ConvexGeometry class
class ConvexGeometry extends Geometry { ConvexGeometry(List vertices) : super() { var faces = [ [ 0, 1, 2 ], [ 0, 2, 1 ] ]; var addPoint = ( vertexId ) { var vertex = vertices[ vertexId ].clone(); var mag = vertex.length(); vertex.x += mag * _randomOffset(); vertex.y += mag * _randomOffset(); vertex.z += mag * _randomOffset(); List hole = []; for ( var f = 0; f < faces.length; ) { var face = faces[ f ]; // for each face, if the vertex can see it, // then we try to add the face's edges into the hole. if ( _visible( face, vertex ) ) { for ( var e = 0; e < 3; e++ ) { var edge = [ face[ e ], face[ ( e + 1 ) % 3 ] ]; var boundary = true; // remove duplicated edges. for ( var h = 0; h < hole.length; h++ ) { if ( _equalEdge( hole[ h ], edge ) ) { hole[ h ] = hole[ hole.length - 1 ]; hole.removeLast(); boundary = false; break; } } if ( boundary ) { hole.add( edge ); } } // remove faces[ f ] faces[ f ] = faces[ faces.length - 1 ]; faces.removeLast(); } else { // not visible f++; } } // construct the new faces formed by the edges of the hole and the vertex for ( var h = 0; h < hole.length; h++ ) { faces.add( [ hole[ h ][ 0 ], hole[ h ][ 1 ], vertexId ] ); } }; for ( var i = 3; i < vertices.length; i++ ) { addPoint( i ); } // Push vertices into `this.vertices`, skipping those inside the hull var id = 0; var newId = new List(vertices.length); // map from old vertex id to new id for ( var i = 0; i < faces.length; i++ ) { var face = faces[ i ]; for ( var j = 0; j < 3; j++ ) { if ( newId[ face[ j ] ] == null ) { newId[ face[ j ] ] = id++; this.vertices.add( vertices[ face[ j ] ] ); } face[ j ] = newId[ face[ j ] ]; } } // Convert faces into instances of THREE.Face3 for ( var i = 0; i < faces.length; i++ ) { this.faces.add( new Face3( faces[ i ][ 0 ], faces[ i ][ 1 ], faces[ i ][ 2 ] ) ); } // Compute UVs for ( var i = 0; i < this.faces.length; i++ ) { var face = this.faces[ i ]; this.faceVertexUvs[ 0 ].add( [ _vertexUv( this.vertices[ face.a ] ), _vertexUv( this.vertices[ face.b ] ), _vertexUv( this.vertices[ face.c ]) ] ); } this.computeCentroids(); this.computeFaceNormals(); this.computeVertexNormals(); } /** * Whether the face is visible from the vertex */ _visible( face, vertex ) { var va = vertices[ face[ 0 ] ]; var vb = vertices[ face[ 1 ] ]; var vc = vertices[ face[ 2 ] ]; var n = _normal( va, vb, vc ); // distance from face to origin var dist = n.dot( va ); return n.dot( vertex ) >= dist; } /** * Face normal */ _normal( va, vb, vc ) { Vector3 cb = new Vector3.zero(); Vector3 ab = new Vector3.zero(); cb = vc - vb; ab = va - vb; cb = cb.cross( ab ); cb.normalize(); return cb; } /** * Detect whether two edges are equal. * Note that when constructing the convex hull, two same edges can only * be of the negative direction. */ _equalEdge( ea, eb ) => ea[ 0 ] == eb[ 1 ] && ea[ 1 ] == eb[ 0 ]; /** * Create a random offset between -1e-6 and 1e-6. */ _randomOffset() => ( new Math.Random().nextDouble() - 0.5 ) * 2 * 1e-6; /** * XXX: Not sure if this is the correct approach. Need someone to review. */ _vertexUv( vertex ) { var mag = vertex.length(); return new UV( vertex.x / mag, vertex.y / mag ); } }
Extends
Geometry > ConvexGeometry
Constructors
new ConvexGeometry(List vertices) #
Creates a new Object instance.
