void test3() {
#ifdef MAKE_TEST3
std::cout << "Multidimensional test:" << std::endl;
// Construct data for the IVP
double T = 1;
// Many dimensions
int n = 5;
// Multidimensional rhs
Eigen::VectorXd y0(2*n);
for(int i = 0; i < n; ++i) {
y0(i)=(i+1.)/n;
y0(i+n)=-1;
}
// Multidimensional rhs
auto f = [n] (Eigen::VectorXd y) {
Eigen::VectorXd fy(2*n);
Eigen::VectorXd g(n);
g(0) = y(0)*(y(1)+y(0));
g(n-1) = y(n-1)*(y(n-1)+y(n-2));
for(int i = 1; i < n-1; ++i) {
g(i) = y(i)*(y(i-1)+y(i+1));
}
Eigen::SparseMatrix<double> C(n,n);
C.reserve(3);
for(int i = 0; i < n; ++i) {
C.insert(i,i) = 2;
if(i < n-1) C.insert(i,i+1) = -1;
if(i >= 1) C.insert(i,i-1) = -1;
}
C.makeCompressed();
fy.head(n) = y.head(n);
Eigen::SparseLU< Eigen::SparseMatrix<double> > solver;
solver.analyzePattern(C);
solver.compute(C);
fy.tail(n) = solver.solve(g);
return fy;
};
// Constructor:
ode45<Eigen::VectorXd> O(f);
// Setup options
O.options.do_statistics = true;
// Solve
auto sol = O.solve(y0, T);
// Print info
O.print();
std::cout << "T = " << sol.back().second << std::endl;
std::cout << "y(T) = " << std::endl << sol.back().first << std::endl;
#endif
}
NatCSI(const std::vector<double> & t, const std::vector<double> & y)
: t(t), y(y), h(t.size()-1), c(t.size()) {
// Size check
assert( ( t.size() == y.size() ) && "Error: mismatched size of t and y!");
// m is the number of conditions (t goes from t_0 to t_n)
// WARNING: m = n+1
m = t.size();
// Vector containing increments (from the right)
for(int i = 0; i < (m - 1); ++i) {
h(i) = t[i+1] - t[i];
// Check that t is sorted
assert( ( h(i) > 0 ) && "Error: array t must be sorted!");
}
// System matrix and rhs as in 3.5.9, we remove first and last row (known by natural contition)
Eigen::SparseMatrix<double> A(m,m);
Eigen::VectorXd b(m);
// WARNING: sparse reserve space
A.reserve(3);
// Fill in natural conditions 3.5.10 for matrix
A.coeffRef(0,0) = 2 / h(0);
A.coeffRef(0,1) = 1 / h(0);
A.coeffRef(m-1,m-2) = 1 / h(m-2);
A.coeffRef(m-1,m-1) = 2 / h(m-2);
// Reuse computation for rhs
double bold = (y[1] - y[0]) / (h(0)*h(0));
b(0) = 3*bold; // Fill in natural conditions 3.5.10
// Fill matrix A and rhs b
for(int i = 1; i < m-1; ++i) {
// PRecompute b_i
double hinv = 1./h(i);
// Fill in a
A.coeffRef(i,i-1) = hinv;
A.coeffRef(i,i) = 2./h(i) + 2./h(i-1);
A.coeffRef(i,i+1) = hinv;
// Reuse computation for rhs b
double bnew = (y[i+1] - y[i]) / (h(i)*h(i));
b(i) = 3. * (bnew + bold);
bold = bnew;
}
b(m-1) = 3*bold; // Fill in natural conditions 3.5.10
// Compress the matrix
A.makeCompressed();
std::cout << A;
// Factorize A and solve system A*c(1:end) = b
Eigen::SparseLU<Eigen::SparseMatrix<double>> lu;
lu.compute(A);
c = lu.solve(b);
}
void testEigen(int m, int n, int nnz, std::vector<int>& rows, std::vector<int>& cols,
std::vector<double>& values, double* matB){
double start, stop, time_to_solve, time_to_build;
double tol=1e-9;
Eigen::SparseMatrix<double> A;
std::vector< Eigen::Triplet<double> > trips;
trips.reserve(m * n);
for (int k = 0; k < nnz; k++){
double _val = values[k];
int i = rows[k];
int j = cols[k];
if (fabs(_val) > tol){
trips.push_back(Eigen::Triplet<double>(i-1,j-1,_val));
}
}
//NOTE: setFromTriples() accumulates contributions to the same (i,j)!
A.resize(m, n);
start = second();
A.setFromTriplets(trips.begin(), trips.end());
stop = second();
time_to_build = stop - start;
Eigen::SparseLU< Eigen::SparseMatrix<double>, Eigen::COLAMDOrdering<int> > solverLU;
Eigen::VectorXd b; b.resize(m);
for (int i = 0; i < m; i++ ) b(i) = matB[i];
printf("\nProcessing in Eigen using LU...\n");
start = second();
solverLU.compute(A);
Eigen::VectorXd X = solverLU.solve(b);
stop = second();
time_to_solve = stop - start;
Eigen::VectorXd ax = A * X;
Eigen::VectorXd bMinusAx = b - ax;
double h_r[m];
for (int i=0; i<m; i++) h_r[i]=bMinusAx(i);
double r_inf = vec_norminf(m, h_r);
printf("(Eigen) |b - A*x| = %E \n", r_inf);
printf("(Eigen) Time to build(sec): %f\n", time_to_build);
printf("(Eigen) Time (sec): %f\n", time_to_solve);
}
//************************************
// Method: SolvePFC
// FullName: PFCal::PFC::SolvePFC
// Access: public
// Returns: PF_RESULT
// Qualifier: 潮流计算模板函数，构造各种方法求解线性方程组
//************************************
PFVoid PFC::Solve(){
PFDouble opml(0.0);
Eigen::SparseLU<PFCore::PFSMatrixXD, PFCore::PFCOLAMDOrdering> solver;
PFCIter = 0;
//0. 初始化计算矩阵及向量大小
this->_InitPFCalMatrix();
do {
//1. 求解功率失配量
cout << "QG DISPATCH..." << endl;
_MakeDPQVector();
//2. 如果达到收敛条件，退出
cout << "MAXDISPATCH\t" << PFCIter << "\t" << dPFCPQ.cwiseAbs().maxCoeff() << endl;
if (dPFCPQ.cwiseAbs().maxCoeff() < PFCEpsm){
this->PFCResult = PF_RESULT_CONVERG;
return;
}
//3. 计算雅可比阵
_MakeJacoMatrix();
//4. 计算电压偏差
solver.compute(PFCJaco);
if (solver.info() != Eigen::Success){
cout << "Solving<stage_1> Failed!" << endl;
this->PFCResult = PF_RESULT_DIVERGE_FAILURE;
return;
}
dPFCVA = solver.solve(dPFCPQ);
if (solver.info() != Eigen::Success){
cout << "Solving<stage_2> Failed!" << endl;
this->PFCResult = PF_RESULT_DIVERGE_FAILURE;
return;
}
//5. 检测是否出现NAN
if(dPFCVA.hasNaN()){
this->PFCResult = PF_RESULT_DIVERGE_NAN;
return;
}
//6. 更新状态量
