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@@ -0,0 +1,2269 @@
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+#include "mixed_integer_quadrangulate.h"
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+#include "local_basis.h"
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+#include "tt.h"
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+
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+// includes for VertexIndexing
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+#include <igl/Pos.h>
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+#include <igl/is_border_vertex.h>
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+#include <igl/vf.h>
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+
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+
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+// includes for poissonSolver
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+#include "gmm/gmm.h"
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+#include <ConstrainedSolver.hh>
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+#include <MISolver.hh>
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+#include <GMM_Tools.hh>
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+//#include "auxmath.h"
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+//#include "sparsesystemdata.h"
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+#include "doublearea.h"
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+#include "per_face_normals.h"
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+
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+//
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+#include "cross_field_missmatch.h"
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+#include "comb_frame_field.h"
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+#include "cut_mesh_from_singularities.h"
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+#include "find_cross_field_singularities.h"
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+#include "compute_frame_field_bisectors.h"
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+
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+#define DEBUGPRINT 0
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+
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+
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+namespace igl {
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+
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+ class SparseMatrixData{
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+ protected:
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+ unsigned int m_nrows;
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+ unsigned int m_ncols;
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+ vector<unsigned int> m_rowind;
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+ vector<unsigned int> m_colind;
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+ vector<double> m_vals;
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+
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+ public:
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+ unsigned int nrows() { return m_nrows ; }
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+ unsigned int ncols() { return m_ncols ; }
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+ unsigned int nentries() { return m_vals.size(); }
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+ vector<unsigned int>& rowind() { return m_rowind ; }
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+ vector<unsigned int>& colind() { return m_colind ; }
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+ vector<double>& vals() { return m_vals ; }
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+
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+ // create an empty matrix with a fixed number of rows
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+ SparseMatrixData()
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+ {
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+ initialize(0,0);
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+ }
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+
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+ // create an empty matrix with a fixed number of rows
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+ void initialize(int nr, int nc) {
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+ assert(nr >= 0 && nc >=0);
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+ m_nrows = nr;
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+ m_ncols = nc;
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+
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+ m_rowind.resize(0);
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+ m_colind.resize(0);
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+ m_vals.resize(0);
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+ }
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+
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+ // add a nonzero entry to the matrix
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+ // no checks are done for coinciding entries
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+ // the interpretation of the repeated entries (replace or add)
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+ // depends on how the actual sparse matrix datastructure is constructed
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+
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+ void addEntryCmplx(unsigned int i, unsigned int j, std::complex<double> val) {
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+ m_rowind.push_back(2*i); m_colind.push_back(2*j); m_vals.push_back( val.real());
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+ m_rowind.push_back(2*i); m_colind.push_back(2*j+1); m_vals.push_back(-val.imag());
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+ m_rowind.push_back(2*i+1); m_colind.push_back(2*j); m_vals.push_back( val.imag());
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+ m_rowind.push_back(2*i+1); m_colind.push_back(2*j+1); m_vals.push_back( val.real());
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+ }
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+
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+ void addEntryReal(unsigned int i, unsigned int j, double val) {
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+ m_rowind.push_back(i); m_colind.push_back(j); m_vals.push_back(val);
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+ }
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+
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+ virtual ~SparseMatrixData() {
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+ }
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+
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+ };
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+
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+ // a small class to manage storage for matrix data
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+ // not using stl vectors: want to make all memory management
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+ // explicit to avoid hidden automatic reallocation
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+ // TODO: redo with STL vectors but with explicit mem. management
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+
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+ class SparseSystemData {
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+ private:
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+ // matrix representation, A[rowind[i],colind[i]] = vals[i]
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+ // right-hand side
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+ SparseMatrixData m_A;
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+ double *m_b;
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+ double *m_x;
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+
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+ public:
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+ SparseMatrixData& A() { return m_A; }
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+ double* b() { return m_b ; }
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+ double* x() { return m_x ; }
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+ unsigned int nrows() { return m_A.nrows(); }
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+
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+ public:
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+
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+ SparseSystemData(): m_A(), m_b(NULL), m_x(NULL){ }
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+
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+ void initialize(unsigned int nr, unsigned int nc) {
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+ m_A.initialize(nr,nc);
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+ m_b = new double[nr];
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+ m_x = new double[nr];
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+ assert(m_b);
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+ std::fill( m_b, m_b+nr, 0.);
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+ }
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+
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+ void addRHSCmplx(unsigned int i, std::complex<double> val) {
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+ assert( 2*i+1 < m_A.nrows());
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+ m_b[2*i] += val.real(); m_b[2*i+1] += val.imag();
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+ }
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+
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+ void setRHSCmplx(unsigned int i, std::complex<double> val) {
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+ assert( 2*i+1 < m_A.nrows());
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+ m_b[2*i] = val.real(); m_b[2*i+1] = val.imag();
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+ }
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+
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+ std::complex<double> getRHSCmplx(unsigned int i) {
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+ assert( 2*i+1 < m_A.nrows());
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+ return std::complex<double>( m_b[2*i], m_b[2*i+1]);
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+ }
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+
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+ double getRHSReal(unsigned int i) {
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+ assert( i < m_A.nrows());
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+ return m_b[i];
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+ }
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+
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+ std::complex<double> getXCmplx(unsigned int i) {
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+ assert( 2*i+1 < m_A.nrows());
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+ return std::complex<double>( m_x[2*i], m_x[2*i+1]);
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+ }
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+
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+ void cleanMem() {
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+ //m_A.cleanup();
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+ delete [] m_b;
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+ delete [] m_x;
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+ }
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+
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+ virtual ~SparseSystemData() {
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+ delete [] m_b;
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+ delete [] m_x;
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+ }
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+ };
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+
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+ struct SeamInfo
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+ {
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+ int v0,v0p,v1,v1p;
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+ int integerVar;
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+ unsigned char MMatch;
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+
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+ SeamInfo(int _v0,
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+ int _v1,
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+ int _v0p,
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+ int _v1p,
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+ int _MMatch,
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+ int _integerVar);
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+
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+ SeamInfo(const SeamInfo &S1);
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+ };
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+
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+ struct MeshSystemInfo
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+ {
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+ ///total number of scalar variables
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+ int num_scalar_variables;
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+ ////number of vertices variables
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+ int num_vert_variables;
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+ ///num of integer for cuts
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+ int num_integer_cuts;
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+ ///this are used for drawing purposes
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+ std::vector<SeamInfo> EdgeSeamInfo;
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+#if 0
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+ ///this are values of integer variables after optimization
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+ std::vector<int> IntegerValues;
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+#endif
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+ };
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+
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+
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+ template <typename DerivedV, typename DerivedF>
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+ class VertexIndexing
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+ {
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+ public:
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+ // Input:
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+ const Eigen::PlainObjectBase<DerivedV> &V;
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+ const Eigen::PlainObjectBase<DerivedF> &F;
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+ const Eigen::PlainObjectBase<DerivedF> &TT;
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+ const Eigen::PlainObjectBase<DerivedF> &TTi;
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+ const Eigen::PlainObjectBase<DerivedV> &PD1;
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+ const Eigen::PlainObjectBase<DerivedV> &PD2;
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+
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+ const Eigen::Matrix<int, Eigen::Dynamic, 3> &Handle_MMatch;
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+ const Eigen::Matrix<int, Eigen::Dynamic, 1> &Handle_Singular; // bool
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+ const Eigen::Matrix<int, Eigen::Dynamic, 1> &Handle_SingularDegree; // vertex;
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+ const Eigen::Matrix<int, Eigen::Dynamic, 3> &Handle_Seams; // 3 bool
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+
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+
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+ ///this handle for mesh TODO: move with the other global variables
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+ MeshSystemInfo Handle_SystemInfo;
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+
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+ // Output:
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+ ///this maps the integer for edge - face
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+ Eigen::MatrixXi Handle_Integer; // TODO: remove it is useless
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+
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+ ///per face indexes of vertex in the solver
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+ Eigen::MatrixXi HandleS_Index;
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+
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+ ///per vertex variable indexes
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+ std::vector<std::vector<int> > HandleV_Integer;
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+
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+ // internal
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+ std::vector<std::vector<int> > VF, VFi;
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+ std::vector<bool> V_border; // bool
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+
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+ VertexIndexing(const Eigen::PlainObjectBase<DerivedV> &_V,
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+ const Eigen::PlainObjectBase<DerivedF> &_F,
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+ const Eigen::PlainObjectBase<DerivedF> &_TT,
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+ const Eigen::PlainObjectBase<DerivedF> &_TTi,
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+ const Eigen::PlainObjectBase<DerivedV> &_PD1,
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+ const Eigen::PlainObjectBase<DerivedV> &_PD2,
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+ const Eigen::Matrix<int, Eigen::Dynamic, 3> &_Handle_MMatch,
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+ const Eigen::Matrix<int, Eigen::Dynamic, 1> &_Handle_Singular,
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+ const Eigen::Matrix<int, Eigen::Dynamic, 1> &_Handle_SingularDegree,
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+ const Eigen::Matrix<int, Eigen::Dynamic, 3> &_Handle_Seams
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+ );
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+
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+ ///vertex to variable mapping
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+ void InitMapping();
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+
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+ void InitFaceIntegerVal();
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+
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+ void InitSeamInfo();
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+
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+
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+ private:
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+ ///this maps back index to vertices
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+ std::vector<int> IndexToVert; // TODO remove it is useless
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+
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+ ///this is used for drawing purposes
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+ std::vector<int> duplicated; // TODO remove it is useless
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+
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+ void FirstPos(const int v, int &f, int &edge);
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+
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+ int AddNewIndex(const int v0);
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+
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+ bool HasIndex(int indexVert,int indexVar);
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+
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+ void GetSeamInfo(const int f0,
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+ const int f1,
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+ const int indexE,
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+ int &v0,int &v1,
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+ int &v0p,int &v1p,
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+ unsigned char &_MMatch,
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+ int &integerVar);
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+ bool IsSeam(const int f0, const int f1);
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+
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+ ///find initial position of the pos to
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+ // assing face to vert inxex correctly
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+ void FindInitialPos(const int vert, int &edge, int &face);
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+
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+
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+ ///intialize the mapping given an initial pos
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+ ///whih must be initialized with FindInitialPos
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+ void MapIndexes(const int vert, const int edge_init, const int f_init);
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+
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+ ///intialize the mapping for a given vertex
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+ void InitMappingSeam(const int vert);
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+
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+ ///intialize the mapping for a given sampled mesh
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+ void InitMappingSeam();
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+
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+ ///test consistency of face variables per vert mapping
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+ void TestSeamMappingFace(const int f);
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+
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+ ///test consistency of face variables per vert mapping
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+ void TestSeamMappingVertex(int indexVert);
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+
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+ ///check consistency of variable mapping across seams
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+ void TestSeamMapping();
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+
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+ };
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+
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+
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+ template <typename DerivedV, typename DerivedF>
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+ class PoissonSolver
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+ {
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+
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+ public:
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+ void SolvePoisson(Eigen::VectorXd Stiffness,
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+ double vector_field_scale=0.1f,
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+ double grid_res=1.f,
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+ bool direct_round=true,
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+ int localIter=0,
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+ bool _integer_rounding=true,
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+ vector<int> roundVertices = vector<int>(),
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+ vector<vector<int> > hardFeatures = vector<vector<int> >());
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+
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+ PoissonSolver(const Eigen::PlainObjectBase<DerivedV> &_V,
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+ const Eigen::PlainObjectBase<DerivedF> &_F,
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+ const Eigen::PlainObjectBase<DerivedF> &_TT,
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+ const Eigen::PlainObjectBase<DerivedF> &_TTi,
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+ const Eigen::PlainObjectBase<DerivedV> &_PD1,
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+ const Eigen::PlainObjectBase<DerivedV> &_PD2,
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+ const Eigen::MatrixXi &_HandleS_Index,
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+ const Eigen::Matrix<int, Eigen::Dynamic, 1>&_Handle_Singular,
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+ const MeshSystemInfo &_Handle_SystemInfo
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+ );
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+
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+ // Input:
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+ // Eigen::MatrixXd V;
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+ // Eigen::MatrixXi F;
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+ // Eigen::MatrixXd PD1;
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+ // Eigen::MatrixXd PD2;
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+ // Eigen::MatrixXi HandleS_Index;
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+ // Eigen::VectorXi Handle_Singular;
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+
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+ const Eigen::PlainObjectBase<DerivedV> &V;
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+ const Eigen::PlainObjectBase<DerivedF> &F;
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+ const Eigen::PlainObjectBase<DerivedF> &TT;
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+ const Eigen::PlainObjectBase<DerivedF> &TTi;
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+ const Eigen::PlainObjectBase<DerivedV> &PD1;
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+ const Eigen::PlainObjectBase<DerivedV> &PD2;
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+ const Eigen::Matrix<int, Eigen::Dynamic, 1> &Handle_Singular; // bool
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+ const Eigen::MatrixXi &HandleS_Index; //todo
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+
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+ const MeshSystemInfo &Handle_SystemInfo;
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+
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+ // Internal:
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+ Eigen::MatrixXd doublearea;
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+ Eigen::VectorXd Handle_Stiffness;
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+ Eigen::PlainObjectBase<DerivedV> N;
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+ std::vector<std::vector<int> > VF;
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+ std::vector<std::vector<int> > VFi;
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+ Eigen::MatrixXd UV; // this is probably useless
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+
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+ // Output:
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+ // per wedge UV coordinates, 6 coordinates (1 face) per row
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+ Eigen::MatrixXd WUV;
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+
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+ ///solver data
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+ SparseSystemData S;
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+
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+ ///vector of unknowns
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+ std::vector< double > X;
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+
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+ ////REAL PART
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+ ///number of fixed vertex
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+ unsigned int n_fixed_vars;
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+
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+ ///the number of REAL variables for vertices
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+ unsigned int n_vert_vars;
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+
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+ ///total number of variables of the system,
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+ ///do not consider constraints, but consider integer vars
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+ unsigned int num_total_vars;
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+
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+ //////INTEGER PART
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+ ///the total number of integer variables
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+ unsigned int n_integer_vars;
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+
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+ ///CONSTRAINT PART
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+ ///number of cuts constraints
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+ unsigned int num_cut_constraint;
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+
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+ // number of user-defined constraints
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+ unsigned int num_userdefined_constraint;
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+
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+ ///total number of constraints equations
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+ unsigned int num_constraint_equations;
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+
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+ ///total size of the system including constraints
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+ unsigned int system_size;
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+
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+ ///if you intend to make integer rotation
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+ ///and translations
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+ bool integer_jumps_bary;
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+
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+ ///vector of blocked vertices
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+ std::vector<int> Hard_constraints;
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+
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+ ///vector of indexes to round
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+ std::vector<int> ids_to_round;
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+
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+ ///vector of indexes to round
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+ std::vector<std::vector<int > > userdefined_constraints;
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+
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+ ///boolean that is true if rounding to integer is needed
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+ bool integer_rounding;
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+
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+ ///START SYSTEM ACCESS METHODS
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+ ///add an entry to the LHS
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+ void AddValA(int Xindex,
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+ int Yindex,
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+ double val);
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+
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+ ///add a complex entry to the LHS
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+ void AddComplexA(int VarXindex,
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+ int VarYindex,
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+ std::complex<double> val);
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+
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+ ///add a velue to the RHS
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+ void AddValB(int Xindex,
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+ double val);
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+
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+ ///add the area term, scalefactor is used to sum up
|
|
|
+ ///and normalize on the overlap zones
|
|
|
+ void AddAreaTerm(int index[3][3][2],double ScaleFactor);
|
|
|
+
|
|
|
+ ///set the diagonal of the matrix (which is zero at the beginning)
|
|
|
+ ///such that the sum of a row or a colums is zero
|
|
|
+ void SetDiagonal(double val[3][3]);
|
|
|
+
|
|
|
+ ///given a vector of scalar values and
|
|
|
+ ///a vector of indexes add such values
|
|
|
+ ///as specified by the indexes
|
|
|
+ void AddRHS(double b[6],
|
|
|
+ int index[3]);
|
|
|
+
|
|
|
+ ///add a 3x3 block matrix to the system matrix...
|
|
|
+ ///indexes are specified in the 3x3 matrix of x,y pairs
|
|
|
+ ///indexes must be multiplied by 2 cause u and v
|
|
|
+ void Add33Block(double val[3][3], int index[3][3][2]);
|
|
|
+
|
|
|
+ ///add a 3x3 block matrix to the system matrix...
|
|
|
+ ///indexes are specified in the 3x3 matrix of x,y pairs
|
|
|
+ ///indexes must be multiplied by 2 cause u and v
|
|
|
+ void Add44Block(double val[4][4],int index[4][4][2]);
|
|
|
+ ///END SYSTEM ACCESS METHODS
|
|
|
+
|
|
|
+ ///START COMMON MATH FUNCTIONS
|
|
|
+ ///return the complex encoding the rotation
|
|
|
+ ///for a given missmatch interval
|
|
|
+ std::complex<double> GetRotationComplex(int interval);
|
|
|
+ ///END COMMON MATH FUNCTIONS
|
|
|
+
|
|
|
+
|
|
|
+ ///START ENERGY MINIMIZATION PART
|
|
|
+ ///initialize the LHS for a given face
|
|
|
+ ///for minimization of Dirichlet's energy
|
|
|
+ void perElementLHS(int f,
|
|
|
+ double val[3][3],
|
|
|
+ int index[3][3][2]);
|
|
|
+
|
|
|
+ ///initialize the RHS for a given face
|
|
|
+ ///for minimization of Dirichlet's energy
|
|
|
+ void perElementRHS(int f,
|
|
|
+ double b[6],
|
|
|
+ double vector_field_scale=1);
|
|
|
+
|
|
|
+ ///evaluate the LHS and RHS for a single face
|
|
|
+ ///for minimization of Dirichlet's energy
|
|
|
+ void PerElementSystemReal(int f,
|
|
|
+ double val[3][3],
|
|
|
+ int index[3][3][2],
|
|
|
+ double b[6],
|
|
|
+ double vector_field_scale=1.0);
|
|
|
+ ///END ENERGY MINIMIZATION PART
|
|
|
+
|
|
|
+ ///START FIXING VERTICES
|
|
|
+ ///set a given vertex as fixed
|
|
|
+ void AddFixedVertex(int v);
|
|
|
+
|
|
|
+ ///find vertex to fix in case we're using
|
|
|
+ ///a vector field NB: multiple components not handled
|
|
|
+ void FindFixedVertField();
|
|
|
+
|
|
|
+ ///find hard constraint depending if using or not
|
|
|
+ ///a vector field
|
|
|
+ void FindFixedVert();
|
|
|
+
|
|
|
+ int GetFirstVertexIndex(int v);
|
|
|
+
|
|
|
+ ///fix the vertices which are flagged as fixed
|
|
|
+ void FixBlockedVertex();
|
|
|
+ ///END FIXING VERTICES
|
|
|
+
|
|
|
+ ///HANDLING SINGULARITY
|
|
|
+ //set the singularity round to integer location
|
|
|
+ void AddSingularityRound();
|
|
|
+
|
|
|
+ void AddToRoundVertices(vector<int> ids);
|
|
|
+
|
|
|
+ ///START GENERIC SYSTEM FUNCTIONS
|
|
|
+ //build the laplacian matrix cyclyng over all rangemaps
|
|
|
+ //and over all faces
|
|
|
+ void BuildLaplacianMatrix(double vfscale=1);
|
|
|
+
|
|
|
+ ///find different sized of the system
|
|
|
+ void FindSizes();
|
|
|
+
|
|
|
+ void AllocateSystem();
|
|
|
+
|
|
|
+ ///intitialize the whole matrix
|
|
|
+ void InitMatrix();
|
|
|
+
|
|
|
+ ///map back coordinates after that
|
|
|
+ ///the system has been solved
|
|
|
+ void MapCoords();
|
|
|
+ ///END GENERIC SYSTEM FUNCTIONS
|
|
|
+
|
|
|
+ ///set the constraints for the inter-range cuts
|
|
|
+ void BuildSeamConstraintsExplicitTranslation();
|
|
|
+
|
|
|
+ ///set the constraints for the inter-range cuts
|
|
|
+ void BuildUserDefinedConstraints();
|
|
|
+
|
|
|
+ ///call of the mixed integer solver
|
|
|
+ void MixedIntegerSolve(double cone_grid_res=1,
|
|
|
+ bool direct_round=true,
|
|
|
+ int localIter=0);
|
|
|
+
|
|
|
+ void clearUserConstraint();
|
|
|
+
|
|
|
+ void addSharpEdgeConstraint(int fid, int vid);
|
|
|
+
|
|
|
+ };
|
|
|
+
|
|
|
+ template <typename DerivedV, typename DerivedF, typename DerivedU>
|
|
|
+ class MIQ
|
|
|
+ {
|
|
|
+ private:
|
|
|
+ const Eigen::PlainObjectBase<DerivedV> &V;
|
|
|
+ const Eigen::PlainObjectBase<DerivedF> &F;
|
|
|
+ Eigen::MatrixXd WUV;
|
|
|
+ // internal
|
|
|
+ Eigen::PlainObjectBase<DerivedF> TT;
|
|
|
+ Eigen::PlainObjectBase<DerivedF> TTi;
|
|
|
+
|
|
|
+ // Stiffness per face
|
|
|
+ Eigen::VectorXd Handle_Stiffness;
|
|
|
+ Eigen::PlainObjectBase<DerivedV> B1, B2, B3;
|
|
|
+
|
|
|
+ public:
|
|
|
+ MIQ(const Eigen::PlainObjectBase<DerivedV> &V_,
|
|
|
+ const Eigen::PlainObjectBase<DerivedF> &F_,
|
|
|
+ const Eigen::PlainObjectBase<DerivedV> &PD1_combed,
|
|
|
+ const Eigen::PlainObjectBase<DerivedV> &PD2_combed,
|
|
|
+ const Eigen::PlainObjectBase<DerivedV> &BIS1_combed,
|
|
|
+ const Eigen::PlainObjectBase<DerivedV> &BIS2_combed,
|
|
|
+ const Eigen::Matrix<int, Eigen::Dynamic, 3> &Handle_MMatch,
|
|
|
+ const Eigen::Matrix<int, Eigen::Dynamic, 1> &Handle_Singular,
|
|
|
+ const Eigen::Matrix<int, Eigen::Dynamic, 1> &Handle_SingularDegree,
|
|
|
+ const Eigen::Matrix<int, Eigen::Dynamic, 3> &Handle_Seams,
|
|
|
+ Eigen::PlainObjectBase<DerivedU> &UV,
|
|
|
+ Eigen::PlainObjectBase<DerivedF> &FUV,
|
|
|
+ double GradientSize = 30.0,
|
|
|
+ double Stiffness = 5.0,
|
|
|
+ bool DirectRound = false,
|
|
|
+ int iter = 5,
|
|
|
+ int localIter = 5,
|
|
|
+ bool DoRound = true,
|
|
|
+ std::vector<int> roundVertices = std::vector<int>(),
|
|
|
+ std::vector<std::vector<int> > hardFeatures = std::vector<std::vector<int> >());
|
|
|
+
|
|
|
+
|
|
|
+ void extractUV(Eigen::PlainObjectBase<DerivedU> &UV_out,
|
|
|
+ Eigen::PlainObjectBase<DerivedF> &FUV_out);
|
|
|
+
|
|
|
+ private:
|
|
|
+ int NumFlips(const MatrixXd& WUV);
|
|
|
+
|
|
|
+ double Distortion(int f, double h, const MatrixXd& WUV);
|
|
|
+
|
|
|
+ double LaplaceDistortion(const int f, double h, const MatrixXd& WUV);
|
|
|
+
|
|
|
+ bool updateStiffeningJacobianDistorsion(double grad_size, const MatrixXd& WUV);
|
|
|
+
|
|
|
+ inline bool IsFlipped(const Vector2d &uv0,
|
|
|
+ const Vector2d &uv1,
|
|
|
+ const Vector2d &uv2);
|
|
|
+
|
|
|
+ inline bool IsFlipped(const int i, const MatrixXd& WUV);
|
|
|
+
|
|
|
+ };
|
|
|
+};
|
|
|
+
|
|
|
+igl::SeamInfo::SeamInfo(int _v0,
|
|
|
+ int _v1,
|
|
|
+ int _v0p,
|
|
|
+ int _v1p,
|
|
|
+ int _MMatch,
|
|
|
+ int _integerVar)
|
|
|
+{
|
|
|
+ v0=_v0;
|
|
|
+ v1=_v1;
|
|
|
+ v0p=_v0p;
|
|
|
+ v1p=_v1p;
|
|
|
+ integerVar=_integerVar;
|
|
|
+ MMatch=_MMatch;
|
|
|
+}
|
|
|
+
|
|
|
+igl::SeamInfo::SeamInfo(const SeamInfo &S1)
|
|
|
+{
|
|
|
+ v0=S1.v0;
|
|
|
+ v1=S1.v1;
|
|
|
+ v0p=S1.v0p;
|
|
|
+ v1p=S1.v1p;
|
|
|
+ integerVar=S1.integerVar;
|
|
|
+ MMatch=S1.MMatch;
|
|
|
+}
|
|
|
+
|
|
|
+
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+igl::VertexIndexing<DerivedV, DerivedF>::VertexIndexing(const Eigen::PlainObjectBase<DerivedV> &_V,
|
|
|
+ const Eigen::PlainObjectBase<DerivedF> &_F,
|
|
|
+ const Eigen::PlainObjectBase<DerivedF> &_TT,
|
|
|
+ const Eigen::PlainObjectBase<DerivedF> &_TTi,
|
|
|
+ const Eigen::PlainObjectBase<DerivedV> &_PD1,
|
|
|
+ const Eigen::PlainObjectBase<DerivedV> &_PD2,
|
|
|
+ const Eigen::Matrix<int, Eigen::Dynamic, 3> &_Handle_MMatch,
|
|
|
+ const Eigen::Matrix<int, Eigen::Dynamic, 1> &_Handle_Singular,
|
|
|
+ const Eigen::Matrix<int, Eigen::Dynamic, 1> &_Handle_SingularDegree,
|
|
|
+ const Eigen::Matrix<int, Eigen::Dynamic, 3> &_Handle_Seams
|
|
|
+
|
|
|
+ ):
|
|
|
+V(_V),
|
|
|
+F(_F),
|
|
|
+TT(_TT),
|
|
|
+TTi(_TTi),
|
|
|
+PD1(_PD1),
|
|
|
+PD2(_PD2),
|
|
|
+Handle_MMatch(_Handle_MMatch),
|
|
|
+Handle_Singular(_Handle_Singular),
|
|
|
+Handle_SingularDegree(_Handle_SingularDegree),
|
|
|
+Handle_Seams(_Handle_Seams)
|
|
|
+{
|
|
|
+
|
|
|
+ V_border = igl::is_border_vertex(V,F);
|
|
|
+ igl::vf(V,F,VF,VFi);
|
|
|
+
|
|
|
+ IndexToVert.clear();
|
|
|
+
|
|
|
+ Handle_SystemInfo.num_scalar_variables=0;
|
|
|
+ Handle_SystemInfo.num_vert_variables=0;
|
|
|
+ Handle_SystemInfo.num_integer_cuts=0;
|
|
|
+
|
|
|
+ duplicated.clear();
|
|
|
+
|
|
|
+ HandleS_Index = Eigen::MatrixXi::Constant(F.rows(),3,-1);
|
|
|
+
|
|
|
+ Handle_Integer = Eigen::MatrixXi::Constant(F.rows(),3,-1);
|
|
|
+
|
|
|
+ HandleV_Integer.resize(V.rows());
|
|
|
+}
|
|
|
+
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::VertexIndexing<DerivedV, DerivedF>::FirstPos(const int v, int &f, int &edge)
|
|
|
+{
|
|
|
+ f = VF[v][0]; // f=v->cVFp();
|
|
|
+ edge = VFi[v][0]; // edge=v->cVFi();
|
|
|
+}
|
|
|
+
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+int igl::VertexIndexing<DerivedV, DerivedF>::AddNewIndex(const int v0)
|
|
|
+{
|
|
|
+ Handle_SystemInfo.num_scalar_variables++;
|
|
|
+ HandleV_Integer[v0].push_back(Handle_SystemInfo.num_scalar_variables);
|
|
|
+ IndexToVert.push_back(v0);
|
|
|
+ return Handle_SystemInfo.num_scalar_variables;
|
|
|
+}
|
|
|
+
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+bool igl::VertexIndexing<DerivedV, DerivedF>::HasIndex(int indexVert,int indexVar)
|
|
|
+{
|
|
|
+ for (unsigned int i=0;i<HandleV_Integer[indexVert].size();i++)
|
|
|
+ if (HandleV_Integer[indexVert][i]==indexVar)return true;
|
|
|
+ return false;
|
|
|
+}
|
|
|
+
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::VertexIndexing<DerivedV, DerivedF>::GetSeamInfo(const int f0,
|
|
|
+ const int f1,
|
|
|
+ const int indexE,
|
|
|
+ int &v0,int &v1,
|
|
|
+ int &v0p,int &v1p,
|
|
|
+ unsigned char &_MMatch,
|
|
|
+ int &integerVar)
|
|
|
+{
|
|
|
+ int edgef0 = indexE;
|
|
|
+ v0 = HandleS_Index(f0,edgef0);
|
|
|
+ v1 = HandleS_Index(f0,(edgef0+1)%3);
|
|
|
+ ////get the index on opposite side
|
|
|
+ assert(TT(f0,edgef0) == f1);
|
|
|
+ int edgef1 = TTi(f0,edgef0);
|
|
|
+ v1p = HandleS_Index(f1,edgef1);
|
|
|
+ v0p = HandleS_Index(f1,(edgef1+1)%3);
|
|
|
+
|
|
|
+ integerVar = Handle_Integer(f0,edgef0);
|
|
|
+ _MMatch = Handle_MMatch(f0,edgef0);
|
|
|
+ assert(F(f0,edgef0) == F(f1,((edgef1+1)%3)));
|
|
|
+ assert(F(f0,((edgef0+1)%3)) == F(f1,edgef1));
|
|
|
+}
|
|
|
+
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+bool igl::VertexIndexing<DerivedV, DerivedF>::IsSeam(const int f0, const int f1)
|
|
|
+{
|
|
|
+ for (int i=0;i<3;i++)
|
|
|
+ {
|
|
|
+ int f_clos = TT(f0,i);
|
|
|
+
|
|
|
+ if (f_clos == -1)
|
|
|
+ continue; ///border
|
|
|
+
|
|
|
+ if (f_clos == f1)
|
|
|
+ return(Handle_Seams(f0,i));
|
|
|
+ }
|
|
|
+ assert(0);
|
|
|
+ return false;
|
|
|
+}
|
|
|
+
|
|
|
+///find initial position of the pos to
|
|
|
+// assing face to vert inxex correctly
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::VertexIndexing<DerivedV, DerivedF>::FindInitialPos(const int vert,
|
|
|
+ int &edge,
|
|
|
+ int &face)
|
|
|
+{
|
|
|
+ int f_init;
|
|
|
+ int edge_init;
|
|
|
+ FirstPos(vert,f_init,edge_init); // todo manually inline the function
|
|
|
+ igl::Pos<DerivedF> VFI(&F,&TT,&TTi,f_init,edge_init);
|
|
|
+
|
|
|
+ bool vertexB = V_border[vert];
|
|
|
+ bool possible_split=false;
|
|
|
+ bool complete_turn=false;
|
|
|
+ do
|
|
|
+ {
|
|
|
+ int curr_f = VFI.Fi();
|
|
|
+ int curr_edge=VFI.Ei();
|
|
|
+ VFI.NextFE();
|
|
|
+ int next_f=VFI.Fi();
|
|
|
+ ///test if I've just crossed a border
|
|
|
+ bool on_border=(TT(curr_f,curr_edge)==-1);
|
|
|
+ //bool mismatch=false;
|
|
|
+ bool seam=false;
|
|
|
+
|
|
|
+ ///or if I've just crossed a seam
|
|
|
+ ///if I'm on a border I MUST start from the one next t othe border
|
|
|
+ if (!vertexB)
|
|
|
+ //seam=curr_f->IsSeam(next_f);
|
|
|
+ seam=IsSeam(curr_f,next_f);
|
|
|
+ if (vertexB)
|
|
|
+ assert(!Handle_Singular(vert));
|
|
|
+ ;
|
|
|
+ //assert(!vert->IsSingular());
|
|
|
+ possible_split=((on_border)||(seam));
|
|
|
+ complete_turn = next_f == f_init;
|
|
|
+ } while ((!possible_split)&&(!complete_turn));
|
|
|
+ face=VFI.Fi();
|
|
|
+ edge=VFI.Ei();
|
|
|
+ ///test that is not on a border
|
|
|
+ //assert(face->FFp(edge)!=face);
|
|
|
+}
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+///intialize the mapping given an initial pos
|
|
|
+///whih must be initialized with FindInitialPos
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::VertexIndexing<DerivedV, DerivedF>::MapIndexes(const int vert,
|
|
|
+ const int edge_init,
|
|
|
+ const int f_init)
|
|
|
+{
|
|
|
+ ///check that is not on border..
|
|
|
+ ///in such case maybe it's non manyfold
|
|
|
+ ///insert an initial index
|
|
|
+ int curr_index=AddNewIndex(vert);
|
|
|
+ ///and initialize the jumping pos
|
|
|
+ igl::Pos<DerivedF> VFI(&F,&TT,&TTi,f_init,edge_init);
|
|
|
+ bool complete_turn=false;
|
|
|
+ do
|
|
|
+ {
|
|
|
+ int curr_f = VFI.Fi();
|
|
|
+ int curr_edge = VFI.Ei();
|
|
|
+ ///assing the current index
|
|
|
+ HandleS_Index(curr_f,curr_edge) = curr_index;
|
|
|
+ VFI.NextFE();
|
|
|
+ int next_f = VFI.Fi();
|
|
|
+ ///test if I've finiseh with the face exploration
|
|
|
+ complete_turn = (next_f==f_init);
|
|
|
+ ///or if I've just crossed a mismatch
|
|
|
+ if (!complete_turn)
|
|
|
+ {
|
|
|
+ bool seam=false;
|
|
|
+ //seam=curr_f->IsSeam(next_f);
|
|
|
+ seam=IsSeam(curr_f,next_f);
|
|
|
+ if (seam)
|
|
|
+ {
|
|
|
+ ///then add a new index
|
|
|
+ curr_index=AddNewIndex(vert);
|
|
|
+ }
|
|
|
+ }
|
|
|
+ } while (!complete_turn);
|
|
|
+}
|
|
|
+
|
|
|
+///intialize the mapping for a given vertex
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::VertexIndexing<DerivedV, DerivedF>::InitMappingSeam(const int vert)
|
|
|
+{
|
|
|
+ ///first rotate until find the first pos after a mismatch
|
|
|
+ ///or a border or return to the first position...
|
|
|
+ int f_init = VF[vert][0];
|
|
|
+ int indexE = VFi[vert][0];
|
|
|
+
|
|
|
+ igl::Pos<DerivedF> VFI(&F,&TT,&TTi,f_init,indexE);
|
|
|
+
|
|
|
+ int edge_init;
|
|
|
+ int face_init;
|
|
|
+ FindInitialPos(vert,edge_init,face_init);
|
|
|
+ MapIndexes(vert,edge_init,face_init);
|
|
|
+}
|
|
|
+
|
|
|
+///intialize the mapping for a given sampled mesh
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::VertexIndexing<DerivedV, DerivedF>::InitMappingSeam()
|
|
|
+{
|
|
|
+ //num_scalar_variables=-1;
|
|
|
+ Handle_SystemInfo.num_scalar_variables=-1;
|
|
|
+ for (unsigned int i=0;i<V.rows();i++)
|
|
|
+ InitMappingSeam(i);
|
|
|
+
|
|
|
+ for (unsigned int j=0;j<V.rows();j++)
|
|
|
+ {
|
|
|
+ assert(HandleV_Integer[j].size()>0);
|
|
|
+ if (HandleV_Integer[j].size()>1)
|
|
|
+ duplicated.push_back(j);
|
|
|
+ }
|
|
|
+}
|
|
|
+
|
|
|
+///test consistency of face variables per vert mapping
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::VertexIndexing<DerivedV, DerivedF>::TestSeamMappingFace(const int f)
|
|
|
+{
|
|
|
+ for (int k=0;k<3;k++)
|
|
|
+ {
|
|
|
+ int indexV=HandleS_Index(f,k);
|
|
|
+ int v = F(f,k);
|
|
|
+ bool has_index=HasIndex(v,indexV);
|
|
|
+ assert(has_index);
|
|
|
+ }
|
|
|
+}
|
|
|
+
|
|
|
+///test consistency of face variables per vert mapping
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::VertexIndexing<DerivedV, DerivedF>::TestSeamMappingVertex(int indexVert)
|
|
|
+{
|
|
|
+ for (unsigned int k=0;k<HandleV_Integer[indexVert].size();k++)
|
|
|
+ {
|
|
|
+ int indexV=HandleV_Integer[indexVert][k];
|
|
|
+
|
|
|
+ ///get faces sharing vertex
|
|
|
+ std::vector<int> faces = VF[indexVert];
|
|
|
+ std::vector<int> indexes = VFi[indexVert];
|
|
|
+
|
|
|
+ for (unsigned int j=0;j<faces.size();j++)
|
|
|
+ {
|
|
|
+ int f = faces[j];
|
|
|
+ int index = indexes[j];
|
|
|
+ assert(F(f,index) == indexVert);
|
|
|
+ assert((index>=0)&&(index<3));
|
|
|
+
|
|
|
+ if (HandleS_Index(f,index) == indexV)
|
|
|
+ return;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ assert(0);
|
|
|
+}
|
|
|
+
|
|
|
+
|
|
|
+///check consistency of variable mapping across seams
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::VertexIndexing<DerivedV, DerivedF>::TestSeamMapping()
|
|
|
+{
|
|
|
+ printf("\n TESTING SEAM INDEXES \n");
|
|
|
+ ///test F-V mapping
|
|
|
+ for (unsigned int j=0;j<F.rows();j++)
|
|
|
+ TestSeamMappingFace(j);
|
|
|
+
|
|
|
+ ///TEST V-F MAPPING
|
|
|
+ for (unsigned int j=0;j<V.rows();j++)
|
|
|
+ TestSeamMappingVertex(j);
|
|
|
+
|
|
|
+}
|
|
|
+
|
|
|
+
|
|
|
+///vertex to variable mapping
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::VertexIndexing<DerivedV, DerivedF>::InitMapping()
|
|
|
+{
|
|
|
+ //use_direction_field=_use_direction_field;
|
|
|
+
|
|
|
+ IndexToVert.clear();
|
|
|
+ duplicated.clear();
|
|
|
+
|
|
|
+ InitMappingSeam();
|
|
|
+
|
|
|
+ Handle_SystemInfo.num_vert_variables=Handle_SystemInfo.num_scalar_variables+1;
|
|
|
+
|
|
|
+ ///end testing...
|
|
|
+ TestSeamMapping();
|
|
|
+}
|
|
|
+
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::VertexIndexing<DerivedV, DerivedF>::InitFaceIntegerVal()
|
|
|
+{
|
|
|
+ Handle_SystemInfo.num_integer_cuts=0;
|
|
|
+ for (unsigned int j=0;j<F.rows();j++)
|
|
|
+ {
|
|
|
+ for (int k=0;k<3;k++)
|
|
|
+ {
|
|
|
+ if (Handle_Seams(j,k))
|
|
|
+ {
|
|
|
+ Handle_Integer(j,k) = Handle_SystemInfo.num_integer_cuts;
|
|
|
+ Handle_SystemInfo.num_integer_cuts++;
|
|
|
+ }
|
|
|
+ else
|
|
|
+ Handle_Integer(j,k)=-1;
|
|
|
+ }
|
|
|
+ }
|
|
|
+}
|
|
|
+
|
|
|
+
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::VertexIndexing<DerivedV, DerivedF>::InitSeamInfo()
|
|
|
+{
|
|
|
+ Handle_SystemInfo.EdgeSeamInfo.clear();
|
|
|
+ for (unsigned int f0=0;f0<F.rows();f0++)
|
|
|
+ {
|
|
|
+ for (int k=0;k<3;k++)
|
|
|
+ {
|
|
|
+ int f1 = TT(f0,k);
|
|
|
+
|
|
|
+ if (f1 == -1)
|
|
|
+ continue;
|
|
|
+
|
|
|
+ bool seam = Handle_Seams(f0,k);
|
|
|
+ if (seam)
|
|
|
+ {
|
|
|
+ int v0,v0p,v1,v1p;
|
|
|
+ unsigned char MM;
|
|
|
+ int integerVar;
|
|
|
+ GetSeamInfo(f0,f1,k,v0,v1,v0p,v1p,MM,integerVar);
|
|
|
+ Handle_SystemInfo.EdgeSeamInfo.push_back(SeamInfo(v0,v1,v0p,v1p,MM,integerVar));
|
|
|
+ }
|
|
|
+ }
|
|
|
+ }
|
|
|
+}
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::SolvePoisson(Eigen::VectorXd Stiffness,
|
|
|
+ double vector_field_scale,
|
|
|
+ double grid_res,
|
|
|
+ bool direct_round,
|
|
|
+ int localIter,
|
|
|
+ bool _integer_rounding,
|
|
|
+ vector<int> roundVertices,
|
|
|
+ vector<vector<int> > hardFeatures)
|
|
|
+{
|
|
|
+ Handle_Stiffness = Stiffness;
|
|
|
+
|
|
|
+ //initialization of flags and data structures
|
|
|
+ integer_rounding=_integer_rounding;
|
|
|
+
|
|
|
+ ids_to_round.clear();
|
|
|
+
|
|
|
+ clearUserConstraint();
|
|
|
+ // copy the user constraints number
|
|
|
+ for (int i = 0; i < hardFeatures.size(); ++i)
|
|
|
+ {
|
|
|
+ addSharpEdgeConstraint(hardFeatures[i][0],hardFeatures[i][1]);
|
|
|
+ }
|
|
|
+
|
|
|
+ ///Initializing Matrix
|
|
|
+
|
|
|
+ int t0=clock();
|
|
|
+
|
|
|
+ ///initialize the matrix ALLOCATING SPACE
|
|
|
+ InitMatrix();
|
|
|
+ if (DEBUGPRINT)
|
|
|
+ printf("\n ALLOCATED THE MATRIX \n");
|
|
|
+
|
|
|
+ ///build the laplacian system
|
|
|
+ BuildLaplacianMatrix(vector_field_scale);
|
|
|
+
|
|
|
+ // add seam constraints
|
|
|
+ BuildSeamConstraintsExplicitTranslation();
|
|
|
+
|
|
|
+ // add user defined constraints
|
|
|
+ BuildUserDefinedConstraints();
|
|
|
+
|
|
|
+ ////add the lagrange multiplier
|
|
|
+ FixBlockedVertex();
|
|
|
+
|
|
|
+ if (DEBUGPRINT)
|
|
|
+ printf("\n BUILT THE MATRIX \n");
|
|
|
+
|
|
|
+ if (integer_rounding)
|
|
|
+ {
|
|
|
+ AddSingularityRound();
|
|
|
+ AddToRoundVertices(roundVertices);
|
|
|
+ }
|
|
|
+
|
|
|
+ int t1=clock();
|
|
|
+ if (DEBUGPRINT) printf("\n time:%d \n",t1-t0);
|
|
|
+ if (DEBUGPRINT) printf("\n SOLVING \n");
|
|
|
+
|
|
|
+ MixedIntegerSolve(grid_res,direct_round,localIter);
|
|
|
+
|
|
|
+ int t2=clock();
|
|
|
+ if (DEBUGPRINT) printf("\n time:%d \n",t2-t1);
|
|
|
+ if (DEBUGPRINT) printf("\n ASSIGNING COORDS \n");
|
|
|
+
|
|
|
+ MapCoords();
|
|
|
+
|
|
|
+ int t3=clock();
|
|
|
+ if (DEBUGPRINT) printf("\n time:%d \n",t3-t2);
|
|
|
+ if (DEBUGPRINT) printf("\n FINISHED \n");
|
|
|
+}
|
|
|
+
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+igl::PoissonSolver<DerivedV, DerivedF>
|
|
|
+::PoissonSolver(const Eigen::PlainObjectBase<DerivedV> &_V,
|
|
|
+ const Eigen::PlainObjectBase<DerivedF> &_F,
|
|
|
+ const Eigen::PlainObjectBase<DerivedF> &_TT,
|
|
|
+ const Eigen::PlainObjectBase<DerivedF> &_TTi,
|
|
|
+ const Eigen::PlainObjectBase<DerivedV> &_PD1,
|
|
|
+ const Eigen::PlainObjectBase<DerivedV> &_PD2,
|
|
|
+ const Eigen::MatrixXi &_HandleS_Index,
|
|
|
+ const Eigen::Matrix<int, Eigen::Dynamic, 1>&_Handle_Singular,
|
|
|
+ const MeshSystemInfo &_Handle_SystemInfo //todo: const?
|
|
|
+):
|
|
|
+V(_V),
|
|
|
+F(_F),
|
|
|
+TT(_TT),
|
|
|
+TTi(_TTi),
|
|
|
+PD1(_PD1),
|
|
|
+PD2(_PD2),
|
|
|
+HandleS_Index(_HandleS_Index),
|
|
|
+Handle_Singular(_Handle_Singular),
|
|
|
+Handle_SystemInfo(_Handle_SystemInfo)
|
|
|
+{
|
|
|
+ UV = Eigen::MatrixXd(V.rows(),2);
|
|
|
+ WUV = Eigen::MatrixXd(F.rows(),6);
|
|
|
+ igl::doublearea(V,F,doublearea);
|
|
|
+ igl::per_face_normals(V,F,N);
|
|
|
+ igl::vf(V,F,VF,VFi);
|
|
|
+}
|
|
|
+
|
|
|
+
|
|
|
+///START SYSTEM ACCESS METHODS
|
|
|
+///add an entry to the LHS
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::AddValA(int Xindex,
|
|
|
+ int Yindex,
|
|
|
+ double val)
|
|
|
+{
|
|
|
+ int size=(int)S.nrows();
|
|
|
+ assert(0 <= Xindex && Xindex < size);
|
|
|
+ assert(0 <= Yindex && Yindex < size);
|
|
|
+ S.A().addEntryReal(Xindex,Yindex,val);
|
|
|
+}
|
|
|
+
|
|
|
+///add a complex entry to the LHS
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::AddComplexA(int VarXindex,
|
|
|
+ int VarYindex,
|
|
|
+ std::complex<double> val)
|
|
|
+{
|
|
|
+ int size=(int)S.nrows()/2;
|
|
|
+ assert(0 <= VarXindex && VarXindex < size);
|
|
|
+ assert(0 <= VarYindex && VarYindex < size);
|
|
|
+ S.A().addEntryCmplx(VarXindex,VarYindex,val);
|
|
|
+}
|
|
|
+
|
|
|
+///add a velue to the RHS
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::AddValB(int Xindex,
|
|
|
+ double val)
|
|
|
+{
|
|
|
+ int size=(int)S.nrows();
|
|
|
+ assert(0 <= Xindex && Xindex < size);
|
|
|
+ S.b()[Xindex] += val;
|
|
|
+}
|
|
|
+
|
|
|
+///add the area term, scalefactor is used to sum up
|
|
|
+///and normalize on the overlap zones
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::AddAreaTerm(int index[3][3][2],double ScaleFactor)
|
|
|
+{
|
|
|
+ const double entry = 0.5*ScaleFactor;
|
|
|
+ double val[3][3]= {
|
|
|
+ {0, entry, -entry},
|
|
|
+ {-entry, 0, entry},
|
|
|
+ {entry, -entry, 0}
|
|
|
+ };
|
|
|
+
|
|
|
+ for (int i=0;i<3;i++)
|
|
|
+ for (int j=0;j<3;j++)
|
|
|
+ {
|
|
|
+ ///add for both u and v
|
|
|
+ int Xindex=index[i][j][0]*2;
|
|
|
+ int Yindex=index[i][j][1]*2;
|
|
|
+
|
|
|
+ AddValA(Xindex+1,Yindex,-val[i][j]);
|
|
|
+ AddValA(Xindex,Yindex+1,val[i][j]);
|
|
|
+ }
|
|
|
+}
|
|
|
+
|
|
|
+///set the diagonal of the matrix (which is zero at the beginning)
|
|
|
+///such that the sum of a row or a colums is zero
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::SetDiagonal(double val[3][3])
|
|
|
+{
|
|
|
+ for (int i=0;i<3;i++)
|
|
|
+ {
|
|
|
+ double sum=0;
|
|
|
+ for (int j=0;j<3;j++)
|
|
|
+ sum+=val[i][j];
|
|
|
+ val[i][i]=-sum;
|
|
|
+ }
|
|
|
+}
|
|
|
+
|
|
|
+///given a vector of scalar values and
|
|
|
+///a vector of indexes add such values
|
|
|
+///as specified by the indexes
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::AddRHS(double b[6],
|
|
|
+ int index[3])
|
|
|
+{
|
|
|
+ for (int i=0;i<3;i++)
|
|
|
+ {
|
|
|
+ double valU=b[i*2];
|
|
|
+ double valV=b[(i*2)+1];
|
|
|
+ AddValB((index[i]*2),valU);
|
|
|
+ AddValB((index[i]*2)+1,valV);
|
|
|
+ }
|
|
|
+}
|
|
|
+
|
|
|
+///add a 3x3 block matrix to the system matrix...
|
|
|
+///indexes are specified in the 3x3 matrix of x,y pairs
|
|
|
+///indexes must be multiplied by 2 cause u and v
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::Add33Block(double val[3][3], int index[3][3][2])
|
|
|
+{
|
|
|
+ for (int i=0;i<3;i++)
|
|
|
+ for (int j=0;j<3;j++)
|
|
|
+ {
|
|
|
+ ///add for both u and v
|
|
|
+ int Xindex=index[i][j][0]*2;
|
|
|
+ int Yindex=index[i][j][1]*2;
|
|
|
+ assert((unsigned)Xindex<(n_vert_vars*2));
|
|
|
+ assert((unsigned)Yindex<(n_vert_vars*2));
|
|
|
+ AddValA(Xindex,Yindex,val[i][j]);
|
|
|
+ AddValA(Xindex+1,Yindex+1,val[i][j]);
|
|
|
+ }
|
|
|
+}
|
|
|
+
|
|
|
+///add a 3x3 block matrix to the system matrix...
|
|
|
+///indexes are specified in the 3x3 matrix of x,y pairs
|
|
|
+///indexes must be multiplied by 2 cause u and v
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::Add44Block(double val[4][4],int index[4][4][2])
|
|
|
+{
|
|
|
+ for (int i=0;i<4;i++)
|
|
|
+ for (int j=0;j<4;j++)
|
|
|
+ {
|
|
|
+ ///add for both u and v
|
|
|
+ int Xindex=index[i][j][0]*2;
|
|
|
+ int Yindex=index[i][j][1]*2;
|
|
|
+ assert((unsigned)Xindex<(n_vert_vars*2));
|
|
|
+ assert((unsigned)Yindex<(n_vert_vars*2));
|
|
|
+ AddValA(Xindex,Yindex,val[i][j]);
|
|
|
+ AddValA(Xindex+1,Yindex+1,val[i][j]);
|
|
|
+ }
|
|
|
+}
|
|
|
+///END SYSTEM ACCESS METHODS
|
|
|
+
|
|
|
+///START COMMON MATH FUNCTIONS
|
|
|
+///return the complex encoding the rotation
|
|
|
+///for a given missmatch interval
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+std::complex<double> igl::PoissonSolver<DerivedV, DerivedF>::GetRotationComplex(int interval)
|
|
|
+{
|
|
|
+ assert((interval>=0)&&(interval<4));
|
|
|
+
|
|
|
+ switch(interval)
|
|
|
+ {
|
|
|
+ case 0:return std::complex<double>(1,0);
|
|
|
+ case 1:return std::complex<double>(0,1);
|
|
|
+ case 2:return std::complex<double>(-1,0);
|
|
|
+ default:return std::complex<double>(0,-1);
|
|
|
+ }
|
|
|
+}
|
|
|
+
|
|
|
+///END COMMON MATH FUNCTIONS
|
|
|
+
|
|
|
+
|
|
|
+///START ENERGY MINIMIZATION PART
|
|
|
+///initialize the LHS for a given face
|
|
|
+///for minimization of Dirichlet's energy
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::perElementLHS(int f,
|
|
|
+ double val[3][3],
|
|
|
+ int index[3][3][2])
|
|
|
+{
|
|
|
+ ///initialize to zero
|
|
|
+ for (int x=0;x<3;x++)
|
|
|
+ for (int y=0;y<3;y++)
|
|
|
+ val[x][y]=0;
|
|
|
+
|
|
|
+ ///get the vertices
|
|
|
+ int v[3];
|
|
|
+ v[0] = F(f,0);
|
|
|
+ v[1] = F(f,1);
|
|
|
+ v[2] = F(f,2);
|
|
|
+
|
|
|
+ ///get the indexes of vertex instance (to consider cuts)
|
|
|
+ ///for the current face
|
|
|
+ int Vindexes[3];
|
|
|
+ Vindexes[0]=HandleS_Index(f,0);
|
|
|
+ Vindexes[1]=HandleS_Index(f,1);
|
|
|
+ Vindexes[2]=HandleS_Index(f,2);
|
|
|
+
|
|
|
+ ///initialize the indexes for the block
|
|
|
+ for (int x=0;x<3;x++)
|
|
|
+ for (int y=0;y<3;y++)
|
|
|
+ {
|
|
|
+ index[x][y][0]=Vindexes[x];
|
|
|
+ index[x][y][1]=Vindexes[y];
|
|
|
+ }
|
|
|
+
|
|
|
+ ///initialize edges
|
|
|
+ Eigen::Matrix<typename DerivedV::Scalar, 3, 1> e[3];
|
|
|
+ for (int k=0;k<3;k++)
|
|
|
+ e[k] = V.row(v[(k+2)%3]) - V.row(v[(k+1)%3]);
|
|
|
+
|
|
|
+ ///then consider area but also considering scale factor dur to overlaps
|
|
|
+
|
|
|
+ double areaT = doublearea(f)/2.0;
|
|
|
+
|
|
|
+ for (int x=0;x<3;x++)
|
|
|
+ for (int y=0;y<3;y++)
|
|
|
+ if (x!=y)
|
|
|
+ {
|
|
|
+ double num = (e[x].dot(e[y]));
|
|
|
+ val[x][y] = num/(4.0*areaT);
|
|
|
+ val[x][y] *= Handle_Stiffness[f];//f->stiffening;
|
|
|
+ }
|
|
|
+
|
|
|
+ ///set the matrix as diagonal
|
|
|
+ SetDiagonal(val);
|
|
|
+}
|
|
|
+
|
|
|
+///initialize the RHS for a given face
|
|
|
+///for minimization of Dirichlet's energy
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::perElementRHS(int f,
|
|
|
+ double b[6],
|
|
|
+ double vector_field_scale)
|
|
|
+{
|
|
|
+
|
|
|
+ /// then set the rhs
|
|
|
+ Eigen::Matrix<typename DerivedV::Scalar, 3, 1> scaled_Kreal;
|
|
|
+ Eigen::Matrix<typename DerivedV::Scalar, 3, 1> scaled_Kimag;
|
|
|
+ Eigen::Matrix<typename DerivedV::Scalar, 3, 1> fNorm = N.row(f);
|
|
|
+ Eigen::Matrix<typename DerivedV::Scalar, 3, 1> p[3];
|
|
|
+ p[0] = V.row(F(f,0));
|
|
|
+ p[1] = V.row(F(f,1));
|
|
|
+ p[2] = V.row(F(f,2));
|
|
|
+
|
|
|
+ Eigen::Matrix<typename DerivedV::Scalar, 3, 1> neg_t[3];
|
|
|
+ neg_t[0] = fNorm.cross(p[2] - p[1]);
|
|
|
+ neg_t[1] = fNorm.cross(p[0] - p[2]);
|
|
|
+ neg_t[2] = fNorm.cross(p[1] - p[0]);
|
|
|
+
|
|
|
+ Eigen::Matrix<typename DerivedV::Scalar, 3, 1> K1,K2;
|
|
|
+ K1 = PD1.row(f);
|
|
|
+ K2 = PD2.row(f);
|
|
|
+
|
|
|
+ scaled_Kreal = K1*(vector_field_scale)/2;
|
|
|
+ scaled_Kimag = K2*(vector_field_scale)/2;
|
|
|
+
|
|
|
+ double stiff_val = Handle_Stiffness[f];
|
|
|
+
|
|
|
+ b[0] = scaled_Kreal.dot(neg_t[0]) * stiff_val;
|
|
|
+ b[1] = scaled_Kimag.dot(neg_t[0]) * stiff_val;
|
|
|
+ b[2] = scaled_Kreal.dot(neg_t[1]) * stiff_val;
|
|
|
+ b[3] = scaled_Kimag.dot(neg_t[1]) * stiff_val;
|
|
|
+ b[4] = scaled_Kreal.dot(neg_t[2]) * stiff_val;
|
|
|
+ b[5] = scaled_Kimag.dot(neg_t[2]) * stiff_val;
|
|
|
+
|
|
|
+ // if (f == 0)
|
|
|
+ // {
|
|
|
+ // cerr << "DEBUG!!!" << endl;
|
|
|
+ //
|
|
|
+ //
|
|
|
+ // for (unsigned z = 0; z<6; ++z)
|
|
|
+ // cerr << b[z] << " ";
|
|
|
+ // cerr << endl;
|
|
|
+ //
|
|
|
+ // scaled_Kreal = K1*(vector_field_scale)/2;
|
|
|
+ // scaled_Kimag = -K2*(vector_field_scale)/2;
|
|
|
+ //
|
|
|
+ // double stiff_val = Handle_Stiffness[f];
|
|
|
+ //
|
|
|
+ // b[0] = scaled_Kreal.dot(neg_t[0]) * stiff_val;
|
|
|
+ // b[1] = scaled_Kimag.dot(neg_t[0]) * stiff_val;
|
|
|
+ // b[2] = scaled_Kreal.dot(neg_t[1]) * stiff_val;
|
|
|
+ // b[3] = scaled_Kimag.dot(neg_t[1]) * stiff_val;
|
|
|
+ // b[4] = scaled_Kreal.dot(neg_t[2]) * stiff_val;
|
|
|
+ // b[5] = scaled_Kimag.dot(neg_t[2]) * stiff_val;
|
|
|
+ //
|
|
|
+ // for (unsigned z = 0; z<6; ++z)
|
|
|
+ // cerr << b[z] << " ";
|
|
|
+ // cerr << endl;
|
|
|
+ //
|
|
|
+ // }
|
|
|
+
|
|
|
+}
|
|
|
+
|
|
|
+///evaluate the LHS and RHS for a single face
|
|
|
+///for minimization of Dirichlet's energy
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::PerElementSystemReal(int f,
|
|
|
+ double val[3][3],
|
|
|
+ int index[3][3][2],
|
|
|
+ double b[6],
|
|
|
+ double vector_field_scale)
|
|
|
+{
|
|
|
+ perElementLHS(f,val,index);
|
|
|
+ perElementRHS(f,b,vector_field_scale);
|
|
|
+}
|
|
|
+///END ENERGY MINIMIZATION PART
|
|
|
+
|
|
|
+///START FIXING VERTICES
|
|
|
+///set a given vertex as fixed
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::AddFixedVertex(int v)
|
|
|
+{
|
|
|
+ n_fixed_vars++;
|
|
|
+ Hard_constraints.push_back(v);
|
|
|
+}
|
|
|
+
|
|
|
+///find vertex to fix in case we're using
|
|
|
+///a vector field NB: multiple components not handled
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::FindFixedVertField()
|
|
|
+{
|
|
|
+ Hard_constraints.clear();
|
|
|
+
|
|
|
+ n_fixed_vars=0;
|
|
|
+ ///fix the first singularity
|
|
|
+ for (unsigned int v=0;v<V.rows();v++)
|
|
|
+ {
|
|
|
+ if (Handle_Singular(v))
|
|
|
+ {
|
|
|
+ AddFixedVertex(v);
|
|
|
+ UV.row(v) << 0,0;
|
|
|
+ return;
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+ ///if anything fixed fix the first
|
|
|
+ AddFixedVertex(0); // TODO HERE IT ISSSSSS
|
|
|
+ UV.row(0) << 0,0;
|
|
|
+ cerr << "No vertices to fix, I am fixing the first vertex to the origin!" << endl;
|
|
|
+}
|
|
|
+
|
|
|
+///find hard constraint depending if using or not
|
|
|
+///a vector field
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::FindFixedVert()
|
|
|
+{
|
|
|
+ Hard_constraints.clear();
|
|
|
+ FindFixedVertField();
|
|
|
+}
|
|
|
+
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+int igl::PoissonSolver<DerivedV, DerivedF>::GetFirstVertexIndex(int v)
|
|
|
+{
|
|
|
+ return HandleS_Index(VF[v][0],VFi[v][0]);
|
|
|
+}
|
|
|
+
|
|
|
+///fix the vertices which are flagged as fixed
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::FixBlockedVertex()
|
|
|
+{
|
|
|
+ int offset_row = n_vert_vars*2 + num_cut_constraint*2;
|
|
|
+
|
|
|
+ unsigned int constr_num = 0;
|
|
|
+ for (unsigned int i=0;i<Hard_constraints.size();i++)
|
|
|
+ {
|
|
|
+ int v = Hard_constraints[i];
|
|
|
+
|
|
|
+ ///get first index of the vertex that must blocked
|
|
|
+ //int index=v->vertex_index[0];
|
|
|
+ int index = GetFirstVertexIndex(v);
|
|
|
+
|
|
|
+ ///multiply times 2 because of uv
|
|
|
+ int indexvert = index*2;
|
|
|
+
|
|
|
+ ///find the first free row to add the constraint
|
|
|
+ int indexRow = (offset_row+constr_num*2);
|
|
|
+ int indexCol = indexRow;
|
|
|
+
|
|
|
+ ///add fixing constraint LHS
|
|
|
+ AddValA(indexRow,indexvert,1);
|
|
|
+ AddValA(indexRow+1,indexvert+1,1);
|
|
|
+
|
|
|
+ ///add fixing constraint RHS
|
|
|
+ AddValB(indexCol, UV(v,0));
|
|
|
+ AddValB(indexCol+1,UV(v,1));
|
|
|
+
|
|
|
+ constr_num++;
|
|
|
+ }
|
|
|
+ assert(constr_num==n_fixed_vars);
|
|
|
+}
|
|
|
+///END FIXING VERTICES
|
|
|
+
|
|
|
+///HANDLING SINGULARITY
|
|
|
+//set the singularity round to integer location
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::AddSingularityRound()
|
|
|
+{
|
|
|
+ for (unsigned int v=0;v<V.rows();v++)
|
|
|
+ {
|
|
|
+ if (Handle_Singular(v))
|
|
|
+ {
|
|
|
+ int index0=GetFirstVertexIndex(v);
|
|
|
+ ids_to_round.push_back( index0*2 );
|
|
|
+ ids_to_round.push_back((index0*2)+1);
|
|
|
+ }
|
|
|
+ }
|
|
|
+}
|
|
|
+
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::AddToRoundVertices(vector<int> ids)
|
|
|
+{
|
|
|
+ for (int i = 0; i < ids.size(); ++i)
|
|
|
+ {
|
|
|
+ if (ids[i] < 0 || ids[i] >= V.rows())
|
|
|
+ cerr << "WARNING: Ignored round vertex constraint, vertex " << ids[i] << " does not exist in the mesh." << endl;
|
|
|
+ int index0 = GetFirstVertexIndex(ids[i]);
|
|
|
+ ids_to_round.push_back( index0*2 );
|
|
|
+ ids_to_round.push_back((index0*2)+1);
|
|
|
+ }
|
|
|
+}
|
|
|
+
|
|
|
+///START GENERIC SYSTEM FUNCTIONS
|
|
|
+//build the laplacian matrix cyclyng over all rangemaps
|
|
|
+//and over all faces
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::BuildLaplacianMatrix(double vfscale)
|
|
|
+{
|
|
|
+ ///then for each face
|
|
|
+ for (unsigned int f=0;f<F.rows();f++)
|
|
|
+ {
|
|
|
+
|
|
|
+ int var_idx[3]; //vertex variable indices
|
|
|
+
|
|
|
+ for(int k = 0; k < 3; ++k)
|
|
|
+ var_idx[k] = HandleS_Index(f,k);
|
|
|
+
|
|
|
+ ///block of variables
|
|
|
+ double val[3][3];
|
|
|
+ ///block of vertex indexes
|
|
|
+ int index[3][3][2];
|
|
|
+ ///righe hand side
|
|
|
+ double b[6];
|
|
|
+ ///compute the system for the given face
|
|
|
+ PerElementSystemReal(f, val,index, b, vfscale);
|
|
|
+
|
|
|
+ //Add the element to the matrix
|
|
|
+ Add33Block(val,index);
|
|
|
+
|
|
|
+ ///add right hand side
|
|
|
+ AddRHS(b,var_idx);
|
|
|
+ }
|
|
|
+}
|
|
|
+
|
|
|
+///find different sized of the system
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::FindSizes()
|
|
|
+{
|
|
|
+ ///find the vertex that need to be fixed
|
|
|
+ FindFixedVert();
|
|
|
+
|
|
|
+ ///REAL PART
|
|
|
+ n_vert_vars = Handle_SystemInfo.num_vert_variables;
|
|
|
+
|
|
|
+ ///INTEGER PART
|
|
|
+ ///the total number of integer variables
|
|
|
+ n_integer_vars = Handle_SystemInfo.num_integer_cuts;
|
|
|
+
|
|
|
+ ///CONSTRAINT PART
|
|
|
+ num_cut_constraint = Handle_SystemInfo.EdgeSeamInfo.size()*2;
|
|
|
+
|
|
|
+ num_constraint_equations = num_cut_constraint*2 + n_fixed_vars*2 + num_userdefined_constraint;
|
|
|
+
|
|
|
+ ///total variable of the system
|
|
|
+ num_total_vars = n_vert_vars*2+n_integer_vars*2;
|
|
|
+
|
|
|
+ ///initialize matrix size
|
|
|
+
|
|
|
+ system_size = num_total_vars + num_constraint_equations;
|
|
|
+
|
|
|
+ if (DEBUGPRINT) printf("\n*** SYSTEM VARIABLES *** \n");
|
|
|
+ if (DEBUGPRINT) printf("* NUM REAL VERTEX VARIABLES %d \n",n_vert_vars);
|
|
|
+
|
|
|
+ if (DEBUGPRINT) printf("\n*** SINGULARITY *** \n ");
|
|
|
+ if (DEBUGPRINT) printf("* NUM SINGULARITY %d\n",(int)ids_to_round.size()/2);
|
|
|
+
|
|
|
+ if (DEBUGPRINT) printf("\n*** INTEGER VARIABLES *** \n");
|
|
|
+ if (DEBUGPRINT) printf("* NUM INTEGER VARIABLES %d \n",(int)n_integer_vars);
|
|
|
+
|
|
|
+ if (DEBUGPRINT) printf("\n*** CONSTRAINTS *** \n ");
|
|
|
+ if (DEBUGPRINT) printf("* NUM FIXED CONSTRAINTS %d\n",n_fixed_vars);
|
|
|
+ if (DEBUGPRINT) printf("* NUM CUTS CONSTRAINTS %d\n",num_cut_constraint);
|
|
|
+ if (DEBUGPRINT) printf("* NUM USER DEFINED CONSTRAINTS %d\n",num_userdefined_constraint);
|
|
|
+
|
|
|
+ if (DEBUGPRINT) printf("\n*** TOTAL SIZE *** \n");
|
|
|
+ if (DEBUGPRINT) printf("* TOTAL VARIABLE SIZE (WITH INTEGER TRASL) %d \n",num_total_vars);
|
|
|
+ if (DEBUGPRINT) printf("* TOTAL CONSTRAINTS %d \n",num_constraint_equations);
|
|
|
+ if (DEBUGPRINT) printf("* MATRIX SIZE %d \n",system_size);
|
|
|
+}
|
|
|
+
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::AllocateSystem()
|
|
|
+{
|
|
|
+ S.initialize(system_size, system_size);
|
|
|
+ printf("\n INITIALIZED SPARSE MATRIX OF %d x %d \n",system_size, system_size);
|
|
|
+}
|
|
|
+
|
|
|
+///intitialize the whole matrix
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::InitMatrix()
|
|
|
+{
|
|
|
+ FindSizes();
|
|
|
+ AllocateSystem();
|
|
|
+}
|
|
|
+
|
|
|
+///map back coordinates after that
|
|
|
+///the system has been solved
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::MapCoords()
|
|
|
+{
|
|
|
+ ///map coords to faces
|
|
|
+ for (unsigned int f=0;f<F.rows();f++)
|
|
|
+ {
|
|
|
+
|
|
|
+ for (int k=0;k<3;k++)
|
|
|
+ {
|
|
|
+ //get the index of the variable in the system
|
|
|
+ int indexUV = HandleS_Index(f,k);
|
|
|
+ ///then get U and V coords
|
|
|
+ double U=X[indexUV*2];
|
|
|
+ double V=X[indexUV*2+1];
|
|
|
+
|
|
|
+ WUV(f,k*2 + 0) = U;
|
|
|
+ WUV(f,k*2 + 1) = V;
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+#if 0
|
|
|
+ ///initialize the vector of integer variables to return their values
|
|
|
+ Handle_SystemInfo.IntegerValues.resize(n_integer_vars*2);
|
|
|
+ int baseIndex = (n_vert_vars)*2;
|
|
|
+ int endIndex = baseIndex+n_integer_vars*2;
|
|
|
+ int index = 0;
|
|
|
+ for (int i=baseIndex; i<endIndex; i++)
|
|
|
+ {
|
|
|
+ ///assert that the value is an integer value
|
|
|
+ double value=X[i];
|
|
|
+ double diff = value-(int)floor(value+0.5);
|
|
|
+ assert(diff<0.00000001);
|
|
|
+ Handle_SystemInfo.IntegerValues[index] = value;
|
|
|
+ index++;
|
|
|
+ }
|
|
|
+#endif
|
|
|
+}
|
|
|
+
|
|
|
+///END GENERIC SYSTEM FUNCTIONS
|
|
|
+
|
|
|
+///set the constraints for the inter-range cuts
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::BuildSeamConstraintsExplicitTranslation()
|
|
|
+{
|
|
|
+ ///add constraint(s) for every seam edge (not halfedge)
|
|
|
+ int offset_row = n_vert_vars;
|
|
|
+ ///current constraint row
|
|
|
+ int constr_row = offset_row;
|
|
|
+ ///current constraint
|
|
|
+ unsigned int constr_num = 0;
|
|
|
+
|
|
|
+ for (unsigned int i=0; i<num_cut_constraint/2; i++)
|
|
|
+ {
|
|
|
+ unsigned char interval = Handle_SystemInfo.EdgeSeamInfo[i].MMatch;
|
|
|
+ if (interval==1)
|
|
|
+ interval=3;
|
|
|
+ else
|
|
|
+ if(interval==3)
|
|
|
+ interval=1;
|
|
|
+
|
|
|
+ int p0 = Handle_SystemInfo.EdgeSeamInfo[i].v0;
|
|
|
+ int p1 = Handle_SystemInfo.EdgeSeamInfo[i].v1;
|
|
|
+ int p0p = Handle_SystemInfo.EdgeSeamInfo[i].v0p;
|
|
|
+ int p1p = Handle_SystemInfo.EdgeSeamInfo[i].v1p;
|
|
|
+
|
|
|
+ std::complex<double> rot = GetRotationComplex(interval);
|
|
|
+
|
|
|
+ ///get the integer variable
|
|
|
+ int integerVar = offset_row+Handle_SystemInfo.EdgeSeamInfo[i].integerVar;
|
|
|
+
|
|
|
+ if (integer_rounding)
|
|
|
+ {
|
|
|
+ ids_to_round.push_back(integerVar*2);
|
|
|
+ ids_to_round.push_back(integerVar*2+1);
|
|
|
+ }
|
|
|
+
|
|
|
+ AddComplexA(constr_row, p0 , rot);
|
|
|
+ AddComplexA(constr_row, p0p, -1);
|
|
|
+ ///then translation...considering the rotation
|
|
|
+ ///due to substitution
|
|
|
+ AddComplexA(constr_row, integerVar, 1);
|
|
|
+
|
|
|
+ AddValB(2*constr_row ,0);
|
|
|
+ AddValB(2*constr_row+1,0);
|
|
|
+ constr_row +=1;
|
|
|
+ constr_num++;
|
|
|
+
|
|
|
+ AddComplexA(constr_row, p1, rot);
|
|
|
+ AddComplexA(constr_row, p1p, -1);
|
|
|
+
|
|
|
+ ///other translation
|
|
|
+ AddComplexA(constr_row, integerVar , 1);
|
|
|
+
|
|
|
+ AddValB(2*constr_row,0);
|
|
|
+ AddValB(2*constr_row+1,0);
|
|
|
+
|
|
|
+ constr_row +=1;
|
|
|
+ constr_num++;
|
|
|
+ }
|
|
|
+}
|
|
|
+
|
|
|
+///set the constraints for the inter-range cuts
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::BuildUserDefinedConstraints()
|
|
|
+{
|
|
|
+ /// the user defined constraints are at the end
|
|
|
+ int offset_row = n_vert_vars*2 + num_cut_constraint*2 + n_fixed_vars*2;
|
|
|
+
|
|
|
+ ///current constraint row
|
|
|
+ int constr_row = offset_row;
|
|
|
+
|
|
|
+ assert(num_userdefined_constraint == userdefined_constraints.size());
|
|
|
+
|
|
|
+ for (unsigned int i=0; i<num_userdefined_constraint; i++)
|
|
|
+ {
|
|
|
+ for (unsigned int j=0; j<userdefined_constraints[i].size()-1; ++j)
|
|
|
+ {
|
|
|
+ AddValA(constr_row, j , userdefined_constraints[i][j]);
|
|
|
+ }
|
|
|
+
|
|
|
+ AddValB(constr_row,userdefined_constraints[i][userdefined_constraints[i].size()-1]);
|
|
|
+
|
|
|
+ constr_row +=1;
|
|
|
+ }
|
|
|
+}
|
|
|
+
|
|
|
+///call of the mixed integer solver
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::MixedIntegerSolve(double cone_grid_res,
|
|
|
+ bool direct_round,
|
|
|
+ int localIter)
|
|
|
+{
|
|
|
+ X = std::vector<double>((n_vert_vars+n_integer_vars)*2);
|
|
|
+
|
|
|
+ ///variables part
|
|
|
+ int ScalarSize = n_vert_vars*2;
|
|
|
+ int SizeMatrix = (n_vert_vars+n_integer_vars)*2;
|
|
|
+
|
|
|
+ if (DEBUGPRINT)
|
|
|
+ printf("\n ALLOCATED X \n");
|
|
|
+
|
|
|
+ ///matrix A
|
|
|
+ gmm::col_matrix< gmm::wsvector< double > > A(SizeMatrix,SizeMatrix); // lhs matrix variables +
|
|
|
+
|
|
|
+ ///constraints part
|
|
|
+ int CsizeX = num_constraint_equations;
|
|
|
+ int CsizeY = SizeMatrix+1;
|
|
|
+ gmm::row_matrix< gmm::wsvector< double > > C(CsizeX,CsizeY); // constraints
|
|
|
+
|
|
|
+ if (DEBUGPRINT)
|
|
|
+ printf("\n ALLOCATED QMM STRUCTURES \n");
|
|
|
+
|
|
|
+ std::vector<double> rhs(SizeMatrix,0); // rhs
|
|
|
+
|
|
|
+ if (DEBUGPRINT)
|
|
|
+ printf("\n ALLOCATED RHS STRUCTURES \n");
|
|
|
+
|
|
|
+ //// copy LHS
|
|
|
+ for(int i = 0; i < (int)S.A().nentries(); ++i)
|
|
|
+ {
|
|
|
+ int row = S.A().rowind()[i];
|
|
|
+ int col = S.A().colind()[i];
|
|
|
+ int size =(int)S.nrows();
|
|
|
+ assert(0 <= row && row < size);
|
|
|
+ assert(0 <= col && col < size);
|
|
|
+
|
|
|
+ // it's either part of the matrix
|
|
|
+ if (row < ScalarSize)
|
|
|
+ {
|
|
|
+ A(row, col) += S.A().vals()[i];
|
|
|
+ }
|
|
|
+ // or it's a part of the constraint
|
|
|
+ else
|
|
|
+ {
|
|
|
+ assert ((unsigned int)row < (n_vert_vars+num_constraint_equations)*2);
|
|
|
+ int r = row - ScalarSize;
|
|
|
+ assert(r < CsizeX);
|
|
|
+ assert(col < CsizeY);
|
|
|
+ C(r , col ) += S.A().vals()[i];
|
|
|
+ }
|
|
|
+ }
|
|
|
+
|
|
|
+ if (DEBUGPRINT)
|
|
|
+ printf("\n SET %d INTEGER VALUES \n",n_integer_vars);
|
|
|
+
|
|
|
+ ///add penalization term for integer variables
|
|
|
+ double penalization = 0.000001;
|
|
|
+ int offline_index = ScalarSize;
|
|
|
+ for(unsigned int i = 0; i < (n_integer_vars)*2; ++i)
|
|
|
+ {
|
|
|
+ int index=offline_index+i;
|
|
|
+ A(index,index)=penalization;
|
|
|
+ }
|
|
|
+
|
|
|
+ if (DEBUGPRINT)
|
|
|
+ printf("\n SET RHS \n");
|
|
|
+
|
|
|
+ // copy RHS
|
|
|
+ for(int i = 0; i < (int)ScalarSize; ++i)
|
|
|
+ {
|
|
|
+ rhs[i] = S.getRHSReal(i) * cone_grid_res;
|
|
|
+ }
|
|
|
+
|
|
|
+ // copy constraint RHS
|
|
|
+ if (DEBUGPRINT)
|
|
|
+ printf("\n SET %d CONSTRAINTS \n",num_constraint_equations);
|
|
|
+
|
|
|
+ for(unsigned int i = 0; i < num_constraint_equations; ++i)
|
|
|
+ {
|
|
|
+ C(i, SizeMatrix) = -S.getRHSReal(ScalarSize + i) * cone_grid_res;
|
|
|
+ }
|
|
|
+
|
|
|
+ ///copy values back into S
|
|
|
+ COMISO::ConstrainedSolver solver;
|
|
|
+
|
|
|
+ solver.misolver().set_local_iters(localIter);
|
|
|
+ solver.misolver().set_direct_rounding(direct_round);
|
|
|
+
|
|
|
+ std::sort(ids_to_round.begin(),ids_to_round.end());
|
|
|
+ std::vector<int>::iterator new_end=std::unique(ids_to_round.begin(),ids_to_round.end());
|
|
|
+ int dist=distance(ids_to_round.begin(),new_end);
|
|
|
+ ids_to_round.resize(dist);
|
|
|
+
|
|
|
+ solver.solve( C, A, X, rhs, ids_to_round, 0.0, false, false);
|
|
|
+}
|
|
|
+
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::clearUserConstraint()
|
|
|
+{
|
|
|
+ num_userdefined_constraint = 0;
|
|
|
+ userdefined_constraints.clear();
|
|
|
+}
|
|
|
+
|
|
|
+template <typename DerivedV, typename DerivedF>
|
|
|
+void igl::PoissonSolver<DerivedV, DerivedF>::addSharpEdgeConstraint(int fid, int vid)
|
|
|
+{
|
|
|
+ // prepare constraint
|
|
|
+ vector<int> c(Handle_SystemInfo.num_vert_variables*2 + 1);
|
|
|
+
|
|
|
+ for (int i = 0; i < c.size(); ++i)
|
|
|
+ {
|
|
|
+ c[i] = 0;
|
|
|
+ }
|
|
|
+
|
|
|
+ int v1 = F(fid,vid);
|
|
|
+ int v2 = F(fid,(vid+1)%3);
|
|
|
+
|
|
|
+ Eigen::Matrix<typename DerivedV::Scalar, 3, 1> e = V.row(v2) - V.row(v1);
|
|
|
+
|
|
|
+ int v1i = GetFirstVertexIndex(v1);
|
|
|
+ int v2i = GetFirstVertexIndex(v2);
|
|
|
+
|
|
|
+ double d1 = fabs(e.dot(PD1.row(fid)));
|
|
|
+ double d2 = fabs(e.dot(PD2.row(fid)));
|
|
|
+
|
|
|
+ int offset = 0;
|
|
|
+
|
|
|
+ if (d1>d2)
|
|
|
+ offset = 1;
|
|
|
+
|
|
|
+ ids_to_round.push_back((v1i * 2) + offset);
|
|
|
+ ids_to_round.push_back((v2i * 2) + offset);
|
|
|
+
|
|
|
+ // add constraint
|
|
|
+ c[(v1i * 2) + offset] = 1;
|
|
|
+ c[(v2i * 2) + offset] = -1;
|
|
|
+
|
|
|
+ // add to the user-defined constraints
|
|
|
+ num_userdefined_constraint++;
|
|
|
+ userdefined_constraints.push_back(c);
|
|
|
+
|
|
|
+}
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+template <typename DerivedV, typename DerivedF, typename DerivedU>
|
|
|
+igl::MIQ<DerivedV, DerivedF, DerivedU>::MIQ(const Eigen::PlainObjectBase<DerivedV> &V_,
|
|
|
+ const Eigen::PlainObjectBase<DerivedF> &F_,
|
|
|
+ const Eigen::PlainObjectBase<DerivedV> &PD1_combed,
|
|
|
+ const Eigen::PlainObjectBase<DerivedV> &PD2_combed,
|
|
|
+ const Eigen::PlainObjectBase<DerivedV> &BIS1_combed,
|
|
|
+ const Eigen::PlainObjectBase<DerivedV> &BIS2_combed,
|
|
|
+ const Eigen::Matrix<int, Eigen::Dynamic, 3> &Handle_MMatch,
|
|
|
+ const Eigen::Matrix<int, Eigen::Dynamic, 1> &Handle_Singular,
|
|
|
+ const Eigen::Matrix<int, Eigen::Dynamic, 1> &Handle_SingularDegree,
|
|
|
+ const Eigen::Matrix<int, Eigen::Dynamic, 3> &Handle_Seams,
|
|
|
+ Eigen::PlainObjectBase<DerivedU> &UV,
|
|
|
+ Eigen::PlainObjectBase<DerivedF> &FUV,
|
|
|
+ double GradientSize,
|
|
|
+ double Stiffness,
|
|
|
+ bool DirectRound,
|
|
|
+ int iter,
|
|
|
+ int localIter,
|
|
|
+ bool DoRound,
|
|
|
+ std::vector<int> roundVertices,
|
|
|
+ std::vector<std::vector<int> > hardFeatures):
|
|
|
+V(V_),
|
|
|
+F(F_)
|
|
|
+{
|
|
|
+ igl::local_basis(V,F,B1,B2,B3);
|
|
|
+ igl::tt(V,F,TT,TTi);
|
|
|
+
|
|
|
+ // Prepare indexing for the linear system
|
|
|
+ VertexIndexing<DerivedV, DerivedF> VInd(V, F, TT, TTi, BIS1_combed, BIS2_combed, Handle_MMatch, Handle_Singular, Handle_SingularDegree, Handle_Seams);
|
|
|
+
|
|
|
+ VInd.InitMapping();
|
|
|
+ VInd.InitFaceIntegerVal();
|
|
|
+ VInd.InitSeamInfo();
|
|
|
+
|
|
|
+ Eigen::PlainObjectBase<DerivedV> PD1_combed_for_poisson, PD2_combed_for_poisson;
|
|
|
+ // Rotate by 90 degrees CCW
|
|
|
+ PD1_combed_for_poisson.setZero(BIS1_combed.rows(),3);
|
|
|
+ PD2_combed_for_poisson.setZero(BIS2_combed.rows(),3);
|
|
|
+ for (unsigned i=0; i<PD1_combed.rows();++i)
|
|
|
+ {
|
|
|
+ double n1 = PD1_combed.row(i).norm();
|
|
|
+ double n2 = PD2_combed.row(i).norm();
|
|
|
+
|
|
|
+ double a1 = atan2(B2.row(i).dot(PD1_combed.row(i)),B1.row(i).dot(PD1_combed.row(i)));
|
|
|
+ double a2 = atan2(B2.row(i).dot(PD2_combed.row(i)),B1.row(i).dot(PD2_combed.row(i)));
|
|
|
+
|
|
|
+ a1 += M_PI/2;
|
|
|
+ a2 += M_PI/2;
|
|
|
+
|
|
|
+
|
|
|
+ PD1_combed_for_poisson.row(i) = cos(a1) * B1.row(i) + sin(a1) * B2.row(i);
|
|
|
+ PD2_combed_for_poisson.row(i) = cos(a2) * B1.row(i) + sin(a2) * B2.row(i);
|
|
|
+
|
|
|
+ PD1_combed_for_poisson.row(i) = PD1_combed_for_poisson.row(i).normalized() * n1;
|
|
|
+ PD2_combed_for_poisson.row(i) = PD2_combed_for_poisson.row(i).normalized() * n2;
|
|
|
+ }
|
|
|
+
|
|
|
+
|
|
|
+ // Assemble the system and solve
|
|
|
+ PoissonSolver<DerivedV, DerivedF> PSolver(V,
|
|
|
+ F,
|
|
|
+ TT,
|
|
|
+ TTi,
|
|
|
+ PD1_combed_for_poisson,
|
|
|
+ PD2_combed_for_poisson,
|
|
|
+ VInd.HandleS_Index,
|
|
|
+ VInd.Handle_Singular,
|
|
|
+ VInd.Handle_SystemInfo);
|
|
|
+ Handle_Stiffness = VectorXd::Constant(F.rows(),1);
|
|
|
+
|
|
|
+
|
|
|
+ if (iter > 0) // do stiffening
|
|
|
+ {
|
|
|
+ for (int i=0;i<iter;i++)
|
|
|
+ {
|
|
|
+ PSolver.SolvePoisson(Handle_Stiffness, GradientSize,1.f,DirectRound,localIter,DoRound,roundVertices,hardFeatures);
|
|
|
+ int nflips=NumFlips(PSolver.WUV);
|
|
|
+ bool folded = updateStiffeningJacobianDistorsion(GradientSize,PSolver.WUV);
|
|
|
+ printf("ITERATION %d FLIPS %d \n",i,nflips);
|
|
|
+ if (!folded)break;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ else
|
|
|
+ {
|
|
|
+ PSolver.SolvePoisson(Handle_Stiffness,GradientSize,1.f,DirectRound,localIter,DoRound,roundVertices,hardFeatures);
|
|
|
+ }
|
|
|
+
|
|
|
+ int nflips=NumFlips(PSolver.WUV);
|
|
|
+ printf("**** END OPTIMIZING #FLIPS %d ****\n",nflips);
|
|
|
+
|
|
|
+ fflush(stdout);
|
|
|
+ WUV = PSolver.WUV;
|
|
|
+
|
|
|
+}
|
|
|
+
|
|
|
+template <typename DerivedV, typename DerivedF, typename DerivedU>
|
|
|
+void igl::MIQ<DerivedV, DerivedF, DerivedU>::extractUV(Eigen::PlainObjectBase<DerivedU> &UV_out,
|
|
|
+ Eigen::PlainObjectBase<DerivedF> &FUV_out)
|
|
|
+{
|
|
|
+ // int f = F.rows();
|
|
|
+ int f = WUV.rows();
|
|
|
+
|
|
|
+ unsigned vtfaceid[f*3];
|
|
|
+ std::vector<double> vtu;
|
|
|
+ std::vector<double> vtv;
|
|
|
+
|
|
|
+ std::vector<std::vector<double> > listUV;
|
|
|
+ unsigned counter = 0;
|
|
|
+
|
|
|
+ for (unsigned i=0; i<f; ++i)
|
|
|
+ {
|
|
|
+ for (unsigned j=0; j<3; ++j)
|
|
|
+ {
|
|
|
+ std::vector<double> t(3);
|
|
|
+ t[0] = WUV(i,j*2 + 0);
|
|
|
+ t[1] = WUV(i,j*2 + 1);
|
|
|
+ t[2] = counter++;
|
|
|
+ listUV.push_back(t);
|
|
|
+ }
|
|
|
+ }
|
|
|
+ std::sort(listUV.begin(),listUV.end());
|
|
|
+
|
|
|
+ counter = 0;
|
|
|
+ unsigned k = 0;
|
|
|
+ while (k < f*3)
|
|
|
+ {
|
|
|
+ double u = listUV[k][0];
|
|
|
+ double v = listUV[k][1];
|
|
|
+ unsigned id = round(listUV[k][2]);
|
|
|
+
|
|
|
+ vtfaceid[id] = counter;
|
|
|
+ vtu.push_back(u);
|
|
|
+ vtv.push_back(v);
|
|
|
+
|
|
|
+ unsigned j=1;
|
|
|
+ while(k+j < f*3 && u == listUV[k+j][0] && v == listUV[k+j][1])
|
|
|
+ {
|
|
|
+ unsigned tid = round(listUV[k+j][2]);
|
|
|
+ vtfaceid[tid] = counter;
|
|
|
+ ++j;
|
|
|
+ }
|
|
|
+ k = k+j;
|
|
|
+ counter++;
|
|
|
+ }
|
|
|
+
|
|
|
+ UV_out.resize(vtu.size(),2);
|
|
|
+ for (unsigned i=0; i<vtu.size(); ++i)
|
|
|
+ {
|
|
|
+ UV_out(i,0) = vtu[i];
|
|
|
+ UV_out(i,1) = vtv[i];
|
|
|
+ }
|
|
|
+
|
|
|
+ FUV_out.resize(f,3);
|
|
|
+
|
|
|
+ unsigned vcounter = 0;
|
|
|
+ for (unsigned i=0; i<f; ++i)
|
|
|
+ {
|
|
|
+ FUV_out(i,0) = vtfaceid[vcounter++];
|
|
|
+ FUV_out(i,1) = vtfaceid[vcounter++];
|
|
|
+ FUV_out(i,2) = vtfaceid[vcounter++];
|
|
|
+ }
|
|
|
+
|
|
|
+}
|
|
|
+
|
|
|
+template <typename DerivedV, typename DerivedF, typename DerivedU>
|
|
|
+int igl::MIQ<DerivedV, DerivedF, DerivedU>::NumFlips(const MatrixXd& WUV)
|
|
|
+{
|
|
|
+ int numFl=0;
|
|
|
+ for (unsigned int i=0;i<F.rows();i++)
|
|
|
+ {
|
|
|
+ if (IsFlipped(i, WUV))
|
|
|
+ numFl++;
|
|
|
+ }
|
|
|
+ return numFl;
|
|
|
+}
|
|
|
+
|
|
|
+template <typename DerivedV, typename DerivedF, typename DerivedU>
|
|
|
+double igl::MIQ<DerivedV, DerivedF, DerivedU>::Distortion(int f, double h, const MatrixXd& WUV)
|
|
|
+{
|
|
|
+ assert(h > 0);
|
|
|
+
|
|
|
+ Vector2d uv0,uv1,uv2;
|
|
|
+
|
|
|
+ uv0 << WUV(f,0), WUV(f,1);
|
|
|
+ uv1 << WUV(f,2), WUV(f,3);
|
|
|
+ uv2 << WUV(f,4), WUV(f,5);
|
|
|
+
|
|
|
+ Eigen::Matrix<typename DerivedV::Scalar, 3, 1> p0 = V.row(F(f,0));
|
|
|
+ Eigen::Matrix<typename DerivedV::Scalar, 3, 1> p1 = V.row(F(f,1));
|
|
|
+ Eigen::Matrix<typename DerivedV::Scalar, 3, 1> p2 = V.row(F(f,2));
|
|
|
+
|
|
|
+ Eigen::Matrix<typename DerivedV::Scalar, 3, 1> norm = (p1 - p0).cross(p2 - p0);
|
|
|
+ double area2 = norm.norm();
|
|
|
+ double area2_inv = 1.0 / area2;
|
|
|
+ norm *= area2_inv;
|
|
|
+
|
|
|
+ if (area2 > 0)
|
|
|
+ {
|
|
|
+ // Singular values of the Jacobian
|
|
|
+ Eigen::Matrix<typename DerivedV::Scalar, 3, 1> neg_t0 = norm.cross(p2 - p1);
|
|
|
+ Eigen::Matrix<typename DerivedV::Scalar, 3, 1> neg_t1 = norm.cross(p0 - p2);
|
|
|
+ Eigen::Matrix<typename DerivedV::Scalar, 3, 1> neg_t2 = norm.cross(p1 - p0);
|
|
|
+
|
|
|
+ Eigen::Matrix<typename DerivedV::Scalar, 3, 1> diffu = (neg_t0 * uv0(0) +neg_t1 *uv1(0) + neg_t2 * uv2(0) )*area2_inv;
|
|
|
+ Eigen::Matrix<typename DerivedV::Scalar, 3, 1> diffv = (neg_t0 * uv0(1) + neg_t1*uv1(1) + neg_t2*uv2(1) )*area2_inv;
|
|
|
+
|
|
|
+ // first fundamental form
|
|
|
+ double I00 = diffu.dot(diffu); // guaranteed non-neg
|
|
|
+ double I01 = diffu.dot(diffv); // I01 = I10
|
|
|
+ double I11 = diffv.dot(diffv); // guaranteed non-neg
|
|
|
+
|
|
|
+ // eigenvalues of a 2x2 matrix
|
|
|
+ // [a00 a01]
|
|
|
+ // [a10 a11]
|
|
|
+ // 1/2 * [ (a00 + a11) +/- sqrt((a00 - a11)^2 + 4 a01 a10) ]
|
|
|
+ double trI = I00 + I11; // guaranteed non-neg
|
|
|
+ double diffDiag = I00 - I11; // guaranteed non-neg
|
|
|
+ double sqrtDet = sqrt(std::max(0.0, diffDiag*diffDiag +
|
|
|
+ 4 * I01 * I01)); // guaranteed non-neg
|
|
|
+ double sig1 = 0.5 * (trI + sqrtDet); // higher singular value
|
|
|
+ double sig2 = 0.5 * (trI - sqrtDet); // lower singular value
|
|
|
+
|
|
|
+ // Avoid sig2 < 0 due to numerical error
|
|
|
+ if (fabs(sig2) < 1.0e-8)
|
|
|
+ sig2 = 0;
|
|
|
+
|
|
|
+ assert(sig1 >= 0);
|
|
|
+ assert(sig2 >= 0);
|
|
|
+
|
|
|
+ if (sig2 < 0) {
|
|
|
+ printf("Distortion will be NaN! sig1^2 is negative (%lg)\n",
|
|
|
+ sig2);
|
|
|
+ }
|
|
|
+
|
|
|
+ // The singular values of the Jacobian are the sqrts of the
|
|
|
+ // eigenvalues of the first fundamental form.
|
|
|
+ sig1 = sqrt(sig1);
|
|
|
+ sig2 = sqrt(sig2);
|
|
|
+
|
|
|
+ // distortion
|
|
|
+ double tao = IsFlipped(f,WUV) ? -1 : 1;
|
|
|
+ double factor = tao / h;
|
|
|
+ double lam = fabs(factor * sig1 - 1) + fabs(factor * sig2 - 1);
|
|
|
+ return lam;
|
|
|
+ }
|
|
|
+ else {
|
|
|
+ return 10; // something "large"
|
|
|
+ }
|
|
|
+}
|
|
|
+
|
|
|
+////////////////////////////////////////////////////////////////////////////
|
|
|
+// Approximate the distortion laplacian using a uniform laplacian on
|
|
|
+// the dual mesh:
|
|
|
+// ___________
|
|
|
+// \-1 / \-1 /
|
|
|
+// \ / 3 \ /
|
|
|
+// \-----/
|
|
|
+// \-1 /
|
|
|
+// \ /
|
|
|
+//
|
|
|
+// @param[in] f facet on which to compute distortion laplacian
|
|
|
+// @param[in] h scaling factor applied to cross field
|
|
|
+// @return distortion laplacian for f
|
|
|
+///////////////////////////////////////////////////////////////////////////
|
|
|
+template <typename DerivedV, typename DerivedF, typename DerivedU>
|
|
|
+double igl::MIQ<DerivedV, DerivedF, DerivedU>::LaplaceDistortion(const int f, double h, const MatrixXd& WUV)
|
|
|
+{
|
|
|
+ double mydist = Distortion(f, h, WUV);
|
|
|
+ double lapl=0;
|
|
|
+ for (int i=0;i<3;i++)
|
|
|
+ {
|
|
|
+ if (TT(f,i) != -1)
|
|
|
+ lapl += (mydist - Distortion(TT(f,i), h, WUV));
|
|
|
+ }
|
|
|
+ return lapl;
|
|
|
+}
|
|
|
+
|
|
|
+template <typename DerivedV, typename DerivedF, typename DerivedU>
|
|
|
+bool igl::MIQ<DerivedV, DerivedF, DerivedU>::updateStiffeningJacobianDistorsion(double grad_size, const MatrixXd& WUV)
|
|
|
+{
|
|
|
+ bool flipped = NumFlips(WUV)>0;
|
|
|
+
|
|
|
+ if (!flipped)
|
|
|
+ return false;
|
|
|
+
|
|
|
+ double maxL=0;
|
|
|
+ double maxD=0;
|
|
|
+
|
|
|
+ if (flipped)
|
|
|
+ {
|
|
|
+ const double c = 1.0;
|
|
|
+ const double d = 5.0;
|
|
|
+
|
|
|
+ for (unsigned int i = 0; i < F.rows(); ++i)
|
|
|
+ {
|
|
|
+ double dist=Distortion(i,grad_size,WUV);
|
|
|
+ if (dist > maxD)
|
|
|
+ maxD=dist;
|
|
|
+
|
|
|
+ double absLap=fabs(LaplaceDistortion(i, grad_size,WUV));
|
|
|
+ if (absLap > maxL)
|
|
|
+ maxL = absLap;
|
|
|
+
|
|
|
+ double stiffDelta = std::min(c * absLap, d);
|
|
|
+
|
|
|
+ Handle_Stiffness[i]+=stiffDelta;
|
|
|
+ }
|
|
|
+ }
|
|
|
+ printf("Maximum Distorsion %4.4f \n",maxD);
|
|
|
+ printf("Maximum Laplacian %4.4f \n",maxL);
|
|
|
+ return flipped;
|
|
|
+}
|
|
|
+
|
|
|
+template <typename DerivedV, typename DerivedF, typename DerivedU>
|
|
|
+inline bool igl::MIQ<DerivedV, DerivedF, DerivedU>::IsFlipped(const Vector2d &uv0,
|
|
|
+ const Vector2d &uv1,
|
|
|
+ const Vector2d &uv2)
|
|
|
+{
|
|
|
+ Vector2d e0 = (uv1-uv0);
|
|
|
+ Vector2d e1 = (uv2-uv0);
|
|
|
+
|
|
|
+ double Area = e0(0)*e1(1) - e0(1)*e1(0);
|
|
|
+ return (Area<=0);
|
|
|
+}
|
|
|
+
|
|
|
+template <typename DerivedV, typename DerivedF, typename DerivedU>
|
|
|
+inline bool igl::MIQ<DerivedV, DerivedF, DerivedU>::IsFlipped(const int i, const MatrixXd& WUV)
|
|
|
+{
|
|
|
+ Vector2d uv0,uv1,uv2;
|
|
|
+ uv0 << WUV(i,0), WUV(i,1);
|
|
|
+ uv1 << WUV(i,2), WUV(i,3);
|
|
|
+ uv2 << WUV(i,4), WUV(i,5);
|
|
|
+
|
|
|
+ return (IsFlipped(uv0,uv1,uv2));
|
|
|
+}
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+
|
|
|
+template <typename DerivedV, typename DerivedF, typename DerivedU>
|
|
|
+IGL_INLINE void igl::mixed_integer_quadrangulate(const Eigen::PlainObjectBase<DerivedV> &V,
|
|
|
+ const Eigen::PlainObjectBase<DerivedF> &F,
|
|
|
+ const Eigen::PlainObjectBase<DerivedV> &PD1_combed,
|
|
|
+ const Eigen::PlainObjectBase<DerivedV> &PD2_combed,
|
|
|
+ const Eigen::PlainObjectBase<DerivedV> &BIS1_combed,
|
|
|
+ const Eigen::PlainObjectBase<DerivedV> &BIS2_combed,
|
|
|
+ const Eigen::Matrix<int, Eigen::Dynamic, 3> &Handle_MMatch,
|
|
|
+ const Eigen::Matrix<int, Eigen::Dynamic, 1> &Handle_Singular,
|
|
|
+ const Eigen::Matrix<int, Eigen::Dynamic, 1> &Handle_SingularDegree,
|
|
|
+ const Eigen::Matrix<int, Eigen::Dynamic, 3> &Handle_Seams,
|
|
|
+ Eigen::PlainObjectBase<DerivedU> &UV,
|
|
|
+ Eigen::PlainObjectBase<DerivedF> &FUV,
|
|
|
+ double GradientSize,
|
|
|
+ double Stiffness,
|
|
|
+ bool DirectRound,
|
|
|
+ int iter,
|
|
|
+ int localIter,
|
|
|
+ bool DoRound,
|
|
|
+ std::vector<int> roundVertices,
|
|
|
+ std::vector<std::vector<int> > hardFeatures)
|
|
|
+{
|
|
|
+ GradientSize = GradientSize/(V.colwise().maxCoeff()-V.colwise().minCoeff()).norm();
|
|
|
+
|
|
|
+ igl::MIQ<DerivedV, DerivedF, DerivedU> miq(V,
|
|
|
+ F,
|
|
|
+ PD1_combed,
|
|
|
+ PD2_combed,
|
|
|
+ BIS1_combed,
|
|
|
+ BIS2_combed,
|
|
|
+ Handle_MMatch,
|
|
|
+ Handle_Singular,
|
|
|
+ Handle_SingularDegree,
|
|
|
+ Handle_Seams,
|
|
|
+ UV,
|
|
|
+ FUV,
|
|
|
+ GradientSize,
|
|
|
+ Stiffness,
|
|
|
+ DirectRound,
|
|
|
+ iter,
|
|
|
+ localIter,
|
|
|
+ DoRound,
|
|
|
+ roundVertices,
|
|
|
+ hardFeatures);
|
|
|
+
|
|
|
+ miq.extractUV(UV,FUV);
|
|
|
+}
|
|
|
+
|
|
|
+template <typename DerivedV, typename DerivedF, typename DerivedU>
|
|
|
+IGL_INLINE void igl::mixed_integer_quadrangulate(const Eigen::PlainObjectBase<DerivedV> &V,
|
|
|
+ const Eigen::PlainObjectBase<DerivedF> &F,
|
|
|
+ const Eigen::PlainObjectBase<DerivedV> &PD1,
|
|
|
+ const Eigen::PlainObjectBase<DerivedV> &PD2,
|
|
|
+ Eigen::PlainObjectBase<DerivedU> &UV,
|
|
|
+ Eigen::PlainObjectBase<DerivedF> &FUV,
|
|
|
+ double GradientSize,
|
|
|
+ double Stiffness,
|
|
|
+ bool DirectRound,
|
|
|
+ int iter,
|
|
|
+ int localIter,
|
|
|
+ bool DoRound,
|
|
|
+ std::vector<int> roundVertices,
|
|
|
+ std::vector<std::vector<int> > hardFeatures)
|
|
|
+{
|
|
|
+ Eigen::PlainObjectBase<DerivedV> BIS1, BIS2;
|
|
|
+ igl::compute_frame_field_bisectors(V, F, PD1, PD2, BIS1, BIS2);
|
|
|
+
|
|
|
+ Eigen::PlainObjectBase<DerivedV> BIS1_combed, BIS2_combed;
|
|
|
+ igl::comb_cross_field(V, F, BIS1, BIS2, BIS1_combed, BIS2_combed);
|
|
|
+
|
|
|
+ Eigen::Matrix<int, Eigen::Dynamic, 3> Handle_MMatch;
|
|
|
+ igl::cross_field_missmatch(V, F, BIS1_combed, BIS2_combed, true, Handle_MMatch);
|
|
|
+
|
|
|
+ Eigen::Matrix<int, Eigen::Dynamic, 1> isSingularity, singularityIndex;
|
|
|
+ igl::find_cross_field_singularities(V, F, Handle_MMatch, isSingularity, singularityIndex);
|
|
|
+
|
|
|
+ Eigen::Matrix<int, Eigen::Dynamic, 3> Handle_Seams;
|
|
|
+ igl::cut_mesh_from_singularities(V, F, Handle_MMatch, isSingularity, singularityIndex, Handle_Seams);
|
|
|
+
|
|
|
+ Eigen::PlainObjectBase<DerivedV> PD1_combed, PD2_combed;
|
|
|
+ igl::comb_frame_field(V, F, PD1, PD2, BIS1_combed, BIS2_combed, PD1_combed, PD2_combed);
|
|
|
+
|
|
|
+ igl::mixed_integer_quadrangulate(V,
|
|
|
+ F,
|
|
|
+ PD1_combed,
|
|
|
+ PD2_combed,
|
|
|
+ BIS1_combed,
|
|
|
+ BIS2_combed,
|
|
|
+ Handle_MMatch,
|
|
|
+ isSingularity,
|
|
|
+ singularityIndex,
|
|
|
+ Handle_Seams,
|
|
|
+ UV,
|
|
|
+ FUV,
|
|
|
+ GradientSize,
|
|
|
+ Stiffness,
|
|
|
+ DirectRound,
|
|
|
+ iter,
|
|
|
+ localIter,
|
|
|
+ DoRound);
|
|
|
+
|
|
|
+}
|
Olga Diamanti