Object instances have no meaningful state, and are only useful through their identity. An Object instance is equal to itself only.
docs inherited from Object
ConvexGeometry(List vertices) : super() { var faces = [ [ 0, 1, 2 ], [ 0, 2, 1 ] ]; var addPoint = ( vertexId ) { var vertex = vertices[ vertexId ].clone(); var mag = vertex.length(); vertex.x += mag * _randomOffset(); vertex.y += mag * _randomOffset(); vertex.z += mag * _randomOffset(); List hole = []; for ( var f = 0; f < faces.length; ) { var face = faces[ f ]; // for each face, if the vertex can see it, // then we try to add the face's edges into the hole. if ( _visible( face, vertex ) ) { for ( var e = 0; e < 3; e++ ) { var edge = [ face[ e ], face[ ( e + 1 ) % 3 ] ]; var boundary = true; // remove duplicated edges. for ( var h = 0; h < hole.length; h++ ) { if ( _equalEdge( hole[ h ], edge ) ) { hole[ h ] = hole[ hole.length - 1 ]; hole.removeLast(); boundary = false; break; } } if ( boundary ) { hole.add( edge ); } } // remove faces[ f ] faces[ f ] = faces[ faces.length - 1 ]; faces.removeLast(); } else { // not visible f++; } } // construct the new faces formed by the edges of the hole and the vertex for ( var h = 0; h < hole.length; h++ ) { faces.add( [ hole[ h ][ 0 ], hole[ h ][ 1 ], vertexId ] ); } }; for ( var i = 3; i < vertices.length; i++ ) { addPoint( i ); } // Push vertices into `this.vertices`, skipping those inside the hull var id = 0; var newId = new List(vertices.length); // map from old vertex id to new id for ( var i = 0; i < faces.length; i++ ) { var face = faces[ i ]; for ( var j = 0; j < 3; j++ ) { if ( newId[ face[ j ] ] == null ) { newId[ face[ j ] ] = id++; this.vertices.add( vertices[ face[ j ] ] ); } face[ j ] = newId[ face[ j ] ]; } } // Convert faces into instances of THREE.Face3 for ( var i = 0; i < faces.length; i++ ) { this.faces.add( new Face3( faces[ i ][ 0 ], faces[ i ][ 1 ], faces[ i ][ 2 ] ) ); } // Compute UVs for ( var i = 0; i < this.faces.length; i++ ) { var face = this.faces[ i ]; this.faceVertexUvs[ 0 ].add( [ _vertexUv( this.vertices[ face.a ] ), _vertexUv( this.vertices[ face.b ] ), _vertexUv( this.vertices[ face.c ]) ] ); } this.computeCentroids(); this.computeFaceNormals(); this.computeVertexNormals(); }
Properties
Operators
Methods
void applyMatrix(Matrix4 matrix) #
inherited from Geometry
void applyMatrix( Matrix4 matrix ) { Matrix4 matrixRotation = new Matrix4.identity(); extractRotation( matrixRotation, matrix); vertices.forEach((vertex) => vertex.applyProjection(matrix)); faces.forEach((face) { face.normal.applyProjection(matrixRotation); face.vertexNormals.forEach((normal) => normal.applyProjection(matrixRotation)); face.centroid.applyProjection(matrix); }); }
void computeBoundingBox() #
inherited from Geometry
void computeBoundingBox() { if ( boundingBox == null ) { boundingBox = new BoundingBox( min: new Vector3.zero(), max: new Vector3.zero() ); } if ( vertices.length > 0 ) { Vector3 position, firstPosition = vertices[ 0 ]; boundingBox.min.setFrom( firstPosition ); boundingBox.max.setFrom( firstPosition ); Vector3 min = boundingBox.min, max = boundingBox.max; num vl = vertices.length; for ( int v = 1; v < vl; v ++ ) { position = vertices[ v ]; if ( position.x < min.x ) { min.x = position.x; } else if ( position.x > max.x ) { max.x = position.x; } if ( position.y < min.y ) { min.y = position.y; } else if ( position.y > max.y ) { max.y = position.y; } if ( position.z < min.z ) { min.z = position.z; } else if ( position.z > max.z ) { max.z = position.z; } } } }