cout << "VOL DISPATCH..." << endl;
opml = _CalOptimalMultiplier();
dPFCVA *= opml;
_UpdateSysState();
//7. 迭代次数增加
++PFCIter;
} while (PFCIter <= PFCMaxIter);
//迭代次数越限
if (PFCIter > PFCMaxIter){
this->PFCResult = PF_RESULT_DIVERGE_OVER_ITER;
return;
}
this->PFCResult = PF_RESULT_DIVERGE;
return;
}
Tvector<T> Tsparse_matrix<T>::solve( const Tvector<T>& b ) const
{
assert( ROWS == b.size() ); // Check dimensions are compatible
// Convert Tvector to an Eigen matrix
Eigen::Matrix<T, -1, 1> B;
B.resize(b.size(),1);
for (std::size_t i=0; i<b.size(); ++i)
{
B(i,0) = b.CONTAINER[i];
}
// Convert Tsparse_matrix to an Eigen::SparseMatrix
Eigen::SparseMatrix<T> A(ROWS,COLS); // Declare Eigen sparse matrix
std::vector<Eigen::Triplet<T>> triplet_list; // Declare list of triplets
for ( std::size_t i=0; i<ROWS; ++i )
{
if ( !S_MATRIX[i].isempty() ) // Check that the row is not empty
{
std::vector<std::size_t> index;
std::vector<T> element;
index = S_MATRIX[i].index_list();
element = S_MATRIX[i].element_list();
std::size_t J = index.size();
for ( std::size_t j=0; j<J; ++j )
{
triplet_list.push_back( Eigen::Triplet<T>( i, index[j], element[j] ));
}
}
}
A.setFromTriplets(triplet_list.begin(), triplet_list.end());
// Setup and solve the system
Eigen::SparseLU< Eigen::SparseMatrix<T> > solverA;
//Eigen::BiCGSTAB<Eigen::SparseMatrix<T>> solverA;
//solverA.analyzePattern(A);
//solverA.factorize(A);
solverA.compute(A);
Eigen::Matrix<T, -1, 1> X;
X.resize(b.size(),1);
X = solverA.solve(B);
// Convert back to a Tvector
Tvector<T> x(COLS,0.0);
for (std::size_t i=0; i<COLS; ++i)
{
x.CONTAINER[i] = X(i,0);
}
return x;
}
int main() {
// Construct data for RK order 4
MatrixXd A = MatrixXd::Zero(4,4);
A(1,0) = .5;
A(2,1) = .5;
A(3,2) = 1;
VectorXd b(4);
b << 1./6, 1./3, 1./3, 1./6;
// Construct data for the IVP
double T = 1;
int n = 5;
VectorXd y0(2*n);
for(int i = 0; i < n; ++i) {
y0(i)=(i+1.)/n;
y0(i+n)=-1;
}
auto f = [n] (VectorXd y) {
VectorXd fy(2*n);
VectorXd g(n);
g(0) = y(0)*(y(1)+y(0));
g(n-1) = y(n-1)*(y(n-1)+y(n-2));
for(int i = 1; i < n-1; ++i) {
g(i) = y(i)*(y(i-1)+y(i+1));
}
Eigen::SparseMatrix<double> C(n,n);
C.reserve(3);
for(int i = 0; i < n; ++i) {
C.insert(i,i) = 2;
if(i < n-1) C.insert(i,i+1) = -1;
if(i >= 1) C.insert(i,i-1) = -1;
}
C.makeCompressed();
fy.head(n) = y.head(n);
Eigen::SparseLU< Eigen::SparseMatrix<double> > solver;
solver.analyzePattern(C);
solver.compute(C);
fy.tail(n) = solver.solve(g);
return fy;
};
errors(f, T, y0, A, b);
}
void ReliefGeneration::CompressHeightField(std::vector<double>& heightField, int resX, int resY)
{
double bbScale = 2;
double alpha = bbScale * 300.0;
double threthold = bbScale * 0.05;
int vertNum = (resX + 1) * (resY + 1);
std::vector<MagicMath::Vector3> DeltaVector(vertNum);
for (int xid = 0; xid < resX; xid++)
{
for (int yid = 0; yid < resY; yid++)
{
int index = xid * (resY + 1) + yid;
MagicMath::Vector3 deltaT(0, 0, 0);
deltaT[0] = heightField.at(index + resY + 1) - heightField.at(index);
deltaT[1] = heightField.at(index + 1) - heightField.at(index);
double deltaMag = deltaT.Normalise();
if (deltaMag > threthold)
{
deltaMag = 0;
}
else
{
deltaMag = log(1 + alpha * deltaMag) / alpha;
}
DeltaVector.at(index) = deltaT * deltaMag;
}
}
std::vector<double> LaplaceField(vertNum);
for (int xid = 1; xid < resX; xid++)
{
for (int yid = 1; yid < resY; yid++)
{
int index = xid * (resY + 1) + yid;
LaplaceField.at(index) = DeltaVector.at(index)[0] - DeltaVector.at(index - resY - 1)[0] +
DeltaVector.at(index)[1] - DeltaVector.at(index - 1)[1];
}
}
DebugLog << "Relief: Construct Matrix" << std::endl;
std::vector< Eigen::Triplet<double> > tripletList;
Eigen::VectorXd b(vertNum, 1);
for (int xid = 0; xid < resX + 1; xid++)
{
for (int yid = 0; yid < resY + 1; yid++)
{
int index = xid * (resY + 1) + yid;
if (xid == 0 || xid == resX || yid == 0 || yid == resY)
{
tripletList.push_back( Eigen::Triplet<double>(index, index, 1) );
b(index) = 0;
}
else
{
tripletList.push_back( Eigen::Triplet<double>(index, index, -4.0) );
tripletList.push_back( Eigen::Triplet<double>(index, index + 1, 1.0) );
tripletList.push_back( Eigen::Triplet<double>(index, index - 1, 1.0) );
tripletList.push_back( Eigen::Triplet<double>(index, index + resY + 1, 1.0) );
tripletList.push_back( Eigen::Triplet<double>(index, index - resY - 1, 1.0) );
b(index) = LaplaceField.at(index);
}
}
}
DebugLog << "Relief: Solve Matrix" << std::endl;
Eigen::SparseMatrix<double, Eigen::ColMajor> matA(vertNum,vertNum);
matA.setFromTriplets(tripletList.begin(), tripletList.end());
Eigen::SparseLU<Eigen::SparseMatrix<double, Eigen::ColMajor> > solver;
solver.compute(matA);
if(solver.info()!= Eigen::Success)
{
DebugLog << "Relief: SuperLU Failed" << std::endl;
}
Eigen::VectorXd res = solver.solve(b);
//Copy results
for (int i = 0; i < vertNum; i++)
{
heightField.at(i) = res(i);
}
}
IGL_INLINE void igl::PolyVectorFieldFinder<DerivedV, DerivedF>::
minQuadWithKnownMini(const Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar> > &Q,
const Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar> > &f,
const Eigen::VectorXi isConstrained,
