three.js/examples/js/libs/earcut.js

/**
 *
 * Earcut https://github.com/mapbox/earcut
 *
 * Copyright (c) 2015, Mapbox
 *
 * Permission to use, copy, modify, and/or distribute this software for any purpose
 * with or without fee is hereby granted, provided that the above copyright notice
 * and this permission notice appear in all copies.
 *
 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH
 * REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
 * FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT,
 * INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS
 * OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER
 * TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF
 * THIS SOFTWARE.
 */
'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 = filterPoints(data, 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(data, 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 sum = 0,
        i, j, last;

    // calculate original winding order of a polygon ring
    for (i = start, j = end - dim; i < end; i += dim) {
        sum += (data[j] - data[i]) * (data[i + 1] + data[j + 1]);
        j = i;
    }

    // link points into circular doubly-linked list in the specified winding order
    if (clockwise === (sum > 0)) {
        for (i = start; i < end; i += dim) last = insertNode(i, last);
    } else {
        for (i = end - dim; i >= start; i -= dim) last = insertNode(i, last);
    }

    return last;
}

// eliminate colinear or duplicate points
function filterPoints(data, start, end) {
    if (!start) return start;
    if (!end) end = start;

    var node = start,
        again;
    do {
        again = false;

        if (!node.steiner && (equals(data, node.i, node.next.i) || orient(data, node.prev.i, node.i, node.next.i) === 0)) {
            removeNode(node);
            node = end = node.prev;
            if (node === node.next) return null;
            again = true;

        } else {
            node = node.next;
        }
    } while (again || node !== end);

    return end;
}

// main ear slicing loop which triangulates a polygon (given as a linked list)
function earcutLinked(data, ear, triangles, dim, minX, minY, size, pass) {
    if (!ear) return;

    // interlink polygon nodes in z-order
    if (!pass && minX !== undefined) indexCurve(data, 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 (isEar(data, ear, minX, minY, size)) {
            // 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(data, filterPoints(data, 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(data, ear, triangles, dim);
                earcutLinked(data, ear, triangles, dim, minX, minY, size, 2);

            // as a last resort, try splitting the remaining polygon into two
            } else if (pass === 2) {
                splitEarcut(data, ear, triangles, dim, minX, minY, size);
            }

            break;
        }
    }
}

// check whether a polygon node forms a valid ear with adjacent nodes
function isEar(data, ear, minX, minY, size) {

    var a = ear.prev.i,
        b = ear.i,
        c = ear.next.i,

        ax = data[a], ay = data[a + 1],
        bx = data[b], by = data[b + 1],
        cx = data[c], cy = data[c + 1],

        abd = ax * by - ay * bx,
        acd = ax * cy - ay * cx,
        cbd = cx * by - cy * bx,
        A = abd - acd - cbd;

    if (A <= 0) return false; // reflex, can't be an ear

    // now make sure we don't have other points inside the potential ear;
    // the code below is a bit verbose and repetitive but this is done for performance

    var cay = cy - ay,
        acx = ax - cx,
        aby = ay - by,
        bax = bx - ax,
        i, px, py, s, t, k, node;

    // if we use z-order curve hashing, iterate through the curve
    if (minX !== undefined) {

        // triangle bbox; min & max are calculated like this for speed
        var minTX = ax < bx ? (ax < cx ? ax : cx) : (bx < cx ? bx : cx),
            minTY = ay < by ? (ay < cy ? ay : cy) : (by < cy ? by : cy),
            maxTX = ax > bx ? (ax > cx ? ax : cx) : (bx > cx ? bx : cx),
            maxTY = ay > by ? (ay > cy ? ay : cy) : (by > cy ? by : cy),

            // z-order range for the current triangle bbox;
            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
        node = ear.nextZ;

        while (node && node.z <= maxZ) {
            i = node.i;
            node = node.nextZ;
            if (i === a || i === c) continue;

            px = data[i];
            py = data[i + 1];

            s = cay * px + acx * py - acd;
            if (s >= 0) {
                t = aby * px + bax * py + abd;
                if (t >= 0) {
                    k = A - s - t;
                    if ((k >= 0) && ((s && t) || (s && k) || (t && k))) return false;
                }
            }
        }

