TubeGeometry class
@author WestLangley / https://github.com/WestLangley @author zz85 / https://github.com/zz85 @author miningold / https://github.com/miningold
Modified from the TorusKnotGeometry by @oosmoxiecode
Creates a tube which extrudes along a 3d spline
Uses parallel transport frames as described in http://www.cs.indiana.edu/pub/techreports/TR425.pdf
class TubeGeometry extends Geometry {
var path, segments;
num nSegments, radius, segmentsRadius;
bool closed;
var grid;
List<Vector3> tangents, normals, binormals;
Object3D debug;
TubeGeometry ( path, [segments = 64, this.radius = 1.0, this.segmentsRadius = 8, closed = false, bool debug])
: grid = [], super() {
if ( debug ) this.debug = new Object3D();
var tangent,
normal,
binormal,
numpoints = segments + 1,
x, y, z,
tx, ty, tz,
u, v,
cx, cy,
pos, pos2 = new Vector3.zero(),
i, j,
ip, jp,
a, b, c, d,
uva, uvb, uvc, uvd;
var frames = _frenetFrames(path, segments, closed);
// consruct the grid
grid.length = numpoints;
for ( i = 0; i < numpoints; i++ ) {
grid[ i ] = new List(this.segmentsRadius);
u = i / ( numpoints - 1 );
pos = path.getPointAt( u );
tangent = tangents[ i ];
normal = normals[ i ];
binormal = binormals[ i ];
if ( debug ) {
this.debug.add(new ArrowHelper(tangent, pos, radius, 0x0000ff));
this.debug.add(new ArrowHelper(normal, pos, radius, 0xff0000));
this.debug.add(new ArrowHelper(binormal, pos, radius, 0x00ff00));
}
for ( j = 0; j < this.segmentsRadius; j++ ) {
v = j / this.segmentsRadius * 2 * Math.PI;
cx = -this.radius * Math.cos( v ); // TODO: Hack: Negating it so it faces outside.
cy = this.radius * Math.sin( v );
pos2.setFrom( pos );
pos2.x += cx * normal.x + cy * binormal.x;
pos2.y += cx * normal.y + cy * binormal.y;
pos2.z += cx * normal.z + cy * binormal.z;
this.grid[ i ][ j ] = _vert( pos2.x, pos2.y, pos2.z );
}
}
// construct the mesh
for ( i = 0; i < this.nSegments; i++ ) {
for ( j = 0; j < this.segmentsRadius; j++ ) {
ip = ( closed ) ? (i + 1) % this.nSegments : i + 1;
jp = (j + 1) % this.segmentsRadius;
a = this.grid[ i ][ j ]; // *** NOT NECESSARILY PLANAR ! ***
b = this.grid[ ip ][ j ];
c = this.grid[ ip ][ jp ];
d = this.grid[ i ][ jp ];
uva = new UV( i / this.nSegments, j / this.segmentsRadius );
uvb = new UV( ( i + 1 ) / this.nSegments, j / this.segmentsRadius );
uvc = new UV( ( i + 1 ) / this.nSegments, ( j + 1 ) / this.segmentsRadius );
uvd = new UV( i / this.nSegments, ( j + 1 ) / this.segmentsRadius );
this.faces.add( new Face4( a, b, c, d ) );
this.faceVertexUvs[ 0 ].add( [ uva, uvb, uvc, uvd ] );
}
}
computeCentroids();
computeFaceNormals();
computeVertexNormals();
}
_vert( x, y, z ) {
vertices.add( new Vector3(x, y, z) );
return vertices.length - 1;
}
// FrenetFrames
TubeGeometry.FrenetFrames(path, segments, closed) {
_frenetFrames(path, segments, closed);
}
// For computing of Frenet frames, exposing the tangents, normals and binormals the spline
_frenetFrames(ppath, psegments, pclosed) {
this.path = ppath;
this.segments = psegments;
this.closed = pclosed;
var
tangent = new Vector3.zero(),
normal = new Vector3.zero(),
binormal = new Vector3.zero(),
mat = new Matrix4.identity(),
theta,
epsilon = 0.0001,
smallest,
tx, ty, tz,
i, u, v;
if(segments is num){
var length = segments;
segments = [];
for ( i = 1; i <= length; i++ ) {
segments.add( i / ( length ));
}
}
this.nSegments = segments.length;
var numpoints = this.nSegments + 1;
// expose internals
tangents = new List<Vector3>(numpoints);
normals = new List<Vector3>(numpoints);
binormals = new List<Vector3>(numpoints);
// compute the tangent vectors for each segment on the path
for ( i = 0; i < numpoints; i++ ) {
tangents[ i ] = (i == 0)? path.getTangentAt( 0 ): path.getTangentAt( segments[i - 1] );
tangents[ i ].normalize();
}
_initialNormal1([lastBinormal = null]) {
// fixed start binormal. Has dangers of 0 vectors
if (lastBinormal==null)
lastBinormal = new Vector3( 0.0, 0.0, 1.0 );
normals[0] = lastBinormal.cross(tangents[0]).normalize();
binormals[0] = tangents[0].cross(normals[0]).normalize();
}
_initialNormal2() {
// This uses the Frenet-Serret formula for deriving binormal
var t2 = path.getTangentAt( epsilon );
normals[0] = (t2 - tangents[0]).normalize();
binormals[0] = tangents[0].cross(normals[0]);
normals[0] = binormals[0].cross(tangents[0]).normalize(); // last binormal x tangent
binormals[0] = tangents[0].cross(normals[0]).normalize();
