Exemplo n.º 1
0
bool key_down(igl::Viewer& viewer, unsigned char key, int modifier)
{
  if (key == 'E')
  {
    extend_arrows = !extend_arrows;
  }

  if (key <'1' || key >'8')
    return false;

  viewer.data.clear();
  viewer.core.show_lines = false;
  viewer.core.show_texture = false;

  if (key == '1')
  {
    // Cross field
    viewer.data.set_mesh(V, F);
    viewer.data.add_edges(extend_arrows ? B - global_scale*X1 : B, B + global_scale*X1 ,Eigen::RowVector3d(1,0,0));
    viewer.data.add_edges(extend_arrows ? B - global_scale*X2 : B, B + global_scale*X2 ,Eigen::RowVector3d(0,0,1));
  }

  if (key == '2')
  {
    // Bisector field
    viewer.data.set_mesh(V, F);
    viewer.data.add_edges(extend_arrows ? B - global_scale*BIS1 : B, B + global_scale*BIS1 ,Eigen::RowVector3d(1,0,0));
    viewer.data.add_edges(extend_arrows ? B - global_scale*BIS2 : B, B + global_scale*BIS2 ,Eigen::RowVector3d(0,0,1));
  }

  if (key == '3')
  {
    // Bisector field combed
    viewer.data.set_mesh(V, F);
    viewer.data.add_edges(extend_arrows ? B - global_scale*BIS1_combed : B, B + global_scale*BIS1_combed ,Eigen::RowVector3d(1,0,0));
    viewer.data.add_edges(extend_arrows ? B - global_scale*BIS2_combed : B, B + global_scale*BIS2_combed ,Eigen::RowVector3d(0,0,1));
  }

  if (key == '4')
  {
    // Singularities and cuts
    viewer.data.set_mesh(V, F);

    // Plot cuts
    int l_count = Seams.sum();
    Eigen::MatrixXd P1(l_count,3);
    Eigen::MatrixXd P2(l_count,3);

    for (unsigned i=0; i<Seams.rows(); ++i)
    {
      for (unsigned j=0; j<Seams.cols(); ++j)
      {
        if (Seams(i,j) != 0)
        {
          P1.row(l_count-1) = V.row(F(i,j));
          P2.row(l_count-1) = V.row(F(i,(j+1)%3));
          l_count--;
        }
      }
    }

    viewer.data.add_edges(P1, P2, Eigen::RowVector3d(1, 0, 0));

    // Plot the singularities as colored dots (red for negative, blue for positive)
    for (unsigned i=0; i<singularityIndex.size();++i)
    {
      if (singularityIndex(i) < 2 && singularityIndex(i) > 0)
        viewer.data.add_points(V.row(i),Eigen::RowVector3d(1,0,0));
      else if (singularityIndex(i) > 2)
        viewer.data.add_points(V.row(i),Eigen::RowVector3d(0,1,0));
    }

  }

  if (key == '5')
  {
    // Singularities and cuts, original field
    // Singularities and cuts
    viewer.data.set_mesh(V, F);
    viewer.data.add_edges(extend_arrows ? B - global_scale*X1_combed : B, B + global_scale*X1_combed ,Eigen::RowVector3d(1,0,0));
    viewer.data.add_edges(extend_arrows ? B - global_scale*X2_combed : B, B + global_scale*X2_combed ,Eigen::RowVector3d(0,0,1));

    // Plot cuts
    int l_count = Seams.sum();
    Eigen::MatrixXd P1(l_count,3);
    Eigen::MatrixXd P2(l_count,3);

    for (unsigned i=0; i<Seams.rows(); ++i)
    {
      for (unsigned j=0; j<Seams.cols(); ++j)
      {
        if (Seams(i,j) != 0)
        {
          P1.row(l_count-1) = V.row(F(i,j));
          P2.row(l_count-1) = V.row(F(i,(j+1)%3));
          l_count--;
        }
      }
    }

    viewer.data.add_edges(P1, P2, Eigen::RowVector3d(1, 0, 0));

