@math.gl/polygon/dist/earcut.js

Polygon/polyline processing utilities

// math.gl
// SPDX-License-Identifier: MIT and ISC
// Copyright (c) vis.gl contributors
import { getPolygonSignedArea, DimIndex } from "./polygon-utils.js";
/**
 * Computes a triangulation of a polygon
 * @param positions a flat array of the vertex positions that define the polygon.
 * @param holeIndices an array of hole indices if any (e.g. [5, 8] for a 12-vertex input would mean one hole with vertices 5–7 and another with 8–11).
 * @param dim the number of elements in each vertex. Size `2` will interpret `positions` as `[x0, y0, x1, y1, ...]` and size `3` will interpret `positions` as `[x0, y0, z0, x1, y1, z1, ...]`. Default `2`.
 * @param areas areas of outer polygon and holes as computed by `getPolygonSignedArea()`. Can be optionally supplied to speed up triangulation
 * @returns array of indices into the `positions` array that describes the triangulation of the polygon
 * Adapted from https://github.com/mapbox/earcut
 */
export function earcut(positions, holeIndices, dim = 2, areas, plane = 'xy') {
    const hasHoles = holeIndices && holeIndices.length;
    const outerLen = hasHoles ? holeIndices[0] * dim : positions.length;
    let outerNode = linkedList(positions, 0, outerLen, dim, true, areas && areas[0], plane);
    const triangles = [];
    if (!outerNode || outerNode.next === outerNode.prev)
        return triangles;
    let invSize;
    let maxX;
    let maxY;
    let minX;
    let minY;
    let x;
    let y;
    if (hasHoles)
        outerNode = eliminateHoles(positions, holeIndices, outerNode, dim, areas, plane);
    // if the shape is not too simple, we'll use z-order curve hash later; calculate polygon bbox
    if (positions.length > 80 * dim) {
        minX = maxX = positions[0];
        minY = maxY = positions[1];
        for (let i = dim; i < outerLen; i += dim) {
            x = positions[i];
            y = positions[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 invSize are later used to transform coords into integers for z-order calculation
        invSize = Math.max(maxX - minX, maxY - minY);
        invSize = invSize !== 0 ? 32767 / invSize : 0;
    }
    earcutLinked(outerNode, triangles, dim, minX, minY, invSize, 0);
    return triangles;
}
// create a circular doubly linked list from polygon points in the specified winding order
function linkedList(data, start, end, dim, clockwise, area, plane) {
    let i;
    let last;
    if (area === undefined) {
        area = getPolygonSignedArea(data, { start, end, size: dim, plane });
    }
    let i0 = DimIndex[plane[0]];
    let i1 = DimIndex[plane[1]];
    // Note that the signed area calculation in math.gl
    // has the opposite sign to that which was originally
    // present in earcut, thus the `< 0` is reversed
    if (clockwise === area < 0) {
        for (i = start; i < end; i += dim)
            last = insertNode(i, data[i + i0], data[i + i1], last);
    }
    else {
        for (i = end - dim; i >= start; i -= dim)
            last = insertNode(i, data[i + i0], data[i + i1], 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;
    let p = start;
    let 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)
                break;
            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, invSize, pass) {
    if (!ear)
        return;
    // interlink polygon nodes in z-order
    if (!pass && invSize)
        indexCurve(ear, minX, minY, invSize);
    let stop = ear;
    let prev;
    let next;
    // iterate through ears, slicing them one by one
    while (ear.prev !== ear.next) {
        prev = ear.prev;
        next = ear.next;
        if (invSize ? isEarHashed(ear, minX, minY, invSize) : isEar(ear)) {
            // cut off the triangle
            triangles.push((prev.i / dim) | 0);
            triangles.push((ear.i / dim) | 0);
            triangles.push((next.i / dim) | 0);
            removeNode(ear);
            // skipping the next vertex 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, invSize, 1);
                // if this didn't work, try curing all small self-intersections locally
            }
            else if (pass === 1) {
                ear = cureLocalIntersections(filterPoints(ear), triangles, dim);
                earcutLinked(ear, triangles, dim, minX, minY, invSize, 2);
                // as a last resort, try splitting the remaining polygon into two
            }
            else if (pass === 2) {
                splitEarcut(ear, triangles, dim, minX, minY, invSize);
            }
            break;
        }
    }
