three.js/src/extras/Earcut.js

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

const Earcut = {

	triangulate: function ( data, holeIndices, dim ) {

		dim = 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 };