ConvexHull.js

import {
	Line3,
	Plane,
	Triangle,
	Vector3
} from 'three';
/**
 * Ported from: https://github.com/maurizzzio/quickhull3d/ by Mauricio Poppe (https://github.com/maurizzzio)
 */

var ConvexHull = ( function () {

	var Visible = 0;
	var Deleted = 1;

	var v1 = new Vector3();

	function ConvexHull() {

		this.tolerance = - 1;

		this.faces = []; // the generated faces of the convex hull
		this.newFaces = []; // this array holds the faces that are generated within a single iteration

		// the vertex lists work as follows:
		//
		// let 'a' and 'b' be 'Face' instances
		// let 'v' be points wrapped as instance of 'Vertex'
		//
		//     [v, v, ..., v, v, v, ...]
		//      ^             ^
		//      |             |
		//  a.outside     b.outside
		//
		this.assigned = new VertexList();
		this.unassigned = new VertexList();

		this.vertices = []; 	// vertices of the hull (internal representation of given geometry data)

	}

	Object.assign( ConvexHull.prototype, {

		toJSON: function () {
			// Original ('src') indices do not include interior vertices,
			// but 'this.vertices' (the list they index) does. Output ('dst')
			// arrays have interior vertices omitted.

			const srcIndices = this.faces.map((f) => f.toArray());
			const uniqueSrcIndices = Array.from(new Set(srcIndices.flat())).sort();

			// Output vertex positions, omitting interior vertices.
			const dstPositions = [];
			for (let i = 0; i < uniqueSrcIndices.length; i++) {
				dstPositions.push(
					this.vertices[uniqueSrcIndices[i]].point.x,
					this.vertices[uniqueSrcIndices[i]].point.y,
					this.vertices[uniqueSrcIndices[i]].point.z,
				);
			}

			// Mapping from 'src' (this.vertices) to 'dst' (dstPositions) indices.
			const srcToDstIndexMap = new Map();
			for (let i = 0; i < uniqueSrcIndices.length; i++) {
				srcToDstIndexMap.set(uniqueSrcIndices[i], i);
			}

			// Output triangles, as indices on dstPositions.
			const dstIndices = [];
			for (let i = 0; i < srcIndices.length; i++) {
				dstIndices.push([
					srcToDstIndexMap.get(srcIndices[i][0]),
					srcToDstIndexMap.get(srcIndices[i][1]),
					srcToDstIndexMap.get(srcIndices[i][2]),
				]);
			}

			return [dstPositions, dstIndices];
		},

		setFromPoints: function ( points ) {

			if ( Array.isArray( points ) !== true ) {

				console.error( 'THREE.ConvexHull: Points parameter is not an array.' );

			}

			if ( points.length < 4 ) {

				console.error( 'THREE.ConvexHull: The algorithm needs at least four points.' );

			}

			this.makeEmpty();

			for ( var i = 0, l = points.length; i < l; i ++ ) {

				this.vertices.push( new VertexNode( points[ i ], i ) );

			}

			this.compute();

			return this;

		},

		setFromObject: function ( object ) {

			var points = [];

			object.updateMatrixWorld( true );

			object.traverse( function ( node ) {

				var i, l, point;

				var geometry = node.geometry;

				if ( geometry === undefined ) return;

				if ( geometry.isGeometry ) {

					geometry = geometry.toBufferGeometry
						? geometry.toBufferGeometry()
						: new BufferGeometry().fromGeometry( geometry );

				}

				if ( geometry.isBufferGeometry ) {

					var attribute = geometry.attributes.position;

					if ( attribute !== undefined ) {

						for ( i = 0, l = attribute.count; i < l; i ++ ) {

							point = new Vector3();

							point.fromBufferAttribute( attribute, i ).applyMatrix4( node.matrixWorld );

							points.push( point );

						}

					}

				}

			} );

			return this.setFromPoints( points );

		},

		containsPoint: function ( point ) {

			var faces = this.faces;

			for ( var i = 0, l = faces.length; i < l; i ++ ) {

				var face = faces[ i ];

				// compute signed distance and check on what half space the point lies

				if ( face.distanceToPoint( point ) > this.tolerance ) return false;

			}

			return true;

		},

		intersectRay: function ( ray, target ) {

			// based on "Fast Ray-Convex Polyhedron Intersection"  by Eric Haines, GRAPHICS GEMS II

			var faces = this.faces;

			var tNear = - Infinity;
			var tFar = Infinity;

			for ( var i = 0, l = faces.length; i < l; i ++ ) {

				var face = faces[ i ];

