File: //var/www/aspa/three/addons/math/ConvexHull.js
import {
Line3,
Plane,
Triangle,
Vector3
} from 'three';
/**
* Ported from: https://github.com/maurizzzio/quickhull3d/ by Mauricio Poppe (https://github.com/maurizzzio)
*/
const Visible = 0;
const Deleted = 1;
const _v1 = new Vector3();
const _line3 = new Line3();
const _plane = new Plane();
const _closestPoint = new Vector3();
const _triangle = new Triangle();
class ConvexHull {
constructor() {
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)
}
setFromPoints( points ) {
// The algorithm needs at least four points.
if ( points.length >= 4 ) {
this.makeEmpty();
for ( let i = 0, l = points.length; i < l; i ++ ) {
this.vertices.push( new VertexNode( points[ i ] ) );
}
this.compute();
}
return this;
}
setFromObject( object ) {
const points = [];
object.updateMatrixWorld( true );
object.traverse( function ( node ) {
const geometry = node.geometry;
if ( geometry !== undefined ) {
const attribute = geometry.attributes.position;
if ( attribute !== undefined ) {
for ( let i = 0, l = attribute.count; i < l; i ++ ) {
const point = new Vector3();
point.fromBufferAttribute( attribute, i ).applyMatrix4( node.matrixWorld );
points.push( point );
}
}
}
} );
return this.setFromPoints( points );
}
containsPoint( point ) {
const faces = this.faces;
for ( let i = 0, l = faces.length; i < l; i ++ ) {
const 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( ray, target ) {
// based on "Fast Ray-Convex Polyhedron Intersection" by Eric Haines, GRAPHICS GEMS II
const faces = this.faces;
let tNear = - Infinity;
let tFar = Infinity;
for ( let i = 0, l = faces.length; i < l; i ++ ) {
const face = faces[ i ];
// interpret faces as planes for the further computation
const vN = face.distanceToPoint( ray.origin );
const 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
const 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( ray ) {
return this.intersectRay( ray, _v1 ) !== null;
}
makeEmpty() {
this.faces = [];
this.vertices = [];
return this;
}
// Adds a vertex to the 'assigned' list of vertices and assigns it to the given face
addVertexToFace( 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( 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' vertex list
removeAllVerticesFromFace( face ) {
if ( face.outside !== null ) {
// reference to the first and last vertex of this face
const start = face.outside;
let 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( face, absorbingFace ) {
const 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
let 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
const nextVertex = vertex.next;
const 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( newFaces ) {
if ( this.unassigned.isEmpty() === false ) {
let vertex = this.unassigned.first();
do {
// buffer 'next' reference, see .deleteFaceVertices()
const nextVertex = vertex.next;
let maxDistance = this.tolerance;
let maxFace = null;
for ( let i = 0; i < newFaces.length; i ++ ) {
const face = newFaces[ i ];
if ( face.mark === Visible ) {
const 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() {
const min = new Vector3();
const max = new Vector3();
const minVertices = [];
const maxVertices = [];
// initially assume that the first vertex is the min/max
for ( let 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 ( let i = 0, l = this.vertices.length; i < l; i ++ ) {
const vertex = this.vertices[ i ];
const point = vertex.point;
// update the min coordinates
for ( let 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 ( let 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() {
const vertices = this.vertices;
const extremes = this.computeExtremes();
const min = extremes.min;
const max = extremes.max;
// 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)
let maxDistance = 0;
let index = 0;
for ( let i = 0; i < 3; i ++ ) {
const distance = max[ i ].point.getComponent( i ) - min[ i ].point.getComponent( i );
if ( distance > maxDistance ) {
maxDistance = distance;
index = i;
}
}
const v0 = min[ index ];
const v1 = max[ index ];
let v2;
let v3;
// 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 ( let i = 0, l = this.vertices.length; i < l; i ++ ) {
const vertex = vertices[ i ];
if ( vertex !== v0 && vertex !== v1 ) {
_line3.closestPointToPoint( vertex.point, true, _closestPoint );
const 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 ( let i = 0, l = this.vertices.length; i < l; i ++ ) {
const vertex = vertices[ i ];
