public SparseMatrixComplex BuildEnergy()
{
//Build Laplace matrix
SparseMatrixDouble d0 = DECDouble.Instance.BuildExteriorDerivative0Form(mesh);;
SparseMatrixDouble star1 = DECDouble.Instance.BuildHodgeStar1Form(mesh);
SparseMatrixDouble L = d0.Transpose() * star1 * d0;
SparseMatrixComplex A = SparseMatrixComplex.Copy(ref L);
//Iterate faces
foreach (TriMesh.Face face in mesh.Faces)
{
//Iterate each halfedge in face
foreach (TriMesh.HalfEdge hf in face.Halfedges)
{
int i = hf.ToVertex.Index;
int j = hf.FromVertex.Index;
Complex value = 0.5 * DDGConstant;
A[i, j] -= value;
A[j, i] += value;
}
}
return(A);
}
public SparseMatrixDouble BuildLaplaceWithNeumannBoundary(TriMesh mesh)
{
SparseMatrixDouble d0 = this.BuildExteriorDerivative0Form(mesh);
D0 = d0;
SparseMatrixDouble star1 = this.BuildHodgeStar1Form(mesh);
Star1 = star1;
SparseMatrixDouble star0 = this.BuildHodgeStar0Form(mesh);
Star0 = star0;
SparseMatrixDouble delta = d0.Transpose() * star1 * d0;
delta += (1.0e-8) * star0;
Laplace = delta;
return(delta);
}
protected DenseMatrixDouble ComputeTrivaialConnection(SparseMatrixDouble d0, SparseMatrixDouble d1, double[] Guassian)
{
DenseMatrixDouble b = CholmodConverter.dConvertArrayToDenseMatrix(ref Guassian, Guassian.Length, 1);
double[] singularValues = new double[Singularities.Count];
//Init with avg of 2
double avgValue = 2.0f / (double)Singularities.Count;
int j = 0;
foreach (KeyValuePair <TriMesh.Vertex, double> vItem in Singularities)
{
int index = vItem.Key.Index;
double value = vItem.Value;
b[index, 0] = Guassian[index] - 2 * Math.PI * value;
j++;
}
for (int i = 0; i < Guassian.Length; i++)
{
b[i, 0] = -b[i, 0];
}
SparseMatrixDouble A = d0.Transpose();
DenseMatrixDouble x = LinearSystemGenericByLib.Instance.SolveLinerSystem(ref A, ref b);
SparseMatrixDouble d1T = d1.Transpose();
SparseMatrixDouble Laplace = d1 * d1T;
DenseMatrixDouble rhs = d1 * x;
DenseMatrixDouble y = LinearSystemGenericByLib.Instance.SolveLinerSystem(ref Laplace, ref rhs);
x = x - d1T * y;
return(x);
}
public Vector3D[] Process()
{
//Build laplace
SparseMatrixDouble star0 = DECDouble.Instance.Star0;
if (star0 == null)
{
star0 = DECDouble.Instance.BuildHodgeStar0Form(mesh);
}
SparseMatrixDouble star1 = DECDouble.Instance.Star1;
if (star1 == null)
{
star1 = DECDouble.Instance.BuildHodgeStar1Form(mesh);
}
SparseMatrixDouble d0 = DECDouble.Instance.D0;
if (d0 == null)
{
d0 = DECDouble.Instance.BuildExteriorDerivative0Form(mesh);
}
SparseMatrixDouble d1 = DECDouble.Instance.D1;
if (d1 == null)
{
d1 = DECDouble.Instance.BuildExteriorDerivative1Form(mesh);
}
if (Singularities == null)
{
Singularities = new List <KeyValuePair <HalfEdgeMesh.Vertex, double> >();
}
if (Singularities.Count == 0)
{
int count = 0;
foreach (TriMesh.Vertex v in mesh.Vertices)
{
if (v.Traits.selectedFlag > 0)
{
count++;
}
}
double avg = 2 / (double)count;
int item = 0;
foreach (TriMesh.Vertex V in mesh.Vertices)
{
if (V.Traits.selectedFlag > 0)
{
if (item % 2 == 0) //2
{
Singularities.Add(new KeyValuePair <HalfEdgeMesh.Vertex, double>(V, -1));
}
if (item % 2 == 1) //2
{
