three.js/examples/js/math/ConvexHull.js

( function () {

	/**
 * 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 THREE.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, {
			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 ] ) );

				}

				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 ) {

						if ( geometry.isGeometry ) {

							console.error( 'THREE.ConvexHull no longer supports Geometry. Use THREE.BufferGeometry instead.' );
							return;

						} else if ( geometry.isBufferGeometry ) {

							var attribute = geometry.attributes.position;

							if ( attribute !== undefined ) {

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

									point = new THREE.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 THREE.Vector3();
				var max = new THREE.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 THREE.Line3();
						plane = new THREE.Plane();
						closestPoint = new THREE.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 THREE.Vector3();
			this.midpoint = new THREE.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, {
			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 THREE.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 ) {

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

		} // 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;

	}();

	THREE.ConvexHull = ConvexHull;

} )();