if ( vertex !== v0 && vertex !== v1 && vertex !== v2 ) {
const distance = Math.abs( _plane.distanceToPoint( vertex.point ) );
if ( distance > maxDistance ) {
maxDistance = distance;
v3 = vertex;
}
}
}
const 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 ( let i = 0; i < 3; i ++ ) {
const 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 ( let i = 0; i < 3; i ++ ) {
const 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 ( let i = 0; i < 4; i ++ ) {
this.faces.push( faces[ i ] );
}
// initial assignment of vertices to the faces of the tetrahedron
for ( let i = 0, l = vertices.length; i < l; i ++ ) {
const vertex = vertices[ i ];
if ( vertex !== v0 && vertex !== v1 && vertex !== v2 && vertex !== v3 ) {
maxDistance = this.tolerance;
let maxFace = null;
for ( let j = 0; j < 4; j ++ ) {
const 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() {
const activeFaces = [];
for ( let i = 0; i < this.faces.length; i ++ ) {
const 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() {
// if the 'assigned' list of vertices is empty, no vertices are left. return with 'undefined'
if ( this.assigned.isEmpty() === false ) {
let eyeVertex, maxDistance = 0;
// grap the first available face and start with the first visible vertex of that face
const eyeFace = this.assigned.first().face;
let vertex = eyeFace.outside;
// now calculate the farthest vertex that face can see
do {
const 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( eyePoint, crossEdge, face, horizon ) {
// moves face's vertices to the 'unassigned' vertex list
this.deleteFaceVertices( face );
face.mark = Deleted;
let 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 {
const twinEdge = edge.twin;
const 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( eyeVertex, horizonEdge ) {
// all the half edges are created in ccw order thus the face is always pointing outside the hull
const 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( eyeVertex, horizon ) {
this.newFaces = [];
let firstSideEdge = null;
let previousSideEdge = null;
for ( let i = 0; i < horizon.length; i ++ ) {
const horizonEdge = horizon[ i ];
// returns the right side edge
const 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( eyeVertex ) {
const 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() {
this.assigned.clear();
this.unassigned.clear();
this.newFaces = [];
return this;
}
compute() {
let 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;
}
}
//
class Face {
constructor() {
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;
}
static create( a, b, c ) {
const face = new Face();
const e0 = new HalfEdge( a, face );
const e1 = new HalfEdge( b, face );
const 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();
}
getEdge( i ) {
let edge = this.edge;
while ( i > 0 ) {
edge = edge.next;
i --;
}
while ( i < 0 ) {
edge = edge.prev;
i ++;
}
return edge;
}
compute() {
const a = this.edge.tail();
const b = this.edge.head();
const 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( point ) {
return this.normal.dot( point ) - this.constant;
}
}
// Entity for a Doubly-Connected Edge List (DCEL).
class HalfEdge {
constructor( vertex, face ) {
this.vertex = vertex;
this.prev = null;
this.next = null;
this.twin = null;
this.face = face;
}
head() {
return this.vertex;
}
tail() {
return this.prev ? this.prev.vertex : null;
}
length() {
const head = this.head();
const tail = this.tail();
if ( tail !== null ) {
return tail.point.distanceTo( head.point );
}
return - 1;
}
lengthSquared() {
const head = this.head();
const tail = this.tail();
if ( tail !== null ) {
return tail.point.distanceToSquared( head.point );
}
return - 1;
}
setTwin( edge ) {
this.twin = edge;
edge.twin = this;
return this;
}
}
// A vertex as a double linked list node.
class VertexNode {
constructor( 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.
class VertexList {
constructor() {
this.head = null;
this.tail = null;
}
first() {
return this.head;
}
last() {
return this.tail;
}
clear() {
this.head = this.tail = null;
return this;
}
// Inserts a vertex before the target vertex
insertBefore( 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( 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( 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( 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( 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( 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() {
return this.head === null;
}
}
export { ConvexHull, Face, HalfEdge, VertexNode, VertexList };