				// interpret faces as planes for the further computation

				var vN = face.distanceToPoint( ray.origin );
				var vD = face.normal.dot( ray.direction );

				// if the origin is on the positive side of a plane (so the plane can "see" the origin) and
				// the ray is turned away or parallel to the plane, there is no intersection

				if ( vN > 0 && vD >= 0 ) return null;

				// compute the distance from the ray’s origin to the intersection with the plane

				var t = ( vD !== 0 ) ? ( - vN / vD ) : 0;

				// only proceed if the distance is positive. a negative distance means the intersection point
				// lies "behind" the origin

				if ( t <= 0 ) continue;

				// now categorized plane as front-facing or back-facing

				if ( vD > 0 ) {

					//  plane faces away from the ray, so this plane is a back-face

					tFar = Math.min( t, tFar );

				} else {

					// front-face

					tNear = Math.max( t, tNear );

				}

				if ( tNear > tFar ) {

					// if tNear ever is greater than tFar, the ray must miss the convex hull

					return null;

				}

			}

			// evaluate intersection point

			// always try tNear first since its the closer intersection point

			if ( tNear !== - Infinity ) {

				ray.at( tNear, target );

			} else {

				ray.at( tFar, target );

			}

			return target;

		},

		intersectsRay: function ( ray ) {

			return this.intersectRay( ray, v1 ) !== null;

		},

		makeEmpty: function () {

			this.faces = [];
			this.vertices = [];

			return this;

		},

		// Adds a vertex to the 'assigned' list of vertices and assigns it to the given face

		addVertexToFace: function ( vertex, face ) {

			vertex.face = face;

			if ( face.outside === null ) {

				this.assigned.append( vertex );

			} else {

				this.assigned.insertBefore( face.outside, vertex );

			}

			face.outside = vertex;

			return this;

		},

		// Removes a vertex from the 'assigned' list of vertices and from the given face

		removeVertexFromFace: function ( vertex, face ) {

			if ( vertex === face.outside ) {

				// fix face.outside link

				if ( vertex.next !== null && vertex.next.face === face ) {

					// face has at least 2 outside vertices, move the 'outside' reference

					face.outside = vertex.next;

				} else {

					// vertex was the only outside vertex that face had

					face.outside = null;

				}

			}

			this.assigned.remove( vertex );

			return this;

		},

		// Removes all the visible vertices that a given face is able to see which are stored in the 'assigned' vertext list

		removeAllVerticesFromFace: function ( face ) {

			if ( face.outside !== null ) {

				// reference to the first and last vertex of this face

				var start = face.outside;
				var end = face.outside;

				while ( end.next !== null && end.next.face === face ) {

					end = end.next;

				}

				this.assigned.removeSubList( start, end );

				// fix references

				start.prev = end.next = null;
				face.outside = null;

				return start;

			}

		},

		// Removes all the visible vertices that 'face' is able to see

		deleteFaceVertices: function ( face, absorbingFace ) {

			var faceVertices = this.removeAllVerticesFromFace( face );

			if ( faceVertices !== undefined ) {

				if ( absorbingFace === undefined ) {

					// mark the vertices to be reassigned to some other face

					this.unassigned.appendChain( faceVertices );


				} else {

					// if there's an absorbing face try to assign as many vertices as possible to it

					var vertex = faceVertices;

					do {

						// we need to buffer the subsequent vertex at this point because the 'vertex.next' reference
						// will be changed by upcoming method calls

						var nextVertex = vertex.next;

						var distance = absorbingFace.distanceToPoint( vertex.point );

						// check if 'vertex' is able to see 'absorbingFace'

						if ( distance > this.tolerance ) {

							this.addVertexToFace( vertex, absorbingFace );

						} else {

							this.unassigned.append( vertex );

						}

						// now assign next vertex

						vertex = nextVertex;

					} while ( vertex !== null );

				}

			}

			return this;

		},

		// Reassigns as many vertices as possible from the unassigned list to the new faces

		resolveUnassignedPoints: function ( newFaces ) {

			if ( this.unassigned.isEmpty() === false ) {

				var vertex = this.unassigned.first();

				do {

					// buffer 'next' reference, see .deleteFaceVertices()

					var nextVertex = vertex.next;

					var maxDistance = this.tolerance;

					var maxFace = null;

					for ( var i = 0; i < newFaces.length; i ++ ) {

						var face = newFaces[ i ];

						if ( face.mark === Visible ) {

							var distance = face.distanceToPoint( vertex.point );

							if ( distance > maxDistance ) {

								maxDistance = distance;
								maxFace = face;