void computeBoundingSphere() #
inherited from Geometry
void computeBoundingSphere() { num radiusSq; var maxRadiusSq = vertices.fold(0, (num curMaxRadiusSq, Vector3 vertex) { radiusSq = vertex.length2; return ( radiusSq > curMaxRadiusSq ) ? radiusSq : curMaxRadiusSq; }); boundingSphere = new BoundingSphere(radius: Math.sqrt(maxRadiusSq) ); }
void computeCentroids() #
inherited from Geometry
void computeCentroids() { faces.forEach((Face face) { face.centroid.setValues( 0.0, 0.0, 0.0 ); face.indices.forEach((idx) { face.centroid.add( vertices[ idx ] ); }); face.centroid /= face.size.toDouble(); }); }
void computeFaceNormals() #
inherited from Geometry
void computeFaceNormals() { faces.forEach((face) { var vA = vertices[ face.a ], vB = vertices[ face.b ], vC = vertices[ face.c ]; Vector3 cb = vC - vB; Vector3 ab = vA - vB; cb = cb.cross( ab ); cb.normalize(); face.normal = cb; }); }
void computeTangents() #
inherited from Geometry
void computeTangents() { // based on http://www.terathon.com/code/tangent.html // tangents go to vertices var f, fl, face; num i, il, vertexIndex, test, w; Vector3 vA, vB, vC; UV uvA, uvB, uvC; List uv; num x1, x2, y1, y2, z1, z2, s1, s2, t1, t2, r; Vector3 sdir = new Vector3.zero(), tdir = new Vector3.zero(), tmp = new Vector3.zero(), tmp2 = new Vector3.zero(), n = new Vector3.zero(), t; List<Vector3> tan1 = vertices.map((_) => new Vector3.zero()).toList(), tan2 = vertices.map((_) => new Vector3.zero()).toList(); var handleTriangle = ( context, a, b, c, ua, ub, uc ) { vA = context.vertices[ a ]; vB = context.vertices[ b ]; vC = context.vertices[ c ]; uvA = uv[ ua ]; uvB = uv[ ub ]; uvC = uv[ uc ]; x1 = vB.x - vA.x; x2 = vC.x - vA.x; y1 = vB.y - vA.y; y2 = vC.y - vA.y; z1 = vB.z - vA.z; z2 = vC.z - vA.z; s1 = uvB.u - uvA.u; s2 = uvC.u - uvA.u; t1 = uvB.v - uvA.v; t2 = uvC.v - uvA.v; r = 1.0 / ( s1 * t2 - s2 * t1 ); sdir.setValues( ( t2 * x1 - t1 * x2 ) * r, ( t2 * y1 - t1 * y2 ) * r, ( t2 * z1 - t1 * z2 ) * r ); tdir.setValues( ( s1 * x2 - s2 * x1 ) * r, ( s1 * y2 - s2 * y1 ) * r, ( s1 * z2 - s2 * z1 ) * r ); tan1[ a ].add( sdir ); tan1[ b ].add( sdir ); tan1[ c ].add( sdir ); tan2[ a ].add( tdir ); tan2[ b ].add( tdir ); tan2[ c ].add( tdir ); }; fl = this.faces.length; for ( f = 0; f < fl; f ++ ) { face = this.faces[ f ]; UV uv = faceVertexUvs[ 0 ][ f ]; // use UV layer 0 for tangents // TODO - Come up with a way to handle an arbitrary number of vertexes var triangles = []; if ( face.size == 3 ) { triangles.add([0, 1, 2]); } else if ( face.size == 4 ) { triangles.add([0, 1, 3]); triangles.add([1, 2, 3]); } triangles.forEach((t) { handleTriangle( this, face.indices[t[0]], face.indices[t[1]], face.indices[t[2]], t[0], t[1], t[2] ); }); } faces.forEach((face) { il = face.vertexNormals.length; for ( i = 0; i < il; i++ ) { n.setFrom( face.vertexNormals[ i ] ); vertexIndex = face.indices[i]; t = tan1[ vertexIndex ]; // Gram-Schmidt orthogonalize tmp.setFrom( t ); tmp.sub( n.scale( n.dot( t ) ) ).normalize(); // Calculate handedness tmp2 = face.vertexNormals[i].cross(t); test = tmp2.dot( tan2[ vertexIndex ] ); w = (test < 0.0) ? -1.0 : 1.0; face.vertexTangents[ i ] = new Vector4( tmp.x, tmp.y, tmp.z, w ); } }); hasTangents = true; }