}
// check whether a polygon node forms a valid ear with adjacent nodes
function isEar(ear) {
    const a = ear.prev;
    const b = ear;
    const 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
    const ax = a.x;
    const bx = b.x;
    const cx = c.x;
    const ay = a.y;
    const by = b.y;
    const cy = c.y;
    // triangle bbox; min & max are calculated like this for speed
    const x0 = ax < bx ? (ax < cx ? ax : cx) : bx < cx ? bx : cx;
    const y0 = ay < by ? (ay < cy ? ay : cy) : by < cy ? by : cy;
    const x1 = ax > bx ? (ax > cx ? ax : cx) : bx > cx ? bx : cx;
    const y1 = ay > by ? (ay > cy ? ay : cy) : by > cy ? by : cy;
    let p = c.next;
    while (p !== a) {
        if (p.x >= x0 &&
            p.x <= x1 &&
            p.y >= y0 &&
            p.y <= y1 &&
            pointInTriangle(ax, ay, bx, by, cx, cy, p.x, p.y) &&
            area(p.prev, p, p.next) >= 0)
            return false;
        p = p.next;
    }
    return true;
}
function isEarHashed(ear, minX, minY, invSize) {
    const a = ear.prev;
    const b = ear;
    const c = ear.next;
    if (area(a, b, c) >= 0)
        return false; // reflex, can't be an ear
    const ax = a.x;
    const bx = b.x;
    const cx = c.x;
    const ay = a.y;
    const by = b.y;
    const cy = c.y;
    // triangle bbox; min & max are calculated like this for speed
    const x0 = ax < bx ? (ax < cx ? ax : cx) : bx < cx ? bx : cx;
    const y0 = ay < by ? (ay < cy ? ay : cy) : by < cy ? by : cy;
    const x1 = ax > bx ? (ax > cx ? ax : cx) : bx > cx ? bx : cx;
    const y1 = ay > by ? (ay > cy ? ay : cy) : by > cy ? by : cy;
    // z-order range for the current triangle bbox;
    const minZ = zOrder(x0, y0, minX, minY, invSize);
    const maxZ = zOrder(x1, y1, minX, minY, invSize);
    let p = ear.prevZ;
    let n = ear.nextZ;
    // look for points inside the triangle in both directions
    while (p && p.z >= minZ && n && n.z <= maxZ) {
        if (p.x >= x0 &&
            p.x <= x1 &&
            p.y >= y0 &&
            p.y <= y1 &&
            p !== a &&
            p !== c &&
            pointInTriangle(ax, ay, bx, by, cx, cy, p.x, p.y) &&
            area(p.prev, p, p.next) >= 0)
            return false;
        p = p.prevZ;
        if (n.x >= x0 &&
            n.x <= x1 &&
            n.y >= y0 &&
            n.y <= y1 &&
            n !== a &&
            n !== c &&
            pointInTriangle(ax, ay, bx, by, cx, cy, n.x, n.y) &&
            area(n.prev, n, n.next) >= 0)
            return false;
        n = n.nextZ;
    }
    // look for remaining points in decreasing z-order
    while (p && p.z >= minZ) {
        if (p.x >= x0 &&
            p.x <= x1 &&
            p.y >= y0 &&
            p.y <= y1 &&
            p !== a &&
            p !== c &&
            pointInTriangle(ax, ay, bx, by, cx, cy, p.x, p.y) &&
            area(p.prev, p, p.next) >= 0)
            return false;
        p = p.prevZ;
    }
    // look for remaining points in increasing z-order
    while (n && n.z <= maxZ) {
        if (n.x >= x0 &&
            n.x <= x1 &&
            n.y >= y0 &&
            n.y <= y1 &&
            n !== a &&
            n !== c &&
            pointInTriangle(ax, ay, bx, by, cx, cy, n.x, n.y) &&
            area(n.prev, n, n.next) >= 0)
            return false;
        n = n.nextZ;
    }
    return true;
}
// go through all polygon nodes and cure small local self-intersections
function cureLocalIntersections(start, triangles, dim) {
    let p = start;
    do {
        const a = p.prev;
        const 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) | 0);
            triangles.push((p.i / dim) | 0);
            triangles.push((b.i / dim) | 0);
            // remove two nodes involved
            removeNode(p);
            removeNode(p.next);
            p = start = b;
        }
        p = p.next;
    } while (p !== start);
    return filterPoints(p);
}
// try splitting polygon into two and triangulate them independently
function splitEarcut(start, triangles, dim, minX, minY, invSize) {
    // look for a valid diagonal that divides the polygon into two
    let a = start;
    do {
        let b = a.next.next;
        while (b !== a.prev) {
            if (a.i !== b.i && isValidDiagonal(a, b)) {
                // split the polygon in two by the diagonal
                let 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, invSize, 0);
                earcutLinked(c, triangles, dim, minX, minY, invSize, 0);
                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, areas, plane) {
    const queue = [];
    let i;