							}

							if ( maxDistance > 1000 * this.tolerance ) break;

						}

					}

					// 'maxFace' can be null e.g. if there are identical vertices

					if ( maxFace !== null ) {

						this.addVertexToFace( vertex, maxFace );

					}

					vertex = nextVertex;

				} while ( vertex !== null );

			}

			return this;

		},

		// Computes the extremes of a simplex which will be the initial hull

		computeExtremes: function () {

			var min = new Vector3();
			var max = new Vector3();

			var minVertices = [];
			var maxVertices = [];

			var i, l, j;

			// initially assume that the first vertex is the min/max

			for ( i = 0; i < 3; i ++ ) {

				minVertices[ i ] = maxVertices[ i ] = this.vertices[ 0 ];

			}

			min.copy( this.vertices[ 0 ].point );
			max.copy( this.vertices[ 0 ].point );

			// compute the min/max vertex on all six directions

			for ( i = 0, l = this.vertices.length; i < l; i ++ ) {

				var vertex = this.vertices[ i ];
				var point = vertex.point;

				// update the min coordinates

				for ( j = 0; j < 3; j ++ ) {

					if ( point.getComponent( j ) < min.getComponent( j ) ) {

						min.setComponent( j, point.getComponent( j ) );
						minVertices[ j ] = vertex;

					}

				}

				// update the max coordinates

				for ( j = 0; j < 3; j ++ ) {

					if ( point.getComponent( j ) > max.getComponent( j ) ) {

						max.setComponent( j, point.getComponent( j ) );
						maxVertices[ j ] = vertex;

					}

				}

			}

			// use min/max vectors to compute an optimal epsilon

			this.tolerance = 3 * Number.EPSILON * (
				Math.max( Math.abs( min.x ), Math.abs( max.x ) ) +
				Math.max( Math.abs( min.y ), Math.abs( max.y ) ) +
				Math.max( Math.abs( min.z ), Math.abs( max.z ) )
			);

			return { min: minVertices, max: maxVertices };

		},

		// Computes the initial simplex assigning to its faces all the points
		// that are candidates to form part of the hull

		computeInitialHull: function () {

			var line3, plane, closestPoint;

			return function computeInitialHull() {

				if ( line3 === undefined ) {

					line3 = new Line3();
					plane = new Plane();
					closestPoint = new Vector3();

				}

				var vertex, vertices = this.vertices;
				var extremes = this.computeExtremes();
				var min = extremes.min;
				var max = extremes.max;

				var v0, v1, v2, v3;
				var i, l, j;

				// 1. Find the two vertices 'v0' and 'v1' with the greatest 1d separation
				// (max.x - min.x)
				// (max.y - min.y)
				// (max.z - min.z)

				var distance, maxDistance = 0;
				var index = 0;

				for ( i = 0; i < 3; i ++ ) {

					distance = max[ i ].point.getComponent( i ) - min[ i ].point.getComponent( i );

					if ( distance > maxDistance ) {

						maxDistance = distance;
						index = i;

					}

				}

				v0 = min[ index ];
				v1 = max[ index ];

				// 2. The next vertex 'v2' is the one farthest to the line formed by 'v0' and 'v1'

				maxDistance = 0;
				line3.set( v0.point, v1.point );

				for ( i = 0, l = this.vertices.length; i < l; i ++ ) {

					vertex = vertices[ i ];

					if ( vertex !== v0 && vertex !== v1 ) {

						line3.closestPointToPoint( vertex.point, true, closestPoint );

						distance = closestPoint.distanceToSquared( vertex.point );

						if ( distance > maxDistance ) {

							maxDistance = distance;
							v2 = vertex;

						}

					}

				}

				// 3. The next vertex 'v3' is the one farthest to the plane 'v0', 'v1', 'v2'

				maxDistance = - 1;
				plane.setFromCoplanarPoints( v0.point, v1.point, v2.point );

				for ( i = 0, l = this.vertices.length; i < l; i ++ ) {

					vertex = vertices[ i ];

					if ( vertex !== v0 && vertex !== v1 && vertex !== v2 ) {

						distance = Math.abs( plane.distanceToPoint( vertex.point ) );

						if ( distance > maxDistance ) {

							maxDistance = distance;
							v3 = vertex;