Singularities.Add(new KeyValuePair <HalfEdgeMesh.Vertex, double>(V, 1));
}
}
}
}
Laplace = d0.Transpose() * star1 * d0;
Laplace = Laplace + (1.0e-8) * star0;
InitProcess(this.mesh);
GenerateFaceNormals();
Vector3D[] VectorFields = ComputeVectorField(0);
return(VectorFields);
}
public void Run()
{
Stopwatch clock = new Stopwatch();
clock.Start();
double step = 0.01;
DECMeshDouble decMesh = new DECMeshDouble(mesh);
SparseMatrixDouble laplace = decMesh.Laplace;
SparseMatrixDouble star0 = decMesh.HodgeStar0Form;
SparseMatrixDouble star1 = decMesh.HodgeStar1Form;
SparseMatrixDouble d0 = decMesh.ExteriorDerivative0Form;
SparseMatrixDouble L = d0.Transpose() * star1 * d0;
SparseMatrixDouble A = star0 + step * L;
A.WriteToFile("A.ma");
double[] xs = new double[mesh.Vertices.Count];
double[] ys = new double[mesh.Vertices.Count];
double[] zs = new double[mesh.Vertices.Count];
foreach (TriMesh.Vertex v in mesh.Vertices)
{
xs[v.Index] = v.Traits.Position.x;
ys[v.Index] = v.Traits.Position.y;
zs[v.Index] = v.Traits.Position.z;
}
double[] rhs1 = star0 * xs;
double[] rhs2 = star0 * ys;
double[] rhs3 = star0 * zs;
//SparseMatrix.WriteVectorToFile("xs.ve", rhs1);
//SparseMatrix.WriteVectorToFile("ys.ve", rhs2);
//SparseMatrix.WriteVectorToFile("zs.ve", rhs3);
DenseMatrixDouble rhsx = new DenseMatrixDouble(mesh.Vertices.Count, 1);
DenseMatrixDouble rhsy = new DenseMatrixDouble(mesh.Vertices.Count, 1);
DenseMatrixDouble rhsz = new DenseMatrixDouble(mesh.Vertices.Count, 1);
for (int i = 0; i < mesh.Vertices.Count; i++)
{
rhsx[i, 0] = rhs1[i];
rhsy[i, 0] = rhs2[i];
rhsz[i, 0] = rhs3[i];
}
DenseMatrixDouble newX = LinearSystemGenericByLib.Instance.SolveLinerSystem(ref A, ref rhsx);
DenseMatrixDouble newY = LinearSystemGenericByLib.Instance.SolveLinerSystem(ref A, ref rhsy);
DenseMatrixDouble newZ = LinearSystemGenericByLib.Instance.SolveLinerSystem(ref A, ref rhsz);
foreach (TriMesh.Vertex v in mesh.Vertices)
{
v.Traits.Position.x = newX[v.Index, 0];
v.Traits.Position.y = newY[v.Index, 0];
v.Traits.Position.z = newZ[v.Index, 0];
}
TriMeshUtil.ScaleToUnit(mesh, 1.0f);
TriMeshUtil.MoveToCenter(mesh);
clock.Stop();
decimal micro = clock.Elapsed.Ticks / 10m;
Console.WriteLine("Total time cost:{0}", micro);
}
public List <double>[] BuildHarmonicBasis(List <List <TriMesh.HalfEdge> > generators)
{
List <double>[] HarmonicBasis;
HarmonicBasis = new List <double> [mesh.HalfEdges.Count];
SparseMatrixDouble laplace = DECDouble.Instance.BuildLaplaceWithNeumannBoundary(mesh);
SparseMatrixDouble star1 = DECDouble.Instance.Star1;
if (star1 == null)
{
star1 = DECDouble.Instance.BuildHodgeStar1Form(mesh);
}
SparseMatrixDouble d0 = DECDouble.Instance.D0;
if (d0 == null)
{
d0 = DECDouble.Instance.BuildExteriorDerivative0Form(mesh);
}
SparseMatrixDouble d1 = DECDouble.Instance.D1;
if (d1 == null)
{
d1 = DECDouble.Instance.BuildExteriorDerivative1Form(mesh);
}
SparseMatrixDouble div = d0.Transpose() * star1;
bool skipBoundary = true;
foreach (List <TriMesh.HalfEdge> loopItem in generators)
{
if (skipBoundary && treeCoTree.IsBoundaryGenerator(loopItem))
{
skipBoundary = false;
continue;
}
