<!-- NEW2 — TEST 2 · THE DISTRICT OF 800 · part 180 -->

            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) {
    const queue = [];

    for (let i = 0, len = holeIndices.length; i < len; i++) {
        const start = holeIndices[i] * dim;
        const end = i < len - 1 ? holeIndices[i + 1] * dim : data.length;
        const list = linkedList(data, start, end, dim, false);
        if (list === list.next) list.steiner = true;
        queue.push(getLeftmost(list));
    }

    queue.sort(compareXYSlope);

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

    return outerNode;
}

function compareXYSlope(a, b) {
    let result = a.x - b.x;
    // when the left-most point of 2 holes meet at a vertex, sort the holes counterclockwise so that when we find
    // the bridge to the outer shell is always the point that they meet at.
    if (result === 0) {
        result = a.y - b.y;
        if (result === 0) {
            const aSlope = (a.next.y - a.y) / (a.next.x - a.x);
            const bSlope = (b.next.y - b.y) / (b.next.x - b.x);
            result = aSlope - bSlope;
        }
    }
    return result;
}

// find a bridge between vertices that connects hole with an outer ring 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
    // unless they intersect at a vertex, then choose the vertex
    if (equals(hole, p)) return p;
    do {
        if (equals(hole, p.next)) return p.next;
        else 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;

    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)) {

            const 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 numMerges;
    let inSize = 1;

    do {