPolygon(outerNode, hole);
filterPoints(b, b.next);
}
}
// David Eberly's algorithm for finding a bridge between hole and outer polygon
function findHoleBridge(hole, outerNode) {
var p = outerNode,
hx = hole.x,
hy = hole.y,
qx = -Infinity,
m;
// find a segment intersected by a ray from the hole's leftmost point to the left;
// segment's endpoint with lesser x will be potential connection point
do {
if (hy <= p.y && hy >= p.next.y) {
var x = p.x + (hy - p.y) * (p.next.x - p.x) / (p.next.y - p.y);
if (x <= hx && x > qx) {
qx = x;
if (x === hx) {
if (hy === p.y) return p;
if (hy === p.next.y) return p.next;
}
m = p.x < p.next.x ? p : p.next;
}
}
p = p.next;
} while (p !== outerNode);
if (!m) return null;
if (hx === qx) return m.prev; // hole touches outer segment; pick lower endpoint
// look for points inside the triangle of hole point, segment intersection and endpoint;
// if there are no points found, we have a valid connection;
// otherwise choose the point of the minimum angle with the ray as connection point
var stop = m,
mx = m.x,
my = m.y,
tanMin = Infinity,
tan;
p = m.next;
while (p !== stop) {
if (hx >= p.x && p.x >= mx &&
pointInTriangle(hy < my ? hx : qx, hy, mx, my, hy < my ? qx : hx, hy, p.x, p.y)) {
tan = Math.abs(hy - p.y) / (hx - p.x); // tangential
if ((tan < tanMin || (tan === tanMin && p.x > m.x)) && locallyInside(p, hole)) {
m = p;
tanMin = tan;
}
}
p = p.next;
}
return m;
}
// interlink polygon nodes in z-order
function indexCurve(start, minX, minY, size) {
var p = start;
do {
if (p.z === null) p.z = zOrder(p.x, p.y, minX, minY, size);
p.prevZ = p.prev;
p.nextZ = p.next;
p = p.next;
} while (p !== start);
p.prevZ.nextZ = null;
p.prevZ = null;
sortLinked(p);
}
// Simon Tatham's linked list merge sort algorithm
// http://www.chiark.greenend.org.uk/~sgtatham/algorithms/listsort.html
function sortLinked(list) {
var i, p, q, e, tail, numMerges, pSize, qSize,
inSize = 1;
do {
p = list;
list = null;
tail = null;
numMerges = 0;
while (p) {
numMerges++;
q = p;
pSize = 0;
for (i = 0; i < inSize; i++) {
pSize++;
q = q.nextZ;
if (!q) break;
}
qSize = inSize;
while (pSize > 0 || (qSize > 0 && q)) {
if (pSize === 0) {
e = q;
q = q.nextZ;
qSize--;
} else if (qSize === 0 || !q) {
e = p;
p = p.nextZ;
pSize--;
} else if (p.z <= q.z) {
e = p;
p = p.nextZ;
pSize--;
} else {
e = q;
q = q.nextZ;
qSize--;
}
if (tail) tail.nextZ = e;
else list = e;
e.prevZ = tail;
tail = e;
}
p = q;
}
tail.nextZ = null;
inSize *= 2;
} while (numMerges > 1);
return list;
}
// z-order of a point given coords and size of the data bounding box
function zOrder(x, y, minX, minY, size) {
// coords are transformed into non-negative 15-bit integer range
x = 32767 * (x - minX) / size;
y = 32767 * (y - minY) / size;
x = (x | (x << 8)) & 0x00FF00FF;
x = (x | (x << 4)) & 0x0F0F0F0F;
x = (x | (x << 2)) & 0x33333333;
x = (x | (x << 1)) & 0x55555555;
y = (y | (y << 8)) & 0x00FF00FF;
y = (y | (y << 4)) & 0x0F0F0F0F;
y = (y | (y << 2)) & 0x33333333;
y = (y | (y << 1)) & 0x55555555;
return x | (y << 1);
}
// find the leftmost node of a polygon ring
function getLeftmost(start) {
var p = start,
leftmost = start;
do {
if (p.x < leftmost.x) leftmost = p;
p = p.next;
} while (p !== start);
return leftmost;
}
// check if a point lies within a convex triangle
function pointInTriangle(ax, ay, bx, by, cx, cy, px, py) {
return (cx - px) * (ay - py) - (ax - px) * (cy - py) >= 0 &&
(ax - px) * (by - py) - (bx - px) * (ay - py) >= 0 &&
(bx - px) * (cy - py) - (cx - px) * (by - py) >= 0;
}
// check if a diagonal between two polygon nodes is valid (lies in polygon interior)
function isValidDiagonal(a, b) {
return a.next.i !== b.i && a.prev.i !== b.i && !intersectsPolygon(a, b) &&
locallyInside(a, b) && locallyInside(b, a) && middleInside(a, b);
}
// 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) {
if ((equals(p1, q1) && equals(p2, q2)) ||
(equals(p1, q2) && equals(p2, q1))) return true;
return area(p1, q1, p2) > 0 !== area(p1, q1, q2) > 0 &&
area(p2, q2, p1) > 0 !== area(p2, q2, q1) > 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)) && (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) {
// vertice index in coordinates array
this.i = i;
// vertex coordinates
this.x = x;
this.y = y;
// previous and next vertice 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;
};