DenseMatrixDouble W = BuildClosedPrimalOneForm(mesh, loopItem);
DenseMatrixDouble divW = div * W;
DenseMatrixDouble u = LinearSystemGenericByLib.Instance.SolveLinerSystem(ref laplace, ref divW);
DenseMatrixDouble h = star1 * (W - (d0 * u));
//Store correspond edge
foreach (TriMesh.Edge edge in mesh.Edges)
{
double value = h[edge.Index, 0];
if (HarmonicBasis[edge.HalfEdge0.Index] == null)
{
HarmonicBasis[edge.HalfEdge0.Index] = new List <double>();
}
HarmonicBasis[edge.HalfEdge0.Index].Add(value);
if (HarmonicBasis[edge.HalfEdge1.Index] == null)
{
HarmonicBasis[edge.HalfEdge1.Index] = new List <double>();
}
HarmonicBasis[edge.HalfEdge1.Index].Add(-value);
}
}
return(HarmonicBasis);
}
public double[] Process(double dt, TriMesh mesh, out Vector3D[] vectorFields, out double maxDistance)
{
DenseMatrixDouble x = null;
int nb = BuildImpulseSingal(mesh, out x);
vectorFields = null;
maxDistance = 0;
if (nb == 0)
{
return(null);
}
SparseMatrixDouble star0 = DECDouble.Instance.Star0;
if (star0 == null)
{
star0 = DECDouble.Instance.BuildHodgeStar0Form(mesh);
}
SparseMatrixDouble star1 = DECDouble.Instance.Star1;
if (star1 == null)
{
star1 = DECDouble.Instance.BuildHodgeStar1Form(mesh);
}
SparseMatrixDouble d0 = DECDouble.Instance.D0;
if (d0 == null)
{
d0 = DECDouble.Instance.BuildExteriorDerivative0Form(mesh);
}
SparseMatrixDouble L = d0.Transpose() * star1 * d0;
L += 1.0e-8 * star0;
//Heat flow:
//[TO DO] edgeLength
double edgelength = MeanEdgeLength(mesh);
dt *= Math.Sqrt(edgelength);
SparseMatrixDouble A = star0 + dt * L;
DenseMatrixDouble u = LinearSystemGenericByLib.Instance.SolveLinerSystem(ref A, ref x);
//Extract geodesic
vectorFields = ComputeVectorField(u, mesh);
DenseMatrixDouble div = ComputeDivergence(mesh, vectorFields);
DenseMatrixDouble phi = LinearSystemGenericByLib.Instance.SolveLinerSystem(ref L, ref div);
SetMinToZero(phi);
double[] VertexDistances = AssignDistance(phi);
double max = double.MinValue;
for (int i = 0; i < VertexDistances.Length; i++)
{
double value = Math.Abs(VertexDistances[i]);
if (max < value)
{
max = value;
}
}
maxDistance = max;
return(VertexDistances);
}
protected DenseMatrixDouble ComputeTrivaialConnection(SparseMatrixDouble d0, SparseMatrixDouble d1, double[] Guassian)
{
DenseMatrixDouble b = CholmodConverter.dConvertArrayToDenseMatrix(ref Guassian, Guassian.Length, 1);
double[] singularValues = new double[Singularities.Count];
//Init with avg of 2
double avgValue = 2.0f / (double)Singularities.Count;
int j = 0;
foreach (KeyValuePair<TriMesh.Vertex, double> vItem in Singularities)
{
int index = vItem.Key.Index;
double value = vItem.Value;
b[index, 0] = Guassian[index] - 2 * Math.PI * value;
j++;
}
for (int i = 0; i < Guassian.Length; i++)
{
b[i, 0] = -b[i, 0];
}
SparseMatrixDouble A = d0.Transpose();
DenseMatrixDouble x = LinearSystemGenericByLib.Instance.SolveLinerSystem(ref A, ref b);
SparseMatrixDouble d1T = d1.Transpose();
SparseMatrixDouble Laplace = d1 * d1T;
DenseMatrixDouble rhs = d1 * x;
DenseMatrixDouble y = LinearSystemGenericByLib.Instance.SolveLinerSystem(ref Laplace, ref rhs);
x = x - d1T * y;
return x;
}