void computeVertexNormals() #
inherited from Geometry
void computeVertexNormals() { List<Vector3> vertices; // create internal buffers for reuse when calling this method repeatedly // (otherwise memory allocation / deallocation every frame is big resource hog) if ( __tmpVertices == null ) { __tmpVertices = []; this.vertices.forEach((_) => __tmpVertices.add(new Vector3.zero())); vertices = __tmpVertices; faces.forEach((face) { face.vertexNormals = new List.generate(face.size, (_) => new Vector3.zero(), growable: false); }); } else { vertices = __tmpVertices; var vl = this.vertices.length; for ( var v = 0; v < vl; v ++ ) { vertices[ v ].setValues( 0.0, 0.0, 0.0 ); } } faces.forEach((Face face) { face.indices.forEach((idx) { vertices[ idx ].add( face.normal ); }); }); vertices.forEach((v) => v.normalize()); faces.forEach((Face face) { var i = 0; face.indices.forEach((idx) { face.vertexNormals[ i++ ].setFrom( vertices[ idx ] ); }); }); }
int mergeVertices() #
inherited from Geometry
int mergeVertices() { Map verticesMap = {}; // Hashmap for looking up vertice by position coordinates (and making sure they are unique) List<Vector3> unique = []; List<int> changes = []; String key; int precisionPoints = 4; // number of decimal points, eg. 4 for epsilon of 0.0001 num precision = Math.pow( 10, precisionPoints ); int i, il; var abcd = 'abcd', o, k, j, jl, u; Vector3 v; il = this.vertices.length; for( i = 0; i < il; i++) { v = this.vertices[i]; key = [ ( v.x * precision ).round().toStringAsFixed(0), ( v.y * precision ).round().toStringAsFixed(0), ( v.z * precision ).round().toStringAsFixed(0) ].join('_' ); if ( verticesMap[ key ] == null ) { verticesMap[ key ] = i; unique.add( v ); //TODO: pretty sure this is an acceptable change in syntax here: //changes[ i ] = unique.length - 1; changes.add( unique.length - 1); } else { //print('Duplicate vertex found. $i could be using ${verticesMap[key]}'); //print('changes len ${changes.length} add at i = $i'); //changes[ i ] = changes[ verticesMap[ key ] ]; changes.add( changes[ verticesMap[ key ] ] ); } } // Start to patch face indices faces.forEach((Face face) { for (var i = 0; i < face.size; i++) { face.indices[i] = changes[ face.indices[i] ]; /* TODO // check dups in (a, b, c, d) and convert to -> face3 var o = [ face.a, face.b, face.c, face.d ]; for ( var k = 3; k > 0; k -- ) { if ( o.indexOf( face[ abcd[ k ] ] ) != k ) { // console.log('faces', face.a, face.b, face.c, face.d, 'dup at', k); o.removeAt( k ); this.faces[ i ] = new THREE.Face3( o[0], o[1], o[2], face.normal, face.color, face.materialIndex ); for ( j = 0, jl = this.faceVertexUvs.length; j < jl; j ++ ) { u = this.faceVertexUvs[ j ][ i ]; if ( u ) u.removeAt( k ); } this.faces[ i ].vertexColors = face.vertexColors; break; } }*/ } }); // Use unique set of vertices var diff = vertices.length - unique.length; vertices = unique; return diff; }