const Eigen::Matrix<std::complex<typename DerivedV::Scalar>, Eigen::Dynamic, 1> &xknown,
Eigen::Matrix<std::complex<typename DerivedV::Scalar>, Eigen::Dynamic, 1> &x)
{
int N = Q.rows();
int nc = xknown.rows();
Eigen::VectorXi known; known.setZero(nc,1);
Eigen::VectorXi unknown; unknown.setZero(N-nc,1);
int indk = 0, indu = 0;
for (int i = 0; i<N; ++i)
if (isConstrained[i])
{
known[indk] = i;
indk++;
}
else
{
unknown[indu] = i;
indu++;
}
Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar>> Quu, Quk;
igl::slice(Q,unknown, unknown, Quu);
igl::slice(Q,unknown, known, Quk);
std::vector<typename Eigen::Triplet<std::complex<typename DerivedV::Scalar> > > tripletList;
Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar> > fu(N-nc,1);
igl::slice(f,unknown, Eigen::VectorXi::Zero(1,1), fu);
Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar> > rhs = (Quk*xknown).sparseView()+.5*fu;
Eigen::SparseLU< Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar>>> solver;
solver.compute(-Quu);
if(solver.info()!=Eigen::Success)
{
std::cerr<<"Decomposition failed!"<<std::endl;
return;
}
Eigen::SparseMatrix<std::complex<typename DerivedV::Scalar>> b = solver.solve(rhs);
if(solver.info()!=Eigen::Success)
{
std::cerr<<"Solving failed!"<<std::endl;
return;
}
indk = 0, indu = 0;
x.setZero(N,1);
for (int i = 0; i<N; ++i)
if (isConstrained[i])
x[i] = xknown[indk++];
else
x[i] = b.coeff(indu++,0);
}
void smooth(VectorField<float> &VF, const vector<int> &v_indices, const int n_unknowns )
{
typedef float T;
int nUnknowns = n_unknowns;
if (nUnknowns == 0)
for (const auto flag : v_indices)
if (flag < 0) nUnknowns++;
//2. build linear system
const int channels = VF.VF.cols();
std::vector< Eigen::Triplet<float> > lhsTriplets;
lhsTriplets.reserve(nUnknowns * 5);
Eigen::Matrix<T, -1, -1> rhs(nUnknowns, channels); //Eigen::MatrixXf rhs(nUnknowns, channels);
rhs.setZero();
for (int i = 0; i < v_indices.size(); i++) {
const int varible_id = v_indices[i];
if (varible_id == -1)
continue;
vector<int> neightbors = VF.VV[i];
#if 0
vector<int> weights = Vf.VVW[i];
T weight = 0;
for (int j = 0; j < weights.size(); j++)
weight += weights[j];
#else //uniform weights
vector<T> weights(neightbors.size(), -1);
T weight = neightbors.size();
#endif
for (int j = 0; j < neightbors.size(); j++) {
int neighbor_v = neightbors[j];
if (v_indices[neighbor_v] == -1) { //boundary
rhs.row(varible_id) -= weights[j] * VF.VF.row(neighbor_v);
}
else {
lhsTriplets.push_back(Eigen::Triplet<float>(
varible_id, v_indices[neighbor_v], weights[j]));
}
}
lhsTriplets.push_back(Eigen::Triplet<float>(
varible_id, varible_id, weight));
// Add f to rhs.
//rhs.row(pid) += VF.VF.row();
}
//3. Solve the sparse linear system of equations
Eigen::SparseMatrix<T> A(nUnknowns, nUnknowns);
A.setFromTriplets(lhsTriplets.begin(), lhsTriplets.end());
Eigen::SparseLU< Eigen::SparseMatrix<T> > solver;
solver.analyzePattern(A);
solver.factorize(A);
Eigen::Matrix<T, -1, -1>result(nUnknowns, channels);
// Eigen::MatrixXf result(nUnknowns, channels);
for (int c = 0; c < channels; ++c)
result.col(c) = solver.solve(rhs.col(c));
//4. Copy results back
for (int i = 0; i < v_indices.size(); i++) {
const int varible_id = v_indices[i];
if (varible_id == -1)
continue;
VF.VF.row(i) = result.row(varible_id);
}
}
void
poisson_blend(mve::FloatImage::ConstPtr src, mve::ByteImage::ConstPtr mask,
mve::FloatImage::Ptr dest, float alpha) {
assert(src->width() == mask->width() && mask->width() == dest->width());
assert(src->height() == mask->height() && mask->height() == dest->height());
assert(src->channels() == 3 && dest->channels() == 3);
assert(mask->channels() == 1);
assert(valid_mask(mask));
const int n = dest->get_pixel_amount();
const int width = dest->width();
const int height = dest->height();
const int channels = dest->channels();
mve::Image<int>::Ptr indices = mve::Image<int>::create(width, height, 1);
indices->fill(-1);
int index = 0;
for (int i = 0; i < n; ++i) {
if (mask->at(i) != 0) {
indices->at(i) = index;
index++;
}
}
const int nnz = index;
std::vector<math::Vec3f> coefficients_b;
coefficients_b.resize(nnz);
std::vector<Eigen::Triplet<float, int> > coefficients_A;
coefficients_A.reserve(nnz); //TODO better estimate...
for (int i = 0; i < n; ++i) {
const int row = indices->at(i);
if (mask->at(i) == 126 || mask->at(i) == 128) {
Eigen::Triplet<float, int> t(row, row, 1.0f);
coefficients_A.push_back(t);
coefficients_b[row] = math::Vec3f(&dest->at(i, 0));
}
if (mask->at(i) == 255) {
const int i01 = indices->at(i - width);
const int i10 = indices->at(i - 1);
const int i11 = indices->at(i);
const int i12 = indices->at(i + 1);
const int i21 = indices->at(i + width);
/* All neighbours should be eighter border conditions or part of the optimization. */
assert(i01 != -1 && i10 != -1 && i11 != -1 && i12 != -1 && i21 != -1);
Eigen::Triplet<float, int> t01(row, i01, 1.0f);
Eigen::Triplet<float, int> t10(row, i10, 1.0f);
Eigen::Triplet<float, int> t11(row, i11, -4.0f);
Eigen::Triplet<float, int> t12(row, i12, 1.0f);
Eigen::Triplet<float, int> t21(row, i21, 1.0f);
Eigen::Triplet<float, int> triplets[] = {t01, t10, t11, t12, t21};
coefficients_A.insert(coefficients_A.end(), triplets, triplets + 5);
