backend/libs/three/extras/Earcut.js

/**
 * Port from https://github.com/mapbox/earcut (v2.2.2)
 */

const Earcut = {
	triangulate: function (data, holeIndices, dim = 2) {
		const hasHoles = holeIndices && holeIndices.length;
		const outerLen = hasHoles ? holeIndices[0] * dim : data.length;
		let outerNode = linkedList(data, 0, outerLen, dim, true);
		const triangles = [];

		if (!outerNode || outerNode.next === outerNode.prev) return triangles;

		let minX, minY, maxX, maxY, x, y, invSize;

		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 (let 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 invSize are later used to transform coords into integers for z-order calculation
			invSize = Math.max(maxX - minX, maxY - minY);
			invSize = invSize !== 0 ? 1 / invSize : 0;
		}

		earcutLinked(outerNode, triangles, dim, minX, minY, invSize);

		return triangles;
	},
};

// create a circular doubly linked list from polygon points in the specified winding order
function linkedList(data, start, end, dim, clockwise) {
	let 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;

	let 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) 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,
		prev,
		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);
			triangles.push(ear.i / dim);
			triangles.push(next.i / dim);

			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,
		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
	let 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, invSize) {
	const 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
	const 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;
	const minZ = zOrder(minTX, minTY, minX, minY, invSize),
		maxZ = zOrder(maxTX, maxTY, minX, minY, invSize);

	let p = ear.prevZ,
		n = ear.nextZ;

	// look for points inside the triangle in both directions
	while (p && p.z >= minZ && n && n.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.prevZ;

		if (n !== ear.prev && n !== ear.next && pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, 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 !== 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;
	}

	// look for remaining points in increasing z-order
	while (n && n.z <= maxZ) {
		if (n !== ear.prev && n !== ear.next && pointInTriangle(a.x, a.y, b.x, b.y, c.x, c.y, 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,
			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 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);
				earcutLinked(c, triangles, dim, minX, minY, invSize);
				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 = [];
	let 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) {
		const b = splitPolygon(outerNode, hole);

		// filter collinear points around the cuts
		filterPoints(outerNode, outerNode.next);
		filterPoints(b, b.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,
		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;
				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; // hole touches outer segment; pick leftmost 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

	const stop = m,
		mx = m.x,
		my = m.y;
	let tanMin = Infinity,
		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 === null) 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 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 && (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 = 32767 * (x - minX) * invSize;
	y = 32767 * (y - minY) * invSize;

	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,
		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) >= 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) && // 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,
		inside = false;
	const px = (a.x + b.x) / 2,
		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 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) {
	const 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) {
	// vertex index in coordinates array
	this.i = i;

	// vertex coordinates
	this.x = x;
	this.y = y;

	// previous and next vertex 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;
}

function signedArea(data, start, end, dim) {
	let sum = 0;
	for (let i = start, j = end - dim; i < end; i += dim) {
		sum += (data[j] - data[i]) * (data[i + 1] + data[j + 1]);
		j = i;
	}

	return sum;
}

export { Earcut };