public void Build(TriMesh mesh)
{
int nBasisCycles = basisCycles.Count;
//Build Matrix A
A = BuildCycleMatrix(mesh, basisCycles);
ApplyCotanWeights(ref A);
//Factorize
LinearSystemGenericByLib.Instance.FactorizationQR(ref A);
K = new DenseMatrixDouble(basisCycles.Count, 1);
b = new DenseMatrixDouble(basisCycles.Count, 1);
//Add constraint of angle defect
for (int i = 0; i < nContractibleCycles; i++)
{
K[i, 0] = -ComputeGeneratorDefect(basisCycles[i]);
}
//Add constraint of Generator
int nGenerators = dualCycles.Count;
for (int i = nContractibleCycles; i < nGenerators + nContractibleCycles; i++)
{
List <TriMesh.HalfEdge> generatorCycle = basisCycles[i];
//Boundary condition
if (treeCotree.IsBoundaryGenerator(generatorCycle))
{
K[i, 0] = -BoundaryLoopCurvature(generatorCycle);
GeneratorOnBoundary[i - nContractibleCycles] = true;
}
//None-Boundary condition
else
{
K[i, 0] = -ComputeGeneratorDefect(generatorCycle);
GeneratorOnBoundary[i - nContractibleCycles] = false;
}
}
//Copy to b
for (int i = 0; i < nBasisCycles; i++)
{
b[i, 0] = K[i, 0];
}
}
public void InitProcess(TriMesh mesh)
{
TreeCoTree treeCotree = new TreeCoTree(mesh);
generatorLoops = treeCotree.ExtractHonologyGenerator(mesh);
HarmonicBasis basis = new HarmonicBasis(mesh);
HarmonicBasis = basis.BuildHarmonicBasis(generatorLoops);
int numberOfHarmBases = basis.NumberOfHarmonicBases(generatorLoops);
//Still need to built
u = InitWithTrivalHolonmy(Laplace, mesh);
HarmonicCoffition = new double[numberOfHarmBases];
if (numberOfHarmBases == 0)
{
return;
}
DenseMatrixDouble b = new DenseMatrixDouble(numberOfHarmBases, 1);
SparseMatrixDouble H = new SparseMatrixDouble(numberOfHarmBases, numberOfHarmBases);
int row = 0;
bool skipBoundaryLoop = true;
for (int i = 0; i < generatorLoops.Count; i++)
{
List <TriMesh.HalfEdge> cycle = generatorLoops[i];
if (skipBoundaryLoop && treeCotree.IsBoundaryGenerator(cycle))
{
skipBoundaryLoop = false;
continue;
}
foreach (TriMesh.HalfEdge hf in cycle)
{
for (int col = 0; col < numberOfHarmBases; col++)
{
H[row, col] += HarmonicBasis[hf.Index][col];
}
}
double value = -GeneratorHolomy(cycle, HarmonicBasis, HarmonicCoffition, u);
b[row, 0] = value;
row++;
}
DenseMatrixDouble x = null;
if (b.F_Norm() > 1.0e-8)
{
x = LinearSystemGenericByLib.Instance.SolveLinerSystem(ref H, ref b);
}
else
{
x = new DenseMatrixDouble(numberOfHarmBases, 1);
}
for (int i = 0; i < numberOfHarmBases; i++)
{
HarmonicCoffition[i] = x[i, 0];
}
}
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 void InitProcess(TriMesh mesh)
{
TreeCoTree treeCotree = new TreeCoTree(mesh);
generatorLoops = treeCotree.ExtractHonologyGenerator(mesh);
HarmonicBasis basis = new HarmonicBasis(mesh);
HarmonicBasis = basis.BuildHarmonicBasis(generatorLoops);
int numberOfHarmBases = basis.NumberOfHarmonicBases(generatorLoops);
//Still need to built
u = InitWithTrivalHolonmy(Laplace, mesh);
HarmonicCoffition = new double[numberOfHarmBases];
if (numberOfHarmBases == 0)
{
return;
}
DenseMatrixDouble b = new DenseMatrixDouble(numberOfHarmBases, 1);
SparseMatrixDouble H = new SparseMatrixDouble(numberOfHarmBases, numberOfHarmBases);
int row = 0;
bool skipBoundaryLoop = true;
for (int i = 0; i < generatorLoops.Count; i++)
{
List<TriMesh.HalfEdge> cycle = generatorLoops[i];
if (skipBoundaryLoop && treeCotree.IsBoundaryGenerator(cycle))
{
skipBoundaryLoop = false;
continue;
}
foreach (TriMesh.HalfEdge hf in cycle)
{
for (int col = 0; col < numberOfHarmBases; col++)
{
H[row, col] += HarmonicBasis[hf.Index][col];
}
}
double value = -GeneratorHolomy(cycle, HarmonicBasis, HarmonicCoffition, u);
b[row, 0] = value;
row++;
}
DenseMatrixDouble x = null;
if (b.F_Norm() > 1.0e-8)
{
x = LinearSystemGenericByLib.Instance.SolveLinerSystem(ref H, ref b);
}
else
{
x = new DenseMatrixDouble(numberOfHarmBases, 1);
}
for (int i = 0; i < numberOfHarmBases; i++)
{
HarmonicCoffition[i] = x[i, 0];
}
}