math::Vec3f l_d = simple_laplacian(i, dest);
math::Vec3f l_s = simple_laplacian(i, src);
coefficients_b[row] = (alpha * l_s + (1.0f - alpha) * l_d);
}
}
SpMat A(nnz, nnz);
A.setFromTriplets(coefficients_A.begin(), coefficients_A.end());
Eigen::SparseLU<SpMat, Eigen::COLAMDOrdering<int> > solver;
solver.compute(A);
for (int channel = 0; channel < channels; ++channel) {
Eigen::VectorXf b(nnz);
for (std::size_t i = 0; i < coefficients_b.size(); ++i)
b[i] = coefficients_b[i][channel];
Eigen::VectorXf x(n);
x = solver.solve(b);
for (int i = 0; i < n; ++i) {
int index = indices->at(i);
if (index != -1) dest->at(i, channel) = x[index];
}
}
}
void MeshDenoisingViaL0Minimization::solveVertices(TriMesh &mesh, Eigen::MatrixXd &initial_vertices_matrix,
std::vector< std::vector<TriMesh::VertexHandle> > &edge_vertex_handle,
std::vector< std::vector<double> > &coef, std::vector<TriMesh::Point> &delta,
double alpha, double beta)
{
Eigen::MatrixXd right_term = initial_vertices_matrix;
Eigen::SparseMatrix<double> coef_matrix((int)mesh.n_vertices(), (int)mesh.n_vertices());
std::vector< Eigen::Triplet<double> > triple; triple.clear();
std::map<TriMesh::VertexHandle, double> vertex_coef;
std::set<TriMesh::EdgeHandle> edge_handle;;
for(TriMesh::VertexIter v_it = mesh.vertices_begin(); v_it != mesh.vertices_end(); v_it++)
{
edge_handle.clear();
vertex_coef.clear();
vertex_coef[*v_it] = 1.0;
for(TriMesh::VertexFaceIter vf_it = mesh.vf_iter(*v_it); vf_it.is_valid(); vf_it++)
{
for(TriMesh::FaceEdgeIter fe_it = mesh.fe_iter(*vf_it); fe_it.is_valid(); fe_it++)
{
edge_handle.insert(*fe_it);
}
}
TriMesh::Point right(0.0, 0.0, 0.0);
for(std::set<TriMesh::EdgeHandle>::iterator s_it = edge_handle.begin(); s_it != edge_handle.end(); s_it++)
{
if(!mesh.is_boundary(*s_it))
{
int index = (*s_it).idx();
TriMesh::VertexHandle v1 = edge_vertex_handle[index][0],
v2 = edge_vertex_handle[index][1],
v3 = edge_vertex_handle[index][2],
v4 = edge_vertex_handle[index][3];
double coe1 = coef[index][0],
coe2 = coef[index][1],
coe3 = coef[index][2],
coe4 = coef[index][3];
TriMesh::Point temp_delta = delta[index];
if(v1 == *v_it)
{
vertex_coef[v1] = vertex_coef[v1] + alpha + beta * coe1 * coe1;
vertex_coef[v2] = vertex_coef[v2] - alpha + beta * coe1 * coe2;
vertex_coef[v3] = vertex_coef[v3] + alpha + beta * coe1 * coe3;
vertex_coef[v4] = vertex_coef[v4] - alpha + beta * coe1 * coe4;
right += temp_delta * beta * coe1;
}
else if(v2 == *v_it)
{
vertex_coef[v1] = vertex_coef[v1] - alpha + beta * coe2 * coe1;
vertex_coef[v2] = vertex_coef[v2] + alpha + beta * coe2 * coe2;
vertex_coef[v3] = vertex_coef[v3] - alpha + beta * coe2 * coe3;
vertex_coef[v4] = vertex_coef[v4] + alpha + beta * coe2 * coe4;
right += temp_delta * beta * coe2;
}
else if(v3 == *v_it)
{
vertex_coef[v1] = vertex_coef[v1] + alpha + beta * coe3 * coe1;
vertex_coef[v2] = vertex_coef[v2] - alpha + beta * coe3 * coe2;
vertex_coef[v3] = vertex_coef[v3] + alpha + beta * coe3 * coe3;
vertex_coef[v4] = vertex_coef[v4] - alpha + beta * coe3 * coe4;
right += temp_delta * beta * coe3;
}
else if(v4 == *v_it)
{
vertex_coef[v1] = vertex_coef[v1] - alpha + beta * coe4 * coe1;
vertex_coef[v2] = vertex_coef[v2] + alpha + beta * coe4 * coe2;
vertex_coef[v3] = vertex_coef[v3] - alpha + beta * coe4 * coe3;
vertex_coef[v4] = vertex_coef[v4] + alpha + beta * coe4 * coe4;
right += temp_delta * beta * coe4;
}
}
}
right_term(v_it->idx(), 0) += right[0];
right_term(v_it->idx(), 1) += right[1];
right_term(v_it->idx(), 2) += right[2];
for(std::map<TriMesh::VertexHandle, double>::iterator m_it = vertex_coef.begin(); m_it != vertex_coef.end(); m_it++)
{
triple.push_back(Eigen::Triplet<double>(v_it->idx(), m_it->first.idx(), m_it->second));
}
}
coef_matrix.setFromTriplets(triple.begin(), triple.end());
Eigen::SparseLU<Eigen::SparseMatrix<double> > solver;
solver.analyzePattern(coef_matrix);
solver.factorize(coef_matrix);
Eigen::MatrixXd vertices_term = solver.solve(right_term);
for(TriMesh::VertexIter v_it = mesh.vertices_begin(); v_it != mesh.vertices_end(); v_it++)
{
int index = v_it->idx();
TriMesh::Point pt = TriMesh::Point(vertices_term(index,0), vertices_term(index,1), vertices_term(index,2));
mesh.set_point(*v_it, pt);
}
}
int main (int argc, char **argv)
{
GetPot cl (argc, argv);
if (cl.search (2, "-h", "--help"))
{
std::cerr << help_text << std::endl;
return 0;
}
const double a =
cl.follow (0.0, "-a");
const double b =
cl.follow (1.0, "-b");
const unsigned int nnodes =
cl.follow (100, 2, "-n", "--nnodes");
const std::string diffusion =
cl.follow ("1.0", 2, "-d", "--diffusion");
const std::string forcing =
cl.follow ("1.0", 2, "-f", "--forcing");
coeff f_coeff (forcing);
coeff a_coeff (diffusion);
const std::string quadrature =
cl.follow ("trapezoidal.so",
2, "-q", "--quadrature-rule");
std::function <void ()> r_r;
void * handle = dlopen (quadrature.c_str (), RTLD_NOW);
if (! handle)
{
std::cerr << "fem1d: cannot load dynamic object!"
<< std::endl;
std::cerr << dlerror ()
<< std::endl;
return (-1);
}
void * sym = dlsym (handle, "register_rules");
if (! sym)
{
std::cerr << "fem1d: cannot load symbol!"
