void Assembler::operKernel(EOExpr<A> oper,const MeshHandler<ORDER>& mesh,
FiniteElement<Integrator, ORDER>& fe, SpMat& OpMat)
{
std::vector<coeff> triplets;
for(auto t=0; t<mesh.num_triangles(); t++)
{
fe.updateElement(mesh.getTriangle(t));
// Vector of vertices indices (link local to global indexing system)
std::vector<UInt> identifiers;
identifiers.resize(ORDER*3);
for( auto q=0; q<ORDER*3; q++)
identifiers[q]=mesh.getTriangle(t)[q].id();
//localM=localMassMatrix(currentelem);
for(int i = 0; i < 3*ORDER; i++)
{
for(int j = 0; j < 3*ORDER; j++)
{
Real s=0;
for(int l = 0;l < Integrator::NNODES; l++)
{
s += oper(fe,i,j,l) * fe.getDet() * fe.getAreaReference()* Integrator::WEIGHTS[l];//(*)
}
triplets.push_back(coeff(identifiers[i],identifiers[j],s));
}
}
}
UInt nnodes = mesh.num_nodes();
OpMat.resize(nnodes, nnodes);
OpMat.setFromTriplets(triplets.begin(),triplets.end());
//cout<<"done!"<<endl;;
}
// The Real Core Function doing the actual mesh processing.
bool FilterHarmonicPlugin::applyFilter(QAction * action, MeshDocument & md, RichParameterSet & par, vcg::CallBackPos * cb)
{
switch(ID(action))
{
case FP_SCALAR_HARMONIC_FIELD :
{
typedef vcg::GridStaticPtr<CMeshO::VertexType, CMeshO::ScalarType> VertexGrid;
typedef double CoeffScalar; // TODO, when moving the code to a class make it a template (CoeffScalar = double)
typedef CMeshO::ScalarType ScalarType;
typedef CMeshO::CoordType CoordType;
typedef CMeshO::VertexType VertexType;
typedef CMeshO::FaceType FaceType;
typedef Eigen::Triplet<CoeffScalar> T;
typedef Eigen::SparseMatrix<CoeffScalar> SpMat; //sparse matrix type of double
CMeshO & m = md.mm()->cm;
vcg::tri::Allocator<CMeshO>::CompactFaceVector(m);
vcg::tri::Allocator<CMeshO>::CompactVertexVector(m);
md.mm()->updateDataMask(MeshModel::MM_FACEFACETOPO | MeshModel::MM_VERTMARK);
vcg::tri::UpdateBounding<CMeshO>::Box(m);
vcg::tri::UpdateTopology<CMeshO>::FaceFace(m);
int n = m.VN();
int fn = m.FN();
std::vector<T> coeffs; // coefficients of the system
std::map<size_t,CoeffScalar> sums; // row sum of the coefficient
SpMat laplaceMat; // the system to be solved
laplaceMat.resize(n, n);
Log("Generating coefficients.`");
cb(0, "Generating coefficients...");
vcg::tri::UpdateFlags<CMeshO>::FaceClearV(m);
// Iterate over the faces
for (size_t i = 0; i < m.face.size(); ++i)
{
CMeshO::FaceType & f = m.face[i];
if (f.IsD())
{
assert(int(i) == fn);
break; // TODO FIX the indexing of vertices
}
assert(!f.IsV());
f.SetV();
// Generate coefficients for each edge
for (int idx = 0; idx < 3; ++idx)
{
CoeffScalar weight;
WeightInfo res = ComputeWeight<FaceType, CoeffScalar>(f, idx, weight);
switch (res)
{
case EdgeAlreadyVisited : continue;
case Success : break;
case BorderEdge :
this->errorMessage = "Mesh not closed, cannot compute harmonic field on mesh containing holes or borders";
return false;
default: assert(0);
}
// if (weight < 0) weight = 0; // TODO check if negative weight may be an issue
// Add the weight to the coefficients vector for both the vertices of the considered edge
size_t v0_idx = vcg::tri::Index(m, f.V0(idx));
size_t v1_idx = vcg::tri::Index(m, f.V1(idx));
coeffs.push_back(T(v0_idx, v1_idx, -weight));
coeffs.push_back(T(v1_idx, v0_idx, -weight));
// Add the weight to the row sum
sums[v0_idx] += weight;
sums[v1_idx] += weight;
}
f.SetV();
}
// Fill the system matrix
Log("Fill the system matrix");
cb(10, "Filling the system matrix...");
laplaceMat.reserve(coeffs.size());
for (std::map<size_t,CoeffScalar>::const_iterator it = sums.begin(); it != sums.end(); ++it)
{