}
_initialNormal3() {
// select an initial normal vector perpenicular to the first tangent vector,
// and in the direction of the smallest tangent xyz component
smallest = double.INFINITY;
tx = ( tangents[ 0 ].x ).abs();
ty = ( tangents[ 0 ].y ).abs();
tz = ( tangents[ 0 ].z ).abs();
if ( tx <= smallest ) {
smallest = tx;
normal.setValues( 1.0, 0.0, 0.0 );
}
if ( ty <= smallest ) {
smallest = ty;
normal.setValues( 0.0, 1.0, 0.0 );
}
if ( tz <= smallest ) {
normal.setValues( 0.0, 0.0, 1.0 );
}
Vector3 vec = tangents[0].cross(normal).normalize();
normals[0] = tangents[0].cross(vec);
binormals[0] = tangents[0].cross(normals[0]);
}
_initialNormal3();
// compute the slowly-varying normal and binormal vectors for each segment on the path
for ( i = 1; i < numpoints; i++ ) {
normals[ i ] = normals[ i-1 ].clone();
binormals[ i ] = binormals[ i-1 ].clone();
Vector3 vec = tangents[i-1].cross(tangents[i]);
if ( vec.length > epsilon ) {
vec.normalize();
theta = Math.acos( tangents[ i-1 ].dot( tangents[ i ] ) );
normals[ i ].applyProjection(makeRotationAxis ( mat, vec, theta ));
}
binormals[i] = tangents[i].cross(normals[i]);
}
// if the curve is closed, postprocess the vectors so the first and last normal vectors are the same
if ( closed ) {
theta = Math.acos( normals[ 0 ].dot( normals[ numpoints-1 ] ) );
theta /= ( numpoints - 1 );
if ( tangents[ 0 ].dot( normals[0].cross(normals[numpoints-1]) ) > 0 ) {
theta = -theta;
}
for ( i = 1; i < numpoints; i++ ) {
// twist a little...
normals[ i ].applyProjection( makeRotationAxis( mat, tangents[ i ], theta * i ) );
binormals[ i ] = tangents[i].cross(normals[i]);
}
}
}
}
Extends
Geometry > TubeGeometry
Constructors
new TubeGeometry(path, [segments = 64, num radius = 1.0, num segmentsRadius = 8, closed = false, bool debug]) #
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
TubeGeometry ( path, [segments = 64, this.radius = 1.0, this.segmentsRadius = 8, closed = false, bool debug])
: grid = [], super() {
if ( debug ) this.debug = new Object3D();
var tangent,
normal,
binormal,
numpoints = segments + 1,
x, y, z,
tx, ty, tz,
u, v,
cx, cy,
pos, pos2 = new Vector3.zero(),
i, j,
ip, jp,
a, b, c, d,
uva, uvb, uvc, uvd;
var frames = _frenetFrames(path, segments, closed);
// consruct the grid
grid.length = numpoints;
for ( i = 0; i < numpoints; i++ ) {
grid[ i ] = new List(this.segmentsRadius);
u = i / ( numpoints - 1 );
pos = path.getPointAt( u );
tangent = tangents[ i ];
normal = normals[ i ];
binormal = binormals[ i ];
if ( debug ) {
this.debug.add(new ArrowHelper(tangent, pos, radius, 0x0000ff));
this.debug.add(new ArrowHelper(normal, pos, radius, 0xff0000));
this.debug.add(new ArrowHelper(binormal, pos, radius, 0x00ff00));
}
for ( j = 0; j < this.segmentsRadius; j++ ) {
v = j / this.segmentsRadius * 2 * Math.PI;
cx = -this.radius * Math.cos( v ); // TODO: Hack: Negating it so it faces outside.
cy = this.radius * Math.sin( v );
pos2.setFrom( pos );
pos2.x += cx * normal.x + cy * binormal.x;
pos2.y += cx * normal.y + cy * binormal.y;
pos2.z += cx * normal.z + cy * binormal.z;
this.grid[ i ][ j ] = _vert( pos2.x, pos2.y, pos2.z );
}
}
// construct the mesh
for ( i = 0; i < this.nSegments; i++ ) {
for ( j = 0; j < this.segmentsRadius; j++ ) {
ip = ( closed ) ? (i + 1) % this.nSegments : i + 1;
jp = (j + 1) % this.segmentsRadius;
a = this.grid[ i ][ j ]; // *** NOT NECESSARILY PLANAR ! ***
b = this.grid[ ip ][ j ];
c = this.grid[ ip ][ jp ];
d = this.grid[ i ][ jp ];
uva = new UV( i / this.nSegments, j / this.segmentsRadius );
uvb = new UV( ( i + 1 ) / this.nSegments, j / this.segmentsRadius );
uvc = new UV( ( i + 1 ) / this.nSegments, ( j + 1 ) / this.segmentsRadius );
uvd = new UV( i / this.nSegments, ( j + 1 ) / this.segmentsRadius );
this.faces.add( new Face4( a, b, c, d ) );
this.faceVertexUvs[ 0 ].add( [ uva, uvb, uvc, uvd ] );
}
}
computeCentroids();
computeFaceNormals();
computeVertexNormals();
}
new TubeGeometry.FrenetFrames(path, segments, closed) #
TubeGeometry.FrenetFrames(path, segments, closed) {
_frenetFrames(path, segments, closed);
}
Properties
var grid #
var grid
bool isDynamic #
inherited from Geometry
bool get isDynamic => _dynamic;
set isDynamic(bool value) => _dynamic = value;
var path #
var path
var segments #
var path, segments
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;
}