<< std::endl;
std::cerr << dlerror ()
<< std::endl;
return (-1);
}
r_r = reinterpret_cast <void (*) ()> (sym);
r_r ();
auto & the_factory = quadrature_factory::instance ();
auto integrate = the_factory.create ("trapezoidal");
if (! integrate)
{
std::cerr << "rule name unknown" << std::endl;
return (-1);
}
mesh m (a, b, nnodes);
Eigen::SparseMatrix<double> A(nnodes, nnodes);
Eigen::Matrix2d mloc;
mloc << 0, 0, 0, 0;
for (unsigned int iel = 0; iel < m.nels; ++iel)
{
mloc << 0, 0, 0, 0;
for (unsigned int inode = 0; inode < 2; ++inode)
{
auto igrad = [=, &m] (double x) -> double
{
return basisfungrad
(x, m.nodes[m.elements[iel][0]],
m.nodes[m.elements[iel][1]],
inode == 0 ? 1.0 : 0.0,
inode == 1 ? 1.0 : 0.0);
};
for (unsigned int jnode = 0; jnode < 2; ++jnode)
{
auto jgrad = [=, &m] (double x) -> double
{
return basisfungrad
(x, m.nodes[m.elements[iel][0]],
m.nodes[m.elements[iel][1]],
jnode == 0 ? 1.0 : 0.0,
jnode == 1 ? 1.0 : 0.0);
};
mloc(inode,jnode) +=
(*integrate) ([=, &m, &igrad, &jgrad, &a_coeff]
(double x) -> double
{
return (igrad (x) *
jgrad (x) *
a_coeff (x));
},
m.nodes[m.elements[iel][0]],
m.nodes[m.elements[iel][1]]);
A.coeffRef(m.elements[iel][inode],
m.elements[iel][jnode]) +=
mloc(inode,jnode);
}
}
}
Eigen::VectorXd f(nnodes);
for (unsigned int ii = 0; ii < nnodes; ++ii)
f(ii) = 0.0;
Eigen::Vector2d vloc;
for (unsigned int iel = 0; iel < m.nels; ++iel)
{
vloc << 0, 0;
for (unsigned int inode = 0; inode < 2; ++inode)
{
auto ifun = [=, &m] (double x) -> double
{
return basisfun
(x, m.nodes[m.elements[iel][0]],
m.nodes[m.elements[iel][1]],
inode == 0 ? 1.0 : 0.0,
inode == 1 ? 1.0 : 0.0);
};
vloc(inode) +=
(*integrate) ([=, &m, &ifun, &f_coeff]
(double x) -> double
{
return (ifun (x) *
f_coeff (x));
},
m.nodes[m.elements[iel][0]],
m.nodes[m.elements[iel][1]]);
f(m.elements[iel][inode]) += vloc(inode);
}
}
f(0) = 0;
f(nnodes - 1) = 0;
A.coeffRef(0,0) = 1.0e10;
A.coeffRef(nnodes-1,nnodes-1) = 1.0e10;
for (unsigned int ii = 1; ii < nnodes; ++ii)
{
A.coeffRef(0, ii) = 0.0;
A.coeffRef(nnodes-1, nnodes-1-ii) = 0.0;
}
Eigen::SparseLU<Eigen::SparseMatrix<double>> solver;
A.makeCompressed ();
solver.analyzePattern(A);
solver.factorize(A);
Eigen::VectorXd uh = solver.solve (f);
for (unsigned int ii = 0; ii < nnodes; ++ii)
std::cout << m.nodes[ii] << " "
<< uh(ii, 0)
<< std:: endl;
return 0;
};
bool fill_hole(std::vector<std::size_t> const & hole, UniGraph const & graph,
mve::TriangleMesh::ConstPtr mesh, mve::MeshInfo const & mesh_info,
std::vector<std::vector<VertexProjectionInfo> > * vertex_projection_infos,
std::vector<TexturePatch::Ptr> * texture_patches) {
mve::TriangleMesh::FaceList const & mesh_faces = mesh->get_faces();
mve::TriangleMesh::VertexList const & vertices = mesh->get_vertices();
std::map<std::size_t, std::set<std::size_t> > tmp;
for (std::size_t const face_id : hole) {
std::size_t const v0 = mesh_faces[face_id * 3];
std::size_t const v1 = mesh_faces[face_id * 3 + 1];
std::size_t const v2 = mesh_faces[face_id * 3 + 2];
tmp[v0].insert(face_id);
tmp[v1].insert(face_id);
tmp[v2].insert(face_id);
}
std::size_t const num_vertices = tmp.size();
/* Only fill small holes. */
if (num_vertices > MAX_HOLE_NUM_FACES) return false;
/* Calculate 2D parameterization using the technique from libremesh/patch2d,
* which was published as sourcecode accompanying the following paper:
*
* Isotropic Surface Remeshing
* Simon Fuhrmann, Jens Ackermann, Thomas Kalbe, Michael Goesele
*/
std::size_t seed = -1;
std::vector<bool> is_border(num_vertices, false);
std::vector<std::vector<std::size_t> > adj_verts_via_border(num_vertices);
/* Index structures to map from local <-> global vertex id. */
std::map<std::size_t, std::size_t> g2l;
std::vector<std::size_t> l2g(num_vertices);
/* Index structure to determine column in matrix/vector. */
std::vector<std::size_t> idx(num_vertices);
std::size_t num_border_vertices = 0;
bool disk_topology = true;
std::map<std::size_t, std::set<std::size_t> >::iterator it = tmp.begin();
for (std::size_t j = 0; j < num_vertices; ++j, ++it) {
std::size_t vertex_id = it->first;
g2l[vertex_id] = j;
l2g[j] = vertex_id;
/* Check topology in original mesh. */
if (mesh_info[vertex_id].vclass != mve::MeshInfo::VERTEX_CLASS_SIMPLE) {
/* Complex/Border vertex in original mesh */
disk_topology = false;
break;
}
/* Check new topology and determine if vertex is now at the border. */
std::vector<std::size_t> const & adj_faces = mesh_info[vertex_id].faces;
std::set<std::size_t> const & adj_hole_faces = it->second;
std::vector<std::pair<std::size_t, std::size_t> > fan;
for (std::size_t k = 0; k < adj_faces.size(); ++k) {
std::size_t adj_face = adj_faces[k];
if (graph.get_label(adj_faces[k]) == 0 &&
adj_hole_faces.find(adj_face) != adj_hole_faces.end()) {
std::size_t curr = adj_faces[k];
std::size_t next = adj_faces[(k + 1) % adj_faces.size()];
std::pair<std::size_t, std::size_t> pair(curr, next);
fan.push_back(pair);
}
}
std::size_t gaps = 0;
for (std::size_t k = 0; k < fan.size(); k++) {
std::size_t curr = fan[k].first;
std::size_t next = fan[(k + 1) % fan.size()].first;
if (fan[k].second != next) {
++gaps;
for (std::size_t l = 0; l < 3; ++l) {
if(mesh_faces[curr * 3 + l] == vertex_id) {
std::size_t second = mesh_faces[curr * 3 + (l + 2) % 3];
adj_verts_via_border[j].push_back(second);
}
if(mesh_faces[next * 3 + l] == vertex_id) {
std::size_t first = mesh_faces[next * 3 + (l + 1) % 3];
adj_verts_via_border[j].push_back(first);
}
}
}
}
is_border[j] = gaps == 1;
/* Check if vertex is now complex. */
if (gaps > 1) {
/* Complex vertex in hole */
disk_topology = false;
break;
}
if (is_border[j]) {
idx[j] = num_border_vertices++;
seed = vertex_id;
} else {
idx[j] = j - num_border_vertices;
}
}
tmp.clear();
/* No disk or genus zero topology */
if (!disk_topology || num_border_vertices == 0) return false;
std::vector<std::size_t> border; border.reserve(num_border_vertices);
std::size_t prev = seed;
std::size_t curr = seed;
while (prev == seed || curr != seed) {
std::size_t next = std::numeric_limits<std::size_t>::max();
std::vector<std::size_t> const & adj_verts = adj_verts_via_border[g2l[curr]];