    let len;
    let start;
    let end;
    let 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, areas && areas[i + 1], plane);
        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++) {
        outerNode = eliminateHole(queue[i], outerNode);
    }
    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) {
    const bridge = findHoleBridge(hole, outerNode);
    if (!bridge) {
        return outerNode;
    }
    const bridgeReverse = splitPolygon(bridge, hole);
    // filter collinear points around the cuts
    filterPoints(bridgeReverse, bridgeReverse.next);
    return filterPoints(bridge, bridge.next);
}
// David Eberly's algorithm for finding a bridge between hole and outer polygon
function findHoleBridge(hole, outerNode) {
    let p = outerNode;
    const hx = hole.x;
    const hy = hole.y;
    let qx = -Infinity;
    let 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 && p.next.y !== p.y) {
            const x = p.x + ((hy - p.y) * (p.next.x - p.x)) / (p.next.y - p.y);
            if (x <= hx && x > qx) {
                qx = x;
                m = p.x < p.next.x ? p : p.next;
                if (x === hx)
                    return m; // hole touches outer segment; pick leftmost endpoint
            }
        }
        p = p.next;
    } while (p !== outerNode);
    if (!m)
        return null;
    // 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
    const stop = m;
    const mx = m.x;
    const my = m.y;
    let tanMin = Infinity;
    let tan;
    p = m;
    do {
        if (hx >= p.x &&
            p.x >= mx &&
            hx !== p.x &&
            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 (locallyInside(p, hole) &&
                (tan < tanMin ||
                    (tan === tanMin && (p.x > m.x || (p.x === m.x && sectorContainsSector(m, p)))))) {
                m = p;
                tanMin = tan;
            }
        }
        p = p.next;
    } while (p !== stop);
    return m;
}
// whether sector in vertex m contains sector in vertex p in the same coordinates
function sectorContainsSector(m, p) {
    return area(m.prev, m, p.prev) < 0 && area(p.next, m, m.next) < 0;
}
// interlink polygon nodes in z-order
function indexCurve(start, minX, minY, invSize) {
    let p = start;
    do {
        if (p.z === 0)
            p.z = zOrder(p.x, p.y, minX, minY, invSize);
        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) {
    let e;
    let i;
    let inSize = 1;
    let numMerges;
    let p;
    let pSize;
    let q;
    let qSize;
    let tail;
    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 && (qSize === 0 || !q || 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 inverse of the longer side of data bbox
function zOrder(x, y, minX, minY, invSize) {
    // coords are transformed into non-negative 15-bit integer range
    x = ((x - minX) * invSize) | 0;
    y = ((y - minY) * invSize) | 0;
    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) {
    let p = start;
    let leftmost = start;
    do {
        if (p.x < leftmost.x || (p.x === leftmost.x && p.y < leftmost.y))
            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) &&
        (ax - px) * (by - py) >= (bx - px) * (ay - py) &&
        (bx - px) * (cy - py) >= (cx - px) * (by - py));
}
// 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) && // dones't intersect other edges
        ((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) {
    const o1 = sign(area(p1, q1, p2));
    const o2 = sign(area(p1, q1, q2));
    const o3 = sign(area(p2, q2, p1));
    const 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) {
    let 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) {
    let p = a;
    let inside = false;
    const px = (a.x + b.x) / 2;
    const 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) {
    const a2 = new Vertex(a.i, a.x, a.y);
    const b2 = new Vertex(b.i, b.x, b.y);
    const an = a.next;
    const 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) {
    const p = new Vertex(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;
}
class Vertex {
    constructor(i, x, y) {
        // previous and next vertex nodes in a polygon ring
        this.prev = null;
        this.next = null;
        // z-order curve value
        this.z = 0;
        // previous and next nodes in z-order
        this.prevZ = null;
        this.nextZ = null;
        // indicates whether this is a steiner point
        this.steiner = false;
        this.i = i;
        this.x = x;
        this.y = y;
    }
}
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