    // Plot the singularities as colored dots (red for negative, blue for positive)
    for (unsigned i=0; i<singularityIndex.size();++i)
    {
      if (singularityIndex(i) < 2 && singularityIndex(i) > 0)
        viewer.data.add_points(V.row(i),Eigen::RowVector3d(1,0,0));
      else if (singularityIndex(i) > 2)
        viewer.data.add_points(V.row(i),Eigen::RowVector3d(0,1,0));
    }
  }

  if (key == '6')
  {
    // Global parametrization UV
    viewer.data.set_mesh(UV, FUV);
    viewer.data.set_uv(UV);
    viewer.core.show_lines = true;
  }

  if (key == '7')
  {
    // Global parametrization in 3D
    viewer.data.set_mesh(V, F);
    viewer.data.set_uv(UV,FUV);
    viewer.core.show_texture = true;
  }

  if (key == '8')
  {
    // Global parametrization in 3D with seams
    viewer.data.set_mesh(V, F);
    viewer.data.set_uv(UV_seams,FUV_seams);
    viewer.core.show_texture = true;
  }

  viewer.data.set_colors(Eigen::RowVector3d(1,1,1));

  // Replace the standard texture with an integer shift invariant texture
  Eigen::Matrix<unsigned char,Eigen::Dynamic,Eigen::Dynamic> texture_R, texture_G, texture_B;
  line_texture(texture_R, texture_G, texture_B);
  viewer.data.set_texture(texture_R, texture_B, texture_G);

  viewer.core.align_camera_center(viewer.data.V,viewer.data.F);

  return false;
}
Exemplo n.º 2
0
IGL_INLINE bool igl::copyleft::boolean::mesh_boolean(
    const Eigen::PlainObjectBase<DerivedVA> & VA,
    const Eigen::PlainObjectBase<DerivedFA> & FA,
    const Eigen::PlainObjectBase<DerivedVB> & VB,
    const Eigen::PlainObjectBase<DerivedFB> & FB,
    const WindingNumberOp& wind_num_op,
    const KeepFunc& keep,
    const ResolveFunc& resolve_fun,
    Eigen::PlainObjectBase<DerivedVC > & VC,
    Eigen::PlainObjectBase<DerivedFC > & FC,
    Eigen::PlainObjectBase<DerivedJ > & J) 
{

#ifdef MESH_BOOLEAN_TIMING
  const auto & tictoc = []() -> double
  {
    static double t_start = igl::get_seconds();
    double diff = igl::get_seconds()-t_start;
    t_start += diff;
    return diff;
  };
  const auto log_time = [&](const std::string& label) -> void {
    std::cout << "mesh_boolean." << label << ": "
      << tictoc() << std::endl;
  };
  tictoc();
#endif

  typedef typename DerivedVC::Scalar Scalar;
  //typedef typename DerivedFC::Scalar Index;
  typedef CGAL::Epeck Kernel;
  typedef Kernel::FT ExactScalar;
  typedef Eigen::Matrix<Scalar,Eigen::Dynamic,3> MatrixX3S;
  //typedef Eigen::Matrix<Index,Eigen::Dynamic,Eigen::Dynamic> MatrixXI;
  typedef Eigen::Matrix<typename DerivedJ::Scalar,Eigen::Dynamic,1> VectorXJ;

  // Generate combined mesh.
  typedef Eigen::Matrix<
    ExactScalar,
    Eigen::Dynamic,
    Eigen::Dynamic,
    DerivedVC::IsRowMajor> MatrixXES;
  MatrixXES V;
  DerivedFC F;
  VectorXJ  CJ;
  {
      DerivedVA VV(VA.rows() + VB.rows(), 3);
      DerivedFC FF(FA.rows() + FB.rows(), 3);
      VV << VA, VB;
      FF << FA, FB.array() + VA.rows();
      //// Handle annoying empty cases
      //if(VA.size()>0)
      //{
      //  VV<<VA;
      //}
      //if(VB.size()>0)
      //{
      //  VV<<VB;
      //}
      //if(FA.size()>0)
      //{
      //  FF<<FA;
      //}
      //if(FB.size()>0)
      //{
      //  FF<<FB.array()+VA.rows();
      //}
      resolve_fun(VV, FF, V, F, CJ);
  }
#ifdef MESH_BOOLEAN_TIMING
  log_time("resolve_self_intersection");
#endif