for (std::size_t adj_vert : adj_verts) {
assert(is_border[g2l[adj_vert]]);
if (adj_vert != prev && adj_vert != curr) {
next = adj_vert;
break;
}
}
if (next != std::numeric_limits<std::size_t>::max()) {
prev = curr;
curr = next;
border.push_back(next);
} else {
/* No new border vertex */
border.clear();
break;
}
/* Loop within border */
if (border.size() > num_border_vertices) break;
}
if (border.size() != num_border_vertices) return false;
float total_length = 0.0f;
float total_projection_length = 0.0f;
for (std::size_t j = 0; j < border.size(); ++j) {
std::size_t vi0 = border[j];
std::size_t vi1 = border[(j + 1) % border.size()];
std::vector<VertexProjectionInfo> const & vpi0 = vertex_projection_infos->at(vi0);
std::vector<VertexProjectionInfo> const & vpi1 = vertex_projection_infos->at(vi0);
/* According to the previous checks (vertex class within the origial
* mesh and boundary) there already has to be at least one projection
* of each border vertex. */
assert(!vpi0.empty() && !vpi1.empty());
math::Vec2f vp0(0.0f), vp1(0.0f);
for (VertexProjectionInfo const & info0 : vpi0) {
for (VertexProjectionInfo const & info1 : vpi1) {
if (info0.texture_patch_id == info1.texture_patch_id) {
vp0 = info0.projection;
vp1 = info1.projection;
break;
}
}
}
total_projection_length += (vp0 - vp1).norm();
math::Vec3f const & v0 = vertices[vi0];
math::Vec3f const & v1 = vertices[vi1];
total_length += (v0 - v1).norm();
}
float radius = total_projection_length / (2.0f * MATH_PI);
if (total_length < std::numeric_limits<float>::epsilon()) return false;
float length = 0.0f;
std::vector<math::Vec2f> projections(num_vertices);
for (std::size_t j = 0; j < border.size(); ++j) {
float angle = 2.0f * MATH_PI * (length / total_length);
projections[g2l[border[j]]] = math::Vec2f(std::cos(angle), std::sin(angle));
math::Vec3f const & v0 = vertices[border[j]];
math::Vec3f const & v1 = vertices[border[(j + 1) % border.size()]];
length += (v0 - v1).norm();
}
typedef Eigen::Triplet<float, int> Triplet;
std::vector<Triplet> coeff;
std::size_t matrix_size = num_vertices - border.size();
Eigen::VectorXf xx(matrix_size), xy(matrix_size);
if (matrix_size != 0) {
Eigen::VectorXf bx(matrix_size);
Eigen::VectorXf by(matrix_size);
for (std::size_t j = 0; j < num_vertices; ++j) {
if (is_border[j]) continue;
std::size_t const vertex_id = l2g[j];
/* Calculate "Mean Value Coordinates" as proposed by Michael S. Floater */
std::map<std::size_t, float> weights;
std::vector<std::size_t> const & adj_faces = mesh_info[vertex_id].faces;
for (std::size_t adj_face : adj_faces) {
std::size_t v0 = mesh_faces[adj_face * 3];
std::size_t v1 = mesh_faces[adj_face * 3 + 1];
std::size_t v2 = mesh_faces[adj_face * 3 + 2];
if (v1 == vertex_id) std::swap(v1, v0);
if (v2 == vertex_id) std::swap(v2, v0);
math::Vec3f v01 = vertices[v1] - vertices[v0];
float v01n = v01.norm();
math::Vec3f v02 = vertices[v2] - vertices[v0];
float v02n = v02.norm();
/* Ensure numerical stability */
if (v01n * v02n < std::numeric_limits<float>::epsilon()) return false;
float alpha = std::acos(v01.dot(v02) / (v01n * v02n));
weights[g2l[v1]] += std::tan(alpha / 2.0f) / v01n;
weights[g2l[v2]] += std::tan(alpha / 2.0f) / v02n;
}
std::map<std::size_t, float>::iterator it;
float sum = 0.0f;
for (it = weights.begin(); it != weights.end(); ++it)
sum += it->second;
assert(sum > 0.0f);
for (it = weights.begin(); it != weights.end(); ++it)
it->second /= sum;
bx[idx[j]] = 0.0f;
by[idx[j]] = 0.0f;
for (it = weights.begin(); it != weights.end(); ++it) {
if (is_border[it->first]) {
std::size_t border_vertex_id = border[idx[it->first]];
bx[idx[j]] += projections[g2l[border_vertex_id]][0] * it->second;
by[idx[j]] += projections[g2l[border_vertex_id]][1] * it->second;
} else {
coeff.push_back(Triplet(idx[j], idx[it->first], -it->second));
}
}
}
for (std::size_t j = 0; j < matrix_size; ++j) {
coeff.push_back(Triplet(j, j, 1.0f));
}
typedef Eigen::SparseMatrix<float> SpMat;
SpMat A(matrix_size, matrix_size);
A.setFromTriplets(coeff.begin(), coeff.end());
Eigen::SparseLU<SpMat> solver;
solver.analyzePattern(A);
solver.factorize(A);
xx = solver.solve(bx);
xy = solver.solve(by);
}
float const max_hole_patch_size = MAX_HOLE_PATCH_SIZE;
int image_size = std::min(std::floor(radius * 1.1f) * 2.0f, max_hole_patch_size);
/* Ensure a minimum scale of one */
image_size += 2 * (1 + texture_patch_border);
int scale = image_size / 2 - texture_patch_border;
for (std::size_t j = 0, k = 0; j < num_vertices; ++j) {
if (is_border[j]) {
projections[j] = projections[j] * scale + image_size / 2;
} else {
projections[j] = math::Vec2f(xx[k], xy[k]) * scale + image_size / 2;
++k;
}
}
mve::ByteImage::Ptr image = mve::ByteImage::create(image_size, image_size, 3);
//DEBUG image->fill_color(*math::Vec4uc(0, 255, 0, 255));
std::vector<math::Vec2f> texcoords; texcoords.reserve(hole.size());
for (std::size_t const face_id : hole) {
for (std::size_t j = 0; j < 3; ++j) {
std::size_t const vertex_id = mesh_faces[face_id * 3 + j];
math::Vec2f const & projection = projections[g2l[vertex_id]];
texcoords.push_back(projection);
}
}
TexturePatch::Ptr texture_patch = TexturePatch::create(0, hole, texcoords, image);
std::size_t texture_patch_id;
#pragma omp critical
{
texture_patches->push_back(texture_patch);
texture_patch_id = texture_patches->size() - 1;
}
for (std::size_t j = 0; j < num_vertices; ++j) {
std::size_t const vertex_id = l2g[j];
std::vector<std::size_t> const & adj_faces = mesh_info[vertex_id].faces;
std::vector<std::size_t> faces; faces.reserve(adj_faces.size());
for (std::size_t adj_face : adj_faces) {
if (graph.get_label(adj_face) == 0) {
faces.push_back(adj_face);
}
}
VertexProjectionInfo info = {texture_patch_id, projections[j], faces};
#pragma omp critical
vertex_projection_infos->at(vertex_id).push_back(info);
}
return true;
}
void
generate_texture_patches(UniGraph const & graph, std::vector<TextureView> const & texture_views,
mve::TriangleMesh::ConstPtr mesh, mve::VertexInfoList::ConstPtr vertex_infos,
std::vector<std::vector<VertexProjectionInfo> > * vertex_projection_infos,
