Spaces:
Running
Running
/** | |
* @author Mugen87 / https://github.com/Mugen87 | |
* | |
* Ported from: https://github.com/maurizzzio/quickhull3d/ by Mauricio Poppe (https://github.com/maurizzzio) | |
* | |
*/ | |
( function () { | |
var Visible = 0; | |
var Deleted = 1; | |
function QuickHull() { | |
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( QuickHull.prototype, { | |
setFromPoints: function ( points ) { | |
if ( Array.isArray( points ) !== true ) { | |
console.error( 'THREE.QuickHull: Points parameter is not an array.' ); | |
} | |
if ( points.length < 4 ) { | |
console.error( 'THREE.QuickHull: 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 ) { | |
var vertices = geometry.vertices; | |
for ( i = 0, l = vertices.length; i < l; i ++ ) { | |
point = vertices[ i ].clone(); | |
point.applyMatrix4( node.matrixWorld ); | |
points.push( point ); | |
} | |
} 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 ); | |
}, | |
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; | |
} | |
} ); | |
// export | |
THREE.QuickHull = QuickHull; | |
} )(); | |