  // Compute winding numbers on each side of each facet.
  const size_t num_faces = F.rows();
  Eigen::MatrixXi W;
  Eigen::VectorXi labels(num_faces);
  std::transform(CJ.data(), CJ.data()+CJ.size(), labels.data(),
      [&](int i) { return i<FA.rows() ? 0:1; });
  bool valid = true;
  if (num_faces > 0) 
  {
    valid = valid & 
      igl::copyleft::cgal::propagate_winding_numbers(V, F, labels, W);
  } else 
  {
    W.resize(0, 4);
  }
  assert((size_t)W.rows() == num_faces);
  if (W.cols() == 2) 
  {
    assert(FB.rows() == 0);
    Eigen::MatrixXi W_tmp(num_faces, 4);
    W_tmp << W, Eigen::MatrixXi::Zero(num_faces, 2);
    W = W_tmp;
  } else {
    assert(W.cols() == 4);
  }
#ifdef MESH_BOOLEAN_TIMING
  log_time("propagate_input_winding_number");
#endif

  // Compute resulting winding number.
  Eigen::MatrixXi Wr(num_faces, 2);
  for (size_t i=0; i<num_faces; i++) 
  {
    Eigen::MatrixXi w_out(1,2), w_in(1,2);
    w_out << W(i,0), W(i,2);
    w_in  << W(i,1), W(i,3);
    Wr(i,0) = wind_num_op(w_out);
    Wr(i,1) = wind_num_op(w_in);
  }
#ifdef MESH_BOOLEAN_TIMING
  log_time("compute_output_winding_number");
#endif

  // Extract boundary separating inside from outside.
  auto index_to_signed_index = [&](size_t i, bool ori) -> int
  {
    return (i+1)*(ori?1:-1);
  };
  //auto signed_index_to_index = [&](int i) -> size_t {
  //    return abs(i) - 1;
  //};
  std::vector<int> selected;
  for(size_t i=0; i<num_faces; i++) 
  {
    auto should_keep = keep(Wr(i,0), Wr(i,1));
    if (should_keep > 0) 
    {
      selected.push_back(index_to_signed_index(i, true));
    } else if (should_keep < 0) 
    {
      selected.push_back(index_to_signed_index(i, false));
    }
  }

  const size_t num_selected = selected.size();
  DerivedFC kept_faces(num_selected, 3);
  DerivedJ  kept_face_indices(num_selected, 1);
  for (size_t i=0; i<num_selected; i++) 
  {
    size_t idx = abs(selected[i]) - 1;
    if (selected[i] > 0) 
    {
      kept_faces.row(i) = F.row(idx);
    } else 
    {
      kept_faces.row(i) = F.row(idx).reverse();
    }
    kept_face_indices(i, 0) = CJ[idx];
  }
#ifdef MESH_BOOLEAN_TIMING
  log_time("extract_output");
#endif

  // Finally, remove duplicated faces and unreferenced vertices.
  {
    DerivedFC G;
    DerivedJ JJ;
    igl::resolve_duplicated_faces(kept_faces, G, JJ);
    igl::slice(kept_face_indices, JJ, 1, J);

#ifdef DOUBLE_CHECK_EXACT_OUTPUT
    {
      // Sanity check on exact output.
      igl::copyleft::cgal::RemeshSelfIntersectionsParam params;
      params.detect_only = true;
      params.first_only = true;
      MatrixXES dummy_VV;
      DerivedFC dummy_FF, dummy_IF;
      Eigen::VectorXi dummy_J, dummy_IM;
      igl::copyleft::cgal::SelfIntersectMesh<
        Kernel,
        MatrixXES, DerivedFC,
        MatrixXES, DerivedFC,
        DerivedFC,
        Eigen::VectorXi,
        Eigen::VectorXi
      > checker(V, G, params,
          dummy_VV, dummy_FF, dummy_IF, dummy_J, dummy_IM);
      if (checker.count != 0) 
      {
        throw "Self-intersection not fully resolved.";
      }
    }
#endif