coeffs.push_back(T(it->first, it->first, it->second));
}
laplaceMat.setFromTriplets(coeffs.begin(), coeffs.end());
// Get the two vertices with value set
VertexGrid vg;
vg.Set(m.vert.begin(), m.vert.end());
vcg::vertex::PointDistanceFunctor<ScalarType> pd;
vcg::tri::Tmark<CMeshO, VertexType> mv;
mv.SetMesh(&m);
mv.UnMarkAll();
CoordType closestP;
ScalarType minDist = 0;
VertexType * vp0 = vcg::GridClosest(vg, pd, mv, par.getPoint3f("point1"), m.bbox.Diag(), minDist, closestP);
VertexType * vp1 = vcg::GridClosest(vg, pd, mv, par.getPoint3f("point2"), m.bbox.Diag(), minDist, closestP);
if (vp0 == NULL || vp1 == NULL || vp0 == vp1)
{
this->errorMessage = "Error occurred for selected points.";
return false;
}
size_t v0_idx = vcg::tri::Index(m, vp0);
size_t v1_idx = vcg::tri::Index(m, vp1);
// Add penalty factor alpha
Log("Setting up the system matrix");
const CoeffScalar alpha = pow(10, 8);
Eigen::Matrix<CoeffScalar, Eigen::Dynamic, 1> b, x; // Unknown and known terms vectors
b.setZero(n);
b(v0_idx) = alpha * par.getFloat("value1");
b(v1_idx) = alpha * par.getFloat("value2");
laplaceMat.coeffRef(v0_idx, v0_idx) += alpha;
laplaceMat.coeffRef(v1_idx, v1_idx) += alpha;
// Solve system laplacianMat x = b
Log("System matrix decomposition...");
cb(20, "System matrix decomposition...");
Eigen::SimplicialLDLT<Eigen::SparseMatrix<CoeffScalar> > solver; // TODO eventually use another solver
solver.compute(laplaceMat);
if(solver.info() != Eigen::Success)
{
// decomposition failed
this->errorMessage = "System matrix decomposition failed: ";
if (solver.info() == Eigen::NumericalIssue)
this->errorMessage += "numerical issue.";
else if (solver.info() == Eigen::NoConvergence)
this->errorMessage += "no convergence.";
else if (solver.info() == Eigen::InvalidInput)
this->errorMessage += "invalid input.";
return false;
}
Log("Solving the system...");
cb(85, "Solving the system...");
x = solver.solve(b);
if(solver.info() != Eigen::Success)
{
// solving failed
this->errorMessage = "System solving failed.";
return false;
}
// Colorize bands for the 0-1 interval
if (par.getBool("colorize"))
{
float steps = 20.0f;
for (size_t i = 0; int(i) < n; ++i)
{
bool on = (int)(x[i]*steps)%2 == 1;
if (on)
{
m.vert[i].C() = vcg::Color4b::ColorRamp(0,2,x[i]);
}
else
{
m.vert[i].C() = vcg::Color4b::White;
}
}
}
// Set field value into vertex quality attribute
for (size_t i = 0; int(i) < n; ++i)
{
m.vert[i].Q() = x[i];
}
cb(100, "Done.");
return true;
}
default : assert(0);
}
return false;
}
void ADMMCut::CalculateQ(const VX _D, SpMat &Q)
{
// Construct Hessian Matrix for D-Qp problem
Q.resize(6 * Ns_, Nd_);
vector<Eigen::Triplet<double>> Q_list;
for (int i = 0; i < Ns_; i++)
{
int u = ptr_dualgraph_->v_orig_id(i);
WF_edge *edge = ptr_frame_->GetNeighborEdge(u);
while (edge != NULL)
{
int e_id = ptr_dualgraph_->e_dual_id(edge->ID());
if (e_id != -1)
{
int v = edge->pvert_->ID();
int j = ptr_dualgraph_->v_dual_id(v);
MX eKuu = ptr_stiff_->eKv(edge->ID());
MX eKeu = ptr_stiff_->eKe(edge->ID());
VX Fe = ptr_stiff_->Fe(edge->ID());
VX Di(6);
VX Dj(6);
if (i < Ns_ && j < Ns_)
{
for (int k = 0; k < 6; k++)
{
Di[k] = _D[6 * i + k];
Dj[k] = _D[6 * j + k];
}
}
else
{
if (i < Ns_)
{
for (int k = 0; k < 6; k++)
{
Di[k] = _D[6 * i + k];
Dj[k] = 0;
}
}
if (j < Ns_)
{
for (int k = 0; k < 6; k++)
{
Di[k] = 0;
Dj[k] = _D[6 * j + k];
}
}
}
VX Gamma = eKuu * Di + eKeu * Dj - Fe;
for (int k = 0; k < 6; k++)
{
Q_list.push_back(Triplet<double>(6 * i + k, e_id, Gamma[k]));
}
}
edge = edge->pnext_;
}
}
Q.setFromTriplets(Q_list.begin(), Q_list.end());
}