						}

					}

				}

				var faces = [];

				if ( plane.distanceToPoint( v3.point ) < 0 ) {

					// the face is not able to see the point so 'plane.normal' is pointing outside the tetrahedron

					faces.push(
						Face.create( v0, v1, v2 ),
						Face.create( v3, v1, v0 ),
						Face.create( v3, v2, v1 ),
						Face.create( v3, v0, v2 )
					);

					// set the twin edge

					for ( i = 0; i < 3; i ++ ) {

						j = ( i + 1 ) % 3;

						// join face[ i ] i > 0, with the first face

						faces[ i + 1 ].getEdge( 2 ).setTwin( faces[ 0 ].getEdge( j ) );

						// join face[ i ] with face[ i + 1 ], 1 <= i <= 3

						faces[ i + 1 ].getEdge( 1 ).setTwin( faces[ j + 1 ].getEdge( 0 ) );

					}

				} else {

					// the face is able to see the point so 'plane.normal' is pointing inside the tetrahedron

					faces.push(
						Face.create( v0, v2, v1 ),
						Face.create( v3, v0, v1 ),
						Face.create( v3, v1, v2 ),
						Face.create( v3, v2, v0 )
					);

					// set the twin edge

					for ( i = 0; i < 3; i ++ ) {

						j = ( i + 1 ) % 3;

						// join face[ i ] i > 0, with the first face

						faces[ i + 1 ].getEdge( 2 ).setTwin( faces[ 0 ].getEdge( ( 3 - i ) % 3 ) );

						// join face[ i ] with face[ i + 1 ]

						faces[ i + 1 ].getEdge( 0 ).setTwin( faces[ j + 1 ].getEdge( 1 ) );

					}

				}

				// the initial hull is the tetrahedron

				for ( i = 0; i < 4; i ++ ) {

					this.faces.push( faces[ i ] );

				}

				// initial assignment of vertices to the faces of the tetrahedron

				for ( i = 0, l = vertices.length; i < l; i ++ ) {

					vertex = vertices[ i ];

					if ( vertex !== v0 && vertex !== v1 && vertex !== v2 && vertex !== v3 ) {

						maxDistance = this.tolerance;
						var maxFace = null;

						for ( j = 0; j < 4; j ++ ) {

							distance = this.faces[ j ].distanceToPoint( vertex.point );

							if ( distance > maxDistance ) {

								maxDistance = distance;
								maxFace = this.faces[ j ];

							}

						}

						if ( maxFace !== null ) {

							this.addVertexToFace( vertex, maxFace );

						}

					}

				}

				return this;

			};

		}(),

		// Removes inactive faces

		reindexFaces: function () {

			var activeFaces = [];

			for ( var i = 0; i < this.faces.length; i ++ ) {

				var face = this.faces[ i ];

				if ( face.mark === Visible ) {

					activeFaces.push( face );

				}

			}

			this.faces = activeFaces;

			return this;

		},

		// Finds the next vertex to create faces with the current hull

		nextVertexToAdd: function () {

			// if the 'assigned' list of vertices is empty, no vertices are left. return with 'undefined'

			if ( this.assigned.isEmpty() === false ) {

				var eyeVertex, maxDistance = 0;

				// grap the first available face and start with the first visible vertex of that face

				var eyeFace = this.assigned.first().face;
				var vertex = eyeFace.outside;

				// now calculate the farthest vertex that face can see

				do {

					var distance = eyeFace.distanceToPoint( vertex.point );

					if ( distance > maxDistance ) {

						maxDistance = distance;
						eyeVertex = vertex;

					}

					vertex = vertex.next;

				} while ( vertex !== null && vertex.face === eyeFace );

				return eyeVertex;

			}

		},

		// Computes a chain of half edges in CCW order called the 'horizon'.
		// For an edge to be part of the horizon it must join a face that can see
		// 'eyePoint' and a face that cannot see 'eyePoint'.

		computeHorizon: function ( eyePoint, crossEdge, face, horizon ) {

			// moves face's vertices to the 'unassigned' vertex list

			this.deleteFaceVertices( face );

			face.mark = Deleted;

			var edge;

			if ( crossEdge === null ) {

				edge = crossEdge = face.getEdge( 0 );

			} else {

				// start from the next edge since 'crossEdge' was already analyzed
				// (actually 'crossEdge.twin' was the edge who called this method recursively)

				edge = crossEdge.next;