    MatrixX3S Vs(V.rows(), V.cols());
    for (size_t i=0; i<(size_t)V.rows(); i++)
    {
      for (size_t j=0; j<(size_t)V.cols(); j++)
      {
        igl::copyleft::cgal::assign_scalar(V(i,j), Vs(i,j));
      }
    }
    Eigen::VectorXi newIM;
    igl::remove_unreferenced(Vs,G,VC,FC,newIM);
  }
#ifdef MESH_BOOLEAN_TIMING
  log_time("clean_up");
#endif
  return valid;
}
Exemplo n.º 3
0
IGL_INLINE void igl::copyleft::boolean::mesh_boolean(
    const Eigen::PlainObjectBase<DerivedVA> & VA,
    const Eigen::PlainObjectBase<DerivedFA> & FA,
    const Eigen::PlainObjectBase<DerivedVB> & VB,
    const Eigen::PlainObjectBase<DerivedFB> & FB,
    const WindingNumberOp& wind_num_op,
    const KeepFunc& keep,
    const ResolveFunc& resolve_fun,
    Eigen::PlainObjectBase<DerivedVC > & VC,
    Eigen::PlainObjectBase<DerivedFC > & FC,
    Eigen::PlainObjectBase<DerivedJ > & J) {

  typedef typename DerivedVC::Scalar Scalar;
  //typedef typename DerivedFC::Scalar Index;
  typedef CGAL::Epeck Kernel;
  typedef Kernel::FT ExactScalar;
  typedef Eigen::Matrix<Scalar,Eigen::Dynamic,3> MatrixX3S;
  //typedef Eigen::Matrix<Index,Eigen::Dynamic,Eigen::Dynamic> MatrixXI;
  typedef Eigen::Matrix<typename DerivedJ::Scalar,Eigen::Dynamic,1> VectorXJ;

  // Generate combined mesh.
  typedef Eigen::Matrix<
    ExactScalar,
    Eigen::Dynamic,
    Eigen::Dynamic,
    DerivedVC::IsRowMajor> MatrixXES;
  MatrixXES V;
  DerivedFC F;
  VectorXJ  CJ;
  {
      DerivedVA VV(VA.rows() + VB.rows(), 3);
      DerivedFC FF(FA.rows() + FB.rows(), 3);
      VV << VA, VB;
      FF << FA, FB.array() + VA.rows();
      //// Handle annoying empty cases
      //if(VA.size()>0)
      //{
      //  VV<<VA;
      //}
      //if(VB.size()>0)
      //{
      //  VV<<VB;
      //}
      //if(FA.size()>0)
      //{
      //  FF<<FA;
      //}
      //if(FB.size()>0)
      //{
      //  FF<<FB.array()+VA.rows();
      //}
      resolve_fun(VV, FF, V, F, CJ);
  }

  // Compute winding numbers on each side of each facet.
  const size_t num_faces = F.rows();
  Eigen::MatrixXi W;
  Eigen::VectorXi labels(num_faces);
  std::transform(CJ.data(), CJ.data()+CJ.size(), labels.data(),
      [&](int i) { return i<FA.rows() ? 0:1; });
  igl::copyleft::cgal::propagate_winding_numbers(V, F, labels, W);
  assert((size_t)W.rows() == num_faces);
  if (W.cols() == 2) {
    assert(FB.rows() == 0);
    Eigen::MatrixXi W_tmp(num_faces, 4);
    W_tmp << W, Eigen::MatrixXi::Zero(num_faces, 2);
    W = W_tmp;
  } else {
    assert(W.cols() == 4);
  }

  // Compute resulting winding number.
  Eigen::MatrixXi Wr(num_faces, 2);
  for (size_t i=0; i<num_faces; i++) {
    Eigen::MatrixXi w_out(1,2), w_in(1,2);
    w_out << W(i,0), W(i,2);
    w_in  << W(i,1), W(i,3);
    Wr(i,0) = wind_num_op(w_out);
    Wr(i,1) = wind_num_op(w_in);
  }

