earcut.js

'use strict';

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;
};