			}

			do {

				var twinEdge = edge.twin;
				var oppositeFace = twinEdge.face;

				if ( oppositeFace.mark === Visible ) {

					if ( oppositeFace.distanceToPoint( eyePoint ) > this.tolerance ) {

						// the opposite face can see the vertex, so proceed with next edge

						this.computeHorizon( eyePoint, twinEdge, oppositeFace, horizon );

					} else {

						// the opposite face can't see the vertex, so this edge is part of the horizon

						horizon.push( edge );

					}

				}

				edge = edge.next;

			} while ( edge !== crossEdge );

			return this;

		},

		// Creates a face with the vertices 'eyeVertex.point', 'horizonEdge.tail' and 'horizonEdge.head' in CCW order

		addAdjoiningFace: function ( eyeVertex, horizonEdge ) {

			// all the half edges are created in ccw order thus the face is always pointing outside the hull

			var face = Face.create( eyeVertex, horizonEdge.tail(), horizonEdge.head() );

			this.faces.push( face );

			// join face.getEdge( - 1 ) with the horizon's opposite edge face.getEdge( - 1 ) = face.getEdge( 2 )

			face.getEdge( - 1 ).setTwin( horizonEdge.twin );

			return face.getEdge( 0 ); // the half edge whose vertex is the eyeVertex


		},

		//  Adds 'horizon.length' faces to the hull, each face will be linked with the
		//  horizon opposite face and the face on the left/right

		addNewFaces: function ( eyeVertex, horizon ) {

			this.newFaces = [];

			var firstSideEdge = null;
			var previousSideEdge = null;

			for ( var i = 0; i < horizon.length; i ++ ) {

				var horizonEdge = horizon[ i ];

				// returns the right side edge

				var sideEdge = this.addAdjoiningFace( eyeVertex, horizonEdge );

				if ( firstSideEdge === null ) {

					firstSideEdge = sideEdge;

				} else {

					// joins face.getEdge( 1 ) with previousFace.getEdge( 0 )

					sideEdge.next.setTwin( previousSideEdge );

				}

				this.newFaces.push( sideEdge.face );
				previousSideEdge = sideEdge;

			}

			// perform final join of new faces

			firstSideEdge.next.setTwin( previousSideEdge );

			return this;

		},

		// Adds a vertex to the hull

		addVertexToHull: function ( eyeVertex ) {

			var horizon = [];

			this.unassigned.clear();

			// remove 'eyeVertex' from 'eyeVertex.face' so that it can't be added to the 'unassigned' vertex list

			this.removeVertexFromFace( eyeVertex, eyeVertex.face );

			this.computeHorizon( eyeVertex.point, null, eyeVertex.face, horizon );

			this.addNewFaces( eyeVertex, horizon );

			// reassign 'unassigned' vertices to the new faces

			this.resolveUnassignedPoints( this.newFaces );

			return	this;

		},

		cleanup: function () {

			this.assigned.clear();
			this.unassigned.clear();
			this.newFaces = [];

			return this;

		},

		compute: function () {

			var vertex;

			this.computeInitialHull();

			// add all available vertices gradually to the hull

			while ( ( vertex = this.nextVertexToAdd() ) !== undefined ) {

				this.addVertexToHull( vertex );

			}

			this.reindexFaces();

			this.cleanup();

			return this;

		}

	} );

	//

	function Face() {

		this.normal = new Vector3();
		this.midpoint = new Vector3();
		this.area = 0;

		this.constant = 0; // signed distance from face to the origin
		this.outside = null; // reference to a vertex in a vertex list this face can see
		this.mark = Visible;
		this.edge = null;

	}

	Object.assign( Face, {

		create: function ( a, b, c ) {

			var face = new Face();

			var e0 = new HalfEdge( a, face );
			var e1 = new HalfEdge( b, face );
			var e2 = new HalfEdge( c, face );

			// join edges

			e0.next = e2.prev = e1;
			e1.next = e0.prev = e2;
			e2.next = e1.prev = e0;

			// main half edge reference

			face.edge = e0;

			return face.compute();

		}

	} );

	Object.assign( Face.prototype, {

		toArray: function () {
			const indices = [];
			let edge = this.edge;
			do {
				indices.push(edge.head().index);
				edge = edge.next;
			} while (edge !== this.edge);
			return indices;
		},

		getEdge: function ( i ) {

			var edge = this.edge;

			while ( i > 0 ) {

				edge = edge.next;
				i --;

