ParametricGeometry class
@author zz85 / https://github.com/zz85 Parametric Surfaces Geometry based on the brilliant article by @prideout http://prideout.net/blog/?p=44
new THREE.ParametricGeometry( parametricFunction, uSegments, ySegements, useTris );
class ParametricGeometry extends Geometry { ParametricGeometry( func(u, v), int slices, int stacks, [bool useTris = false] ) : super() { var verts = this.vertices; var faces = this.faces; var uvs = this.faceVertexUvs[ 0 ]; var i, il, j, p; var u, v; var stackCount = stacks + 1; var sliceCount = slices + 1; for ( i = 0; i <= stacks; i ++ ) { v = i / stacks; for ( j = 0; j <= slices; j ++ ) { u = j / slices; p = func( u, v ); verts.add( p ); } } var a, b, c, d; var uva, uvb, uvc, uvd; for ( i = 0; i < stacks; i ++ ) { for ( j = 0; j < slices; j ++ ) { a = i * sliceCount + j; b = i * sliceCount + j + 1; c = (i + 1) * sliceCount + j; d = (i + 1) * sliceCount + j + 1; uva = new UV( j / slices, i / stacks ); uvb = new UV( ( j + 1 ) / slices, i / stacks ); uvc = new UV( j / slices, ( i + 1 ) / stacks ); uvd = new UV( ( j + 1 ) / slices, ( i + 1 ) / stacks ); if ( useTris ) { faces.add( new Face3( a, b, c ) ); faces.add( new Face3( b, d, c ) ); uvs.add( [ uva, uvb, uvc ] ); uvs.add( [ uvb, uvd, uvc ] ); } else { faces.add( new Face4( a, b, d, c ) ); uvs.add( [ uva, uvb, uvd, uvc ] ); } } } // console.log(this); // magic bullet // var diff = this.mergeVertices(); // console.log('removed ', diff, ' vertices by merging'); computeCentroids(); computeFaceNormals(); computeVertexNormals(); } }
Extends
Geometry > ParametricGeometry
Constructors
new ParametricGeometry(func(u, v), int slices, int stacks, [bool useTris = false]) #
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
ParametricGeometry( func(u, v), int slices, int stacks, [bool useTris = false] ) : super() { var verts = this.vertices; var faces = this.faces; var uvs = this.faceVertexUvs[ 0 ]; var i, il, j, p; var u, v; var stackCount = stacks + 1; var sliceCount = slices + 1; for ( i = 0; i <= stacks; i ++ ) { v = i / stacks; for ( j = 0; j <= slices; j ++ ) { u = j / slices; p = func( u, v ); verts.add( p ); } } var a, b, c, d; var uva, uvb, uvc, uvd; for ( i = 0; i < stacks; i ++ ) { for ( j = 0; j < slices; j ++ ) { a = i * sliceCount + j; b = i * sliceCount + j + 1; c = (i + 1) * sliceCount + j; d = (i + 1) * sliceCount + j + 1; uva = new UV( j / slices, i / stacks ); uvb = new UV( ( j + 1 ) / slices, i / stacks ); uvc = new UV( j / slices, ( i + 1 ) / stacks ); uvd = new UV( ( j + 1 ) / slices, ( i + 1 ) / stacks ); if ( useTris ) { faces.add( new Face3( a, b, c ) ); faces.add( new Face3( b, d, c ) ); uvs.add( [ uva, uvb, uvc ] ); uvs.add( [ uvb, uvd, uvc ] ); } else { faces.add( new Face4( a, b, d, c ) ); uvs.add( [ uva, uvb, uvd, uvc ] ); } } } // console.log(this); // magic bullet // var diff = this.mergeVertices(); // console.log('removed ', diff, ' vertices by merging'); computeCentroids(); computeFaceNormals(); 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; }