std::vector<TexturePatch> * texture_patches) {
util::WallTimer timer;
mve::TriangleMesh::FaceList const & mesh_faces = mesh->get_faces();
mve::TriangleMesh::VertexList const & vertices = mesh->get_vertices();
vertex_projection_infos->resize(vertices.size());
std::size_t num_patches = 0;
std::cout << "\tRunning... " << std::flush;
#pragma omp parallel for schedule(dynamic)
for (std::size_t i = 0; i < texture_views.size(); ++i) {
std::vector<std::vector<std::size_t> > subgraphs;
int const label = i + 1;
graph.get_subgraphs(label, &subgraphs);
std::list<TexturePatchCandidate> candidates;
for (std::size_t j = 0; j < subgraphs.size(); ++j) {
candidates.push_back(generate_candidate(label, texture_views[i], subgraphs[j], mesh));
}
/* Merge candidates which contain the same image content. */
std::list<TexturePatchCandidate>::iterator it, sit;
for (it = candidates.begin(); it != candidates.end(); ++it) {
for (sit = candidates.begin(); sit != candidates.end();) {
Rect<int> bounding_box = sit->bounding_box;
if (it != sit && bounding_box.is_inside(&it->bounding_box)) {
TexturePatch::Faces & faces = it->texture_patch.get_faces();
TexturePatch::Faces & ofaces = sit->texture_patch.get_faces();
faces.insert(faces.end(), ofaces.begin(), ofaces.end());
TexturePatch::Texcoords & texcoords = it->texture_patch.get_texcoords();
TexturePatch::Texcoords & otexcoords = sit->texture_patch.get_texcoords();
math::Vec2f offset;
offset[0] = sit->bounding_box.min_x - it->bounding_box.min_x;
offset[1] = sit->bounding_box.min_y - it->bounding_box.min_y;
for (std::size_t i = 0; i < otexcoords.size(); ++i) {
texcoords.push_back(otexcoords[i] + offset);
}
sit = candidates.erase(sit);
} else {
++sit;
}
}
}
it = candidates.begin();
for (; it != candidates.end(); ++it) {
std::size_t texture_patch_id;
#pragma omp critical
{
texture_patches->push_back(it->texture_patch);
texture_patch_id = num_patches++;
}
std::vector<std::size_t> const & faces = it->texture_patch.get_faces();
std::vector<math::Vec2f> const & texcoords = it->texture_patch.get_texcoords();
for (std::size_t i = 0; i < faces.size(); ++i) {
std::size_t const face_id = faces[i];
std::size_t const face_pos = face_id * 3;
for (std::size_t j = 0; j < 3; ++j) {
std::size_t const vertex_id = mesh_faces[face_pos + j];
math::Vec2f const projection = texcoords[i * 3 + j];
VertexProjectionInfo info = {texture_patch_id, projection, {face_id}};
#pragma omp critical
vertex_projection_infos->at(vertex_id).push_back(info);
}
}
}
}
merge_vertex_projection_infos(vertex_projection_infos);
std::size_t num_holes = 0;
std::size_t num_hole_faces = 0;
//if (!settings.skip_hole_filling) {
{
std::vector<std::vector<std::size_t> > subgraphs;
graph.get_subgraphs(0, &subgraphs);
#pragma omp parallel for schedule(dynamic)
for (std::size_t i = 0; i < subgraphs.size(); ++i) {
std::vector<std::size_t> const & subgraph = subgraphs[i];
std::map<std::size_t, std::set<std::size_t> > tmp;
for (std::size_t const face_id : subgraph) {
std::size_t const v0 = mesh_faces[face_id * 3];
std::size_t const v1 = mesh_faces[face_id * 3 + 1];
std::size_t const v2 = mesh_faces[face_id * 3 + 2];
tmp[v0].insert(face_id);
tmp[v1].insert(face_id);
tmp[v2].insert(face_id);
}
std::size_t const num_vertices = tmp.size();
/* Only fill small holes. */
if (num_vertices > 100) {
//std::cerr << "Hole to large" << std::endl;
continue;
}
/* Calculate 2D parameterization using the technique from libremesh/patch2d,
* which was published as sourcecode accompanying the following paper:
*
* Isotropic Surface Remeshing
* Simon Fuhrmann, Jens Ackermann, Thomas Kalbe, Michael Goesele
*/
std::size_t seed = -1;
std::vector<bool> is_border(num_vertices, false);
std::vector<std::vector<std::size_t> > adj_verts_via_border(num_vertices);
/* Index structures to map from local <-> global vertex id. */
std::map<std::size_t, std::size_t> g2l;
std::vector<std::size_t> l2g(num_vertices);
/* Index structure to determine column in matrix/vector. */
std::vector<std::size_t> idx(num_vertices);
std::size_t num_border_vertices = 0;
bool disk_topology = true;
std::map<std::size_t, std::set<std::size_t> >::iterator it = tmp.begin();
for (std::size_t j = 0; j < num_vertices; ++j, ++it) {
std::size_t vertex_id = it->first;
g2l[vertex_id] = j;
l2g[j] = vertex_id;
/* Check topology in original mesh. */
if (vertex_infos->at(vertex_id).vclass != mve::VERTEX_CLASS_SIMPLE) {
//std::cerr << "Complex/Border vertex in original mesh" << std::endl;
disk_topology = false;
break;
}
/* Check new topology and determine if vertex is now at the border. */
std::vector<std::size_t> const & adj_faces = vertex_infos->at(vertex_id).faces;
std::set<std::size_t> const & adj_hole_faces = it->second;
std::vector<std::pair<std::size_t, std::size_t> > fan;
for (std::size_t k = 0; k < adj_faces.size(); ++k) {
std::size_t adj_face = adj_faces[k];
if (graph.get_label(adj_faces[k]) == 0 &&
adj_hole_faces.find(adj_face) != adj_hole_faces.end()) {
std::size_t curr = adj_faces[k];
std::size_t next = adj_faces[(k + 1) % adj_faces.size()];
std::pair<std::size_t, std::size_t> pair(curr, next);
fan.push_back(pair);
}
}
std::size_t gaps = 0;
for (std::size_t k = 0; k < fan.size(); k++) {
std::size_t curr = fan[k].first;
std::size_t next = fan[(k + 1) % fan.size()].first;
if (fan[k].second != next) {
++gaps;
for (std::size_t l = 0; l < 3; ++l) {
if(mesh_faces[curr * 3 + l] == vertex_id) {
std::size_t second = mesh_faces[curr * 3 + (l + 2) % 3];
adj_verts_via_border[j].push_back(second);
}
if(mesh_faces[next * 3 + l] == vertex_id) {
std::size_t first = mesh_faces[next * 3 + (l + 1) % 3];
adj_verts_via_border[j].push_back(first);
}
}
}
}
is_border[j] = gaps == 1;
/* Check if vertex is now complex. */
if (gaps > 1) {
//std::cerr << "Complex vertex in hole" << std::endl;
disk_topology = false;
break;
}
if (is_border[j]) {
idx[j] = num_border_vertices++;
seed = vertex_id;
} else {
idx[j] = j - num_border_vertices;
}
}
tmp.clear();
if (!disk_topology) continue;
if (num_border_vertices == 0) {
//std::cerr << "Genus zero topology" << std::endl;
continue;
}