			}

			while ( i < 0 ) {

				edge = edge.prev;
				i ++;

			}

			return edge;

		},

		compute: function () {

			var triangle;

			return function compute() {

				if ( triangle === undefined ) triangle = new Triangle();

				var a = this.edge.tail();
				var b = this.edge.head();
				var c = this.edge.next.head();

				triangle.set( a.point, b.point, c.point );

				triangle.getNormal( this.normal );
				triangle.getMidpoint( this.midpoint );
				this.area = triangle.getArea();

				this.constant = this.normal.dot( this.midpoint );

				return this;

			};

		}(),

		distanceToPoint: function ( point ) {

			return this.normal.dot( point ) - this.constant;

		}

	} );

	// Entity for a Doubly-Connected Edge List (DCEL).

	function HalfEdge( vertex, face ) {

		this.vertex = vertex;
		this.prev = null;
		this.next = null;
		this.twin = null;
		this.face = face;

	}

	Object.assign( HalfEdge.prototype, {

		head: function () {

			return this.vertex;

		},

		tail: function () {

			return this.prev ? this.prev.vertex : null;

		},

		length: function () {

			var head = this.head();
			var tail = this.tail();

			if ( tail !== null ) {

				return tail.point.distanceTo( head.point );

			}

			return - 1;

		},

		lengthSquared: function () {

			var head = this.head();
			var tail = this.tail();

			if ( tail !== null ) {

				return tail.point.distanceToSquared( head.point );

			}

			return - 1;

		},

		setTwin: function ( edge ) {

			this.twin = edge;
			edge.twin = this;

			return this;

		}

	} );

	// A vertex as a double linked list node.

	function VertexNode( point, index ) {

		this.point = point;
		// index in the input array
		this.index = index;
		this.prev = null;
		this.next = null;
		// the face that is able to see this vertex
		this.face = null;

	}

	// A double linked list that contains vertex nodes.

	function VertexList() {

		this.head = null;
		this.tail = null;

	}

	Object.assign( VertexList.prototype, {

		first: function () {

			return this.head;

		},

		last: function () {

			return this.tail;

		},

		clear: function () {

			this.head = this.tail = null;

			return this;

		},

		// Inserts a vertex before the target vertex

		insertBefore: function ( target, vertex ) {

			vertex.prev = target.prev;
			vertex.next = target;

			if ( vertex.prev === null ) {

				this.head = vertex;

			} else {

				vertex.prev.next = vertex;

			}

			target.prev = vertex;

			return this;

		},

		// Inserts a vertex after the target vertex

		insertAfter: function ( target, vertex ) {

			vertex.prev = target;
			vertex.next = target.next;

			if ( vertex.next === null ) {

				this.tail = vertex;

			} else {

				vertex.next.prev = vertex;

			}

			target.next = vertex;

			return this;

		},

		// Appends a vertex to the end of the linked list

		append: function ( vertex ) {

			if ( this.head === null ) {

				this.head = vertex;

			} else {

				this.tail.next = vertex;

			}

			vertex.prev = this.tail;
			vertex.next = null; // the tail has no subsequent vertex

			this.tail = vertex;

			return this;

		},

		// Appends a chain of vertices where 'vertex' is the head.

		appendChain: function ( vertex ) {

			if ( this.head === null ) {

				this.head = vertex;

			} else {

				this.tail.next = vertex;

			}

			vertex.prev = this.tail;

			// ensure that the 'tail' reference points to the last vertex of the chain

			while ( vertex.next !== null ) {

				vertex = vertex.next;

			}

			this.tail = vertex;

			return this;

		},

		// Removes a vertex from the linked list

		remove: function ( vertex ) {

			if ( vertex.prev === null ) {

				this.head = vertex.next;

			} else {

				vertex.prev.next = vertex.next;

			}

			if ( vertex.next === null ) {

				this.tail = vertex.prev;

			} else {

				vertex.next.prev = vertex.prev;

			}

			return this;

		},

		// Removes a list of vertices whose 'head' is 'a' and whose 'tail' is b

		removeSubList: function ( a, b ) {

			if ( a.prev === null ) {

				this.head = b.next;

			} else {

				a.prev.next = b.next;

			}

			if ( b.next === null ) {

				this.tail = a.prev;

			} else {

				b.next.prev = a.prev;

			}

			return this;

		},

		isEmpty: function () {

			return this.head === null;

		}

	} );

	return ConvexHull;

} )();

export { ConvexHull };