  // Extract boundary separating inside from outside.
  auto index_to_signed_index = [&](size_t i, bool ori) -> int{
    return (i+1)*(ori?1:-1);
  };
  //auto signed_index_to_index = [&](int i) -> size_t {
  //    return abs(i) - 1;
  //};
  std::vector<int> selected;
  for(size_t i=0; i<num_faces; i++) {
    auto should_keep = keep(Wr(i,0), Wr(i,1));
    if (should_keep > 0) {
      selected.push_back(index_to_signed_index(i, true));
    } else if (should_keep < 0) {
      selected.push_back(index_to_signed_index(i, false));
    }
  }

  const size_t num_selected = selected.size();
  DerivedFC kept_faces(num_selected, 3);
  DerivedJ  kept_face_indices(num_selected, 1);
  for (size_t i=0; i<num_selected; i++) {
    size_t idx = abs(selected[i]) - 1;
    if (selected[i] > 0) {
      kept_faces.row(i) = F.row(idx);
    } else {
      kept_faces.row(i) = F.row(idx).reverse();
    }
    kept_face_indices(i, 0) = CJ[idx];
  }

  // Finally, remove duplicated faces and unreferenced vertices.
  {
    DerivedFC G;
    DerivedJ JJ;
    igl::resolve_duplicated_faces(kept_faces, G, JJ);
    igl::slice(kept_face_indices, JJ, 1, J);

    MatrixX3S Vs(V.rows(), V.cols());
    for (size_t i=0; i<(size_t)V.rows(); i++)
    {
      for (size_t j=0; j<(size_t)V.cols(); j++)
      {
        igl::copyleft::cgal::assign_scalar(V(i,j), Vs(i,j));
      }
    }
    Eigen::VectorXi newIM;
    igl::remove_unreferenced(Vs,G,VC,FC,newIM);
  }
}
Exemplo n.º 4
0
void fromIntEigenMatrix_16(const Eigen::MatrixXi& from_mat, int **&to_mat)
{
    fromIntEigenMatrix_16(from_mat, to_mat, from_mat.rows(), from_mat.cols());
}
Exemplo n.º 5
0
IGL_INLINE bool igl::arap_dof_precomputation(
  const Eigen::MatrixXd & V, 
  const Eigen::MatrixXi & F,
  const LbsMatrixType & M,
  const Eigen::Matrix<int,Eigen::Dynamic,1> & G,
  ArapDOFData<LbsMatrixType, SSCALAR> & data)
{
  using namespace Eigen;
  typedef Matrix<SSCALAR, Dynamic, Dynamic> MatrixXS;
  // number of mesh (domain) vertices
  int n = V.rows();
  // cache problem size
  data.n = n;
  // dimension of mesh
  data.dim = V.cols();
  assert(data.dim == M.rows()/n);
  assert(data.dim*n == M.rows());
  if(data.dim == 3)
  {
    // Check if z-coordinate is all zeros
    if(V.col(2).minCoeff() == 0 && V.col(2).maxCoeff() == 0)
    {
      data.effective_dim = 2;
    }
  }else
  {
    data.effective_dim = data.dim;
  }
  // Number of handles
  data.m = M.cols()/data.dim/(data.dim+1);
  assert(data.m*data.dim*(data.dim+1) == M.cols());
  //assert(m == C.rows());

  //printf("n=%d; dim=%d; m=%d;\n",n,data.dim,data.m);

  // Build cotangent laplacian
  SparseMatrix<double> Lcot;
  //printf("cotmatrix()\n");
  cotmatrix(V,F,Lcot);
  // Discrete laplacian (should be minus matlab version)
  SparseMatrix<double> Lapl = -2.0*Lcot;
#ifdef EXTREME_VERBOSE
  cout<<"LaplIJV=["<<endl;print_ijv(Lapl,1);cout<<endl<<"];"<<
    endl<<"Lapl=sparse(LaplIJV(:,1),LaplIJV(:,2),LaplIJV(:,3),"<<
    Lapl.rows()<<","<<Lapl.cols()<<");"<<endl;
#endif

