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'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; | |
}; |