        // then look for points in decreasing z-order
        node = ear.prevZ;

        while (node && node.z >= minZ) {
            i = node.i;
            node = node.prevZ;
            if (i === a || i === c) continue;

            px = data[i];
            py = data[i + 1];

            s = cay * px + acx * py - acd;
            if (s >= 0) {
                t = aby * px + bax * py + abd;
                if (t >= 0) {
                    k = A - s - t;
                    if ((k >= 0) && ((s && t) || (s && k) || (t && k))) return false;
                }
            }
        }

    // if we don't use z-order curve hash, simply iterate through all other points
    } else {
        node = ear.next.next;

        while (node !== ear.prev) {
            i = node.i;
            node = node.next;

            px = data[i];
            py = data[i + 1];

            s = cay * px + acx * py - acd;
            if (s >= 0) {
                t = aby * px + bax * py + abd;
                if (t >= 0) {
                    k = A - s - t;
                    if ((k >= 0) && ((s && t) || (s && k) || (t && k))) return false;
                }
            }
        }
    }

    return true;
}

// go through all polygon nodes and cure small local self-intersections
function cureLocalIntersections(data, start, triangles, dim) {
    var node = start;
    do {
        var a = node.prev,
            b = node.next.next;

        // a self-intersection where edge (v[i-1],v[i]) intersects (v[i+1],v[i+2])
        if (a.i !== b.i && intersects(data, a.i, node.i, node.next.i, b.i) &&
                locallyInside(data, a, b) && locallyInside(data, b, a) &&
                orient(data, a.i, node.i, b.i) && orient(data, a.i, node.next.i, b.i)) {

            triangles.push(a.i / dim);
            triangles.push(node.i / dim);
            triangles.push(b.i / dim);

            // remove two nodes involved
            removeNode(node);
            removeNode(node.next);

            node = start = b;
        }
        node = node.next;
    } while (node !== start);

    return node;
}

// try splitting polygon into two and triangulate them independently
function splitEarcut(data, 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(data, a, b)) {
                // split the polygon in two by the diagonal
                var c = splitPolygon(a, b);

                // filter colinear points around the cuts
                a = filterPoints(data, a, a.next);
                c = filterPoints(data, c, c.next);

                // run earcut on each half
                earcutLinked(data, a, triangles, dim, minX, minY, size);
                earcutLinked(data, 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;
        list = filterPoints(data, list);
        if (list) queue.push(getLeftmost(data, list));
    }

    queue.sort(function (a, b) {
        return data[a.i] - data[b.i];
    });

    // process holes from left to right
    for (i = 0; i < queue.length; i++) {
        eliminateHole(data, queue[i], outerNode);
        outerNode = filterPoints(data, outerNode, outerNode.next);
    }

    return outerNode;
}

// find a bridge between vertices that connects hole with an outer ring and and link it
function eliminateHole(data, holeNode, outerNode) {
    outerNode = findHoleBridge(data, holeNode, outerNode);
    if (outerNode) {
        var b = splitPolygon(outerNode, holeNode);
        filterPoints(data, b, b.next);
    }
}

// David Eberly's algorithm for finding a bridge between hole and outer polygon
function findHoleBridge(data, holeNode, outerNode) {
    var node = outerNode,
        i = holeNode.i,
        px = data[i],
        py = data[i + 1],
        qMax = -Infinity,
        mNode, a, b;

    // 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 {
        a = node.i;
        b = node.next.i;

        if (py <= data[a + 1] && py >= data[b + 1]) {
            var qx = data[a] + (py - data[a + 1]) * (data[b] - data[a]) / (data[b + 1] - data[a + 1]);
            if (qx <= px && qx > qMax) {
                qMax = qx;
                mNode = data[a] < data[b] ? node : node.next;
            }
        }
        node = node.next;
    } while (node !== outerNode);

    if (!mNode) return null;

    // look for points strictly 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 bx = data[mNode.i],
        by = data[mNode.i + 1],
        pbd = px * by - py * bx,
        pcd = px * py - py * qMax,
        cpy = py - py,
        pcx = px - qMax,
        pby = py - by,
        bpx = bx - px,
        A = pbd - pcd - (qMax * by - py * bx),
        sign = A <= 0 ? -1 : 1,
        stop = mNode,
        tanMin = Infinity,
        mx, my, amx, s, t, tan;

    node = mNode.next;

    while (node !== stop) {

        mx = data[node.i];
        my = data[node.i + 1];
        amx = px - mx;

        if (amx >= 0 && mx >= bx) {
            s = (cpy * mx + pcx * my - pcd) * sign;
            if (s >= 0) {
                t = (pby * mx + bpx * my + pbd) * sign;

                if (t >= 0 && A * sign - s - t >= 0) {
                    tan = Math.abs(py - my) / amx; // tangential
                    if ((tan < tanMin || (tan === tanMin && mx > bx)) &&
                            locallyInside(data, node, holeNode)) {
                        mNode = node;
                        tanMin = tan;
                    }
                }
            }
        }

        node = node.next;
    }

    return mNode;
}

// interlink polygon nodes in z-order
function indexCurve(data, start, minX, minY, size) {
    var node = start;

    do {
        if (node.z === null) node.z = zOrder(data[node.i], data[node.i + 1], minX, minY, size);
        node.prevZ = node.prev;
        node.nextZ = node.next;
        node = node.next;
    } while (node !== start);

    node.prevZ.nextZ = null;
    node.prevZ = null;

    sortLinked(node);
}

// 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(data, start) {
    var node = start,
        leftmost = start;
    do {
        if (data[node.i] < data[leftmost.i]) leftmost = node;
        node = node.next;
    } while (node !== start);

    return leftmost;
}

// check if a diagonal between two polygon nodes is valid (lies in polygon interior)
function isValidDiagonal(data, a, b) {
    return a.next.i !== b.i && a.prev.i !== b.i &&
           !intersectsPolygon(data, a, a.i, b.i) &&
           locallyInside(data, a, b) && locallyInside(data, b, a) &&
           middleInside(data, a, a.i, b.i);
}

// winding order of triangle formed by 3 given points
function orient(data, p, q, r) {
    var o = (data[q + 1] - data[p + 1]) * (data[r] - data[q]) - (data[q] - data[p]) * (data[r + 1] - data[q + 1]);
    return o > 0 ? 1 :
           o < 0 ? -1 : 0;
}

// check if two points are equal
function equals(data, p1, p2) {
    return data[p1] === data[p2] && data[p1 + 1] === data[p2 + 1];
}

// check if two segments intersect
function intersects(data, p1, q1, p2, q2) {
    return orient(data, p1, q1, p2) !== orient(data, p1, q1, q2) &&
           orient(data, p2, q2, p1) !== orient(data, p2, q2, q1);
}

// check if a polygon diagonal intersects any polygon segments
function intersectsPolygon(data, start, a, b) {
    var node = start;
    do {
        var p1 = node.i,
            p2 = node.next.i;

        if (p1 !== a && p2 !== a && p1 !== b && p2 !== b && intersects(data, p1, p2, a, b)) return true;

        node = node.next;
    } while (node !== start);

    return false;
}

// check if a polygon diagonal is locally inside the polygon
function locallyInside(data, a, b) {
    return orient(data, a.prev.i, a.i, a.next.i) === -1 ?
        orient(data, a.i, b.i, a.next.i) !== -1 && orient(data, a.i, a.prev.i, b.i) !== -1 :
        orient(data, a.i, b.i, a.prev.i) === -1 || orient(data, a.i, a.next.i, b.i) === -1;
}

// check if the middle point of a polygon diagonal is inside the polygon
function middleInside(data, start, a, b) {
    var node = start,
        inside = false,
        px = (data[a] + data[b]) / 2,
        py = (data[a + 1] + data[b + 1]) / 2;
    do {
        var p1 = node.i,
            p2 = node.next.i;

        if (((data[p1 + 1] > py) !== (data[p2 + 1] > py)) &&
                (px < (data[p2] - data[p1]) * (py - data[p1 + 1]) / (data[p2 + 1] - data[p1 + 1]) + data[p1]))
            inside = !inside;

        node = node.next;
    } while (node !== start);

    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),
        b2 = new Node(b.i),
        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, last) {
    var node = new Node(i);

    if (!last) {
        node.prev = node;
        node.next = node;

    } else {
        node.next = last.next;
        node.prev = last;
        last.next.prev = node;
        last.next = node;
    }
    return node;
}

function removeNode(node) {
    node.next.prev = node.prev;
    node.prev.next = node.next;

    if (node.prevZ) node.prevZ.nextZ = node.nextZ;
    if (node.nextZ) node.nextZ.prevZ = node.prevZ;
}

function Node(i) {
    // vertex coordinates
    this.i = i;

    // 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;
}