  // Get group sum scatter matrix, when applied sums all entries of the same
  // group according to G
  SparseMatrix<double> G_sum;
  if(G.size() == 0)
  {
    speye(n,G_sum);
  }else
  {
    // groups are defined per vertex, convert to per face using mode
    Eigen::Matrix<int,Eigen::Dynamic,1> GG;
    if(data.energy == ARAP_ENERGY_TYPE_ELEMENTS)
    {
      MatrixXi GF(F.rows(),F.cols());
      for(int j = 0;j<F.cols();j++)
      {
        Matrix<int,Eigen::Dynamic,1> GFj;
        slice(G,F.col(j),GFj);
        GF.col(j) = GFj;
      }
      mode<int>(GF,2,GG);
    }else
    {
      GG=G;
    }
    //printf("group_sum_matrix()\n");
    group_sum_matrix(GG,G_sum);
  }

#ifdef EXTREME_VERBOSE
  cout<<"G_sumIJV=["<<endl;print_ijv(G_sum,1);cout<<endl<<"];"<<
    endl<<"G_sum=sparse(G_sumIJV(:,1),G_sumIJV(:,2),G_sumIJV(:,3),"<<
    G_sum.rows()<<","<<G_sum.cols()<<");"<<endl;
#endif

  // Get covariance scatter matrix, when applied collects the covariance matrices
  // used to fit rotations to during optimization
  SparseMatrix<double> CSM;
  //printf("covariance_scatter_matrix()\n");
  covariance_scatter_matrix(V,F,data.energy,CSM);
#ifdef EXTREME_VERBOSE
  cout<<"CSMIJV=["<<endl;print_ijv(CSM,1);cout<<endl<<"];"<<
    endl<<"CSM=sparse(CSMIJV(:,1),CSMIJV(:,2),CSMIJV(:,3),"<<
    CSM.rows()<<","<<CSM.cols()<<");"<<endl;
#endif
  

  // Build the covariance matrix "constructor". This is a set of *scatter*
  // matrices that when multiplied on the right by column of the transformation
  // matrix entries (the degrees of freedom) L, we get a stack of dim by 1
  // covariance matrix column, with a column in the stack for each rotation
  // *group*. The output is a list of matrices because we construct each column
  // in the stack of covariance matrices with an independent matrix-vector
  // multiplication.
  //
  // We want to build S which is a stack of dim by dim covariance matrices.
  // Thus S is dim*g by dim, where dim is the number of dimensions and g is the
  // number of groups. We can precompute dim matrices CSM_M such that column i
  // in S is computed as S(:,i) = CSM_M{i} * L, where L is a column of the
  // skinning transformation matrix values. To be clear, the covariance matrix
  // for group k is then given as the dim by dim matrix pulled from the stack:
  // S((k-1)*dim + 1:dim,:)

  // Apply group sum to each dimension's block of covariance scatter matrix
  SparseMatrix<double> G_sum_dim;
  repdiag(G_sum,data.dim,G_sum_dim);
  CSM = G_sum_dim * CSM;
#ifdef EXTREME_VERBOSE
  cout<<"CSMIJV=["<<endl;print_ijv(CSM,1);cout<<endl<<"];"<<
    endl<<"CSM=sparse(CSMIJV(:,1),CSMIJV(:,2),CSMIJV(:,3),"<<
    CSM.rows()<<","<<CSM.cols()<<");"<<endl;
#endif

  //printf("CSM_M()\n");
  // Precompute CSM times M for each dimension
  data.CSM_M.resize(data.dim);
#ifdef EXTREME_VERBOSE
  cout<<"data.CSM_M = cell("<<data.dim<<",1);"<<endl;
#endif
  // span of integers from 0 to n-1
  Eigen::Matrix<int,Eigen::Dynamic,1> span_n(n);
  for(int i = 0;i<n;i++)
  {
    span_n(i) = i;
  }

  // span of integers from 0 to M.cols()-1
  Eigen::Matrix<int,Eigen::Dynamic,1> span_mlbs_cols(M.cols());
  for(int i = 0;i<M.cols();i++)
  {
    span_mlbs_cols(i) = i;
  }