std::vector<std::size_t> border; border.reserve(num_border_vertices);
std::size_t prev = seed;
std::size_t curr = seed;
while (prev == seed || curr != seed) {
std::size_t next = std::numeric_limits<std::size_t>::max();
std::vector<std::size_t> const & adj_verts = adj_verts_via_border[g2l[curr]];
for (std::size_t adj_vert : adj_verts) {
assert(is_border[g2l[adj_vert]]);
if (adj_vert != prev && adj_vert != curr) {
next = adj_vert;
break;
}
}
if (next != std::numeric_limits<std::size_t>::max()) {
prev = curr;
curr = next;
border.push_back(next);
} else {
//std::cerr << "No new border vertex" << std::endl;
border.clear();
break;
}
if (border.size() > num_border_vertices) {
//std::cerr << "Loop within border" << std::endl;
break;
}
}
if (border.size() != num_border_vertices) {
continue;
}
float total_length = 0.0f;
float total_projection_length = 0.0f;
for (std::size_t j = 0; j < border.size(); ++j) {
std::size_t vi0 = border[j];
std::size_t vi1 = border[(j + 1) % border.size()];
std::vector<VertexProjectionInfo> const & vpi0 = vertex_projection_infos->at(vi0);
std::vector<VertexProjectionInfo> const & vpi1 = vertex_projection_infos->at(vi0);
/* According to the previous checks (vertex class within the origial
* mesh and boundary) there already has to be at least one projection
* of each border vertex. */
assert(!vpi0.empty() && !vpi1.empty());
math::Vec2f vp0(0.0f), vp1(0.0f);
for (VertexProjectionInfo const & info0 : vpi0) {
for (VertexProjectionInfo const & info1 : vpi1) {
if (info0.texture_patch_id == info1.texture_patch_id) {
vp0 = info0.projection;
vp1 = info1.projection;
break;
}
}
}
total_projection_length += (vp0 - vp1).norm();
math::Vec3f const & v0 = vertices[vi0];
math::Vec3f const & v1 = vertices[vi1];
total_length += (v0 - v1).norm();
}
float radius = total_projection_length / (2.0f * MATH_PI);
float length = 0.0f;
std::vector<math::Vec2f> projections(num_vertices);
for (std::size_t j = 0; j < border.size(); ++j) {
float angle = 2.0f * MATH_PI * (length / total_length);
projections[g2l[border[j]]] = math::Vec2f(std::cos(angle), std::sin(angle));
math::Vec3f const & v0 = vertices[border[j]];
math::Vec3f const & v1 = vertices[border[(j + 1) % border.size()]];
length += (v0 - v1).norm();
}
typedef Eigen::Triplet<float, int> Triplet;
std::vector<Triplet> coeff;
std::size_t matrix_size = num_vertices - border.size();
Eigen::VectorXf xx(matrix_size), xy(matrix_size);
if (matrix_size != 0) {
Eigen::VectorXf bx(matrix_size);
Eigen::VectorXf by(matrix_size);
for (std::size_t j = 0; j < num_vertices; ++j) {
if (is_border[j]) continue;
std::size_t const vertex_id = l2g[j];
/* Calculate "Mean Value Coordinates" as proposed by Michael S. Floater */
std::map<std::size_t, float> weights;
std::vector<std::size_t> const & adj_faces = vertex_infos->at(vertex_id).faces;
for (std::size_t adj_face : adj_faces) {
std::size_t v0 = mesh_faces[adj_face * 3];
std::size_t v1 = mesh_faces[adj_face * 3 + 1];
std::size_t v2 = mesh_faces[adj_face * 3 + 2];
if (v1 == vertex_id) std::swap(v1, v0);
if (v2 == vertex_id) std::swap(v2, v0);
math::Vec3f v01 = vertices[v1] - vertices[v0];
float v01n = v01.norm();
math::Vec3f v02 = vertices[v2] - vertices[v0];
float v02n = v02.norm();
float alpha = std::acos(v01.dot(v02) / (v01n * v02n));
weights[g2l[v1]] += std::tan(alpha / 2.0f) / v01n;
weights[g2l[v2]] += std::tan(alpha / 2.0f) / v02n;
}
std::map<std::size_t, float>::iterator it;
float sum = 0.0f;
for (it = weights.begin(); it != weights.end(); ++it)
sum += it->second;
for (it = weights.begin(); it != weights.end(); ++it)
it->second /= sum;
bx[idx[j]] = 0.0f;
by[idx[j]] = 0.0f;
for (it = weights.begin(); it != weights.end(); ++it) {
if (is_border[it->first]) {
std::size_t border_vertex_id = border[idx[it->first]];
bx[idx[j]] += projections[g2l[border_vertex_id]][0] * it->second;
by[idx[j]] += projections[g2l[border_vertex_id]][1] * it->second;
} else {
coeff.push_back(Triplet(idx[j], idx[it->first], -it->second));
}
}
}
for (std::size_t j = 0; j < matrix_size; ++j) {
coeff.push_back(Triplet(j, j, 1.0f));
}
typedef Eigen::SparseMatrix<float> SpMat;
SpMat A(matrix_size, matrix_size);
A.setFromTriplets(coeff.begin(), coeff.end());
Eigen::SparseLU<SpMat> solver;
solver.analyzePattern(A);
solver.factorize(A);
xx = solver.solve(bx);
xy = solver.solve(by);
}
int image_size = std::floor(radius * 1.1f) * 2 + 4;
int scale = image_size / 2 - texture_patch_border;
for (std::size_t j = 0, k = 0; j < num_vertices; ++j) {
if (!is_border[j]) {
projections[j] = math::Vec2f(xx[k], xy[k]) * scale + image_size / 2;
++k;
} else {
projections[j] = projections[j] * scale + image_size / 2;
}
}
mve::ByteImage::Ptr image = mve::ByteImage::create(image_size, image_size, 3);
//DEBUG image->fill_color(*math::Vec4uc(0, 255, 0, 255));
std::vector<math::Vec2f> texcoords; texcoords.reserve(subgraph.size());
for (std::size_t const face_id : subgraph) {
for (std::size_t j = 0; j < 3; ++j) {
std::size_t const vertex_id = mesh_faces[face_id * 3 + j];
math::Vec2f const & projection = projections[g2l[vertex_id]];
texcoords.push_back(projection);
}
}
TexturePatch texture_patch(0, subgraph, texcoords, image);
std::size_t texture_patch_id;
#pragma omp critical
{
texture_patches->push_back(texture_patch);
texture_patch_id = num_patches++;
num_hole_faces += subgraph.size();
++num_holes;
}
for (std::size_t j = 0; j < num_vertices; ++j) {
std::size_t const vertex_id = l2g[j];
std::vector<std::size_t> const & adj_faces = vertex_infos->at(vertex_id).faces;
std::vector<std::size_t> faces; faces.reserve(adj_faces.size());
for (std::size_t adj_face : adj_faces) {
if (graph.get_label(adj_face) == 0) {
faces.push_back(adj_face);
}
}
VertexProjectionInfo info = {texture_patch_id, projections[j], faces};
#pragma omp critical
vertex_projection_infos->at(vertex_id).push_back(info);
}
}
}
merge_vertex_projection_infos(vertex_projection_infos);
std::cout << "done. (Took " << timer.get_elapsed_sec() << "s)" << std::endl;
std::cout << "\t" << num_patches << " texture patches." << std::endl;
std::cout << "\t" << num_holes << " holes (" << num_hole_faces << " faces)." << std::endl;
}