  // number of groups
  int k = CSM.rows()/data.dim;
  for(int i = 0;i<data.dim;i++)
  {
    //printf("CSM_M(): Mi\n");
    LbsMatrixType M_i;
    //printf("CSM_M(): slice\n");
    slice(M,(span_n.array()+i*n).matrix(),span_mlbs_cols,M_i);
    LbsMatrixType M_i_dim;
    data.CSM_M[i].resize(k*data.dim,data.m*data.dim*(data.dim+1));
    assert(data.CSM_M[i].cols() == M.cols());
    for(int j = 0;j<data.dim;j++)
    {
      SparseMatrix<double> CSMj;
      //printf("CSM_M(): slice\n");
      slice(
        CSM,
        colon<int>(j*k,(j+1)*k-1),
        colon<int>(j*n,(j+1)*n-1),
        CSMj);
      assert(CSMj.rows() == k);
      assert(CSMj.cols() == n);
      LbsMatrixType CSMjM_i = CSMj * M_i;
      if(is_sparse(CSMjM_i))
      {
        // Convert to full
        MatrixXd CSMjM_ifull;
        //printf("CSM_M(): full\n");
        full(CSMjM_i,CSMjM_ifull);
//        printf("CSM_M[%d]: %d %d\n",i,data.CSM_M[i].rows(),data.CSM_M[i].cols());
//        printf("CSM_M[%d].block(%d*%d=%d,0,%d,%d): %d %d\n",i,j,k,CSMjM_i.rows(),CSMjM_i.cols(),
//            data.CSM_M[i].block(j*k,0,CSMjM_i.rows(),CSMjM_i.cols()).rows(),
//            data.CSM_M[i].block(j*k,0,CSMjM_i.rows(),CSMjM_i.cols()).cols());
//        printf("CSM_MjMi: %d %d\n",i,CSMjM_i.rows(),CSMjM_i.cols());
//        printf("CSM_MjM_ifull: %d %d\n",i,CSMjM_ifull.rows(),CSMjM_ifull.cols());
        data.CSM_M[i].block(j*k,0,CSMjM_i.rows(),CSMjM_i.cols()) = CSMjM_ifull;
      }else
      {
        data.CSM_M[i].block(j*k,0,CSMjM_i.rows(),CSMjM_i.cols()) = CSMjM_i;
      }
    }
#ifdef EXTREME_VERBOSE
    cout<<"CSM_Mi=["<<endl<<data.CSM_M[i]<<endl<<"];"<<endl;
#endif
  }

  // precompute arap_rhs matrix
  //printf("arap_rhs()\n");
  SparseMatrix<double> K;
  arap_rhs(V,F,V.cols(),data.energy,K);
//#ifdef EXTREME_VERBOSE
//  cout<<"KIJV=["<<endl;print_ijv(K,1);cout<<endl<<"];"<<
//    endl<<"K=sparse(KIJV(:,1),KIJV(:,2),KIJV(:,3),"<<
//    K.rows()<<","<<K.cols()<<");"<<endl;
//#endif
  // Precompute left muliplication by M and right multiplication by G_sum
  SparseMatrix<double> G_sumT = G_sum.transpose();
  SparseMatrix<double> G_sumT_dim_dim;
  repdiag(G_sumT,data.dim*data.dim,G_sumT_dim_dim);
  LbsMatrixType MT = M.transpose();
  // If this is a bottle neck then consider reordering matrix multiplication
  data.M_KG = -4.0 * (MT * (K * G_sumT_dim_dim));
//#ifdef EXTREME_VERBOSE
//  cout<<"data.M_KGIJV=["<<endl;print_ijv(data.M_KG,1);cout<<endl<<"];"<<
//    endl<<"data.M_KG=sparse(data.M_KGIJV(:,1),data.M_KGIJV(:,2),data.M_KGIJV(:,3),"<<
//    data.M_KG.rows()<<","<<data.M_KG.cols()<<");"<<endl;
//#endif

  // Precompute system matrix
  //printf("A()\n");
  SparseMatrix<double> A;
  repdiag(Lapl,data.dim,A);
  data.Q = MT * (A * M);
//#ifdef EXTREME_VERBOSE
//  cout<<"QIJV=["<<endl;print_ijv(data.Q,1);cout<<endl<<"];"<<
//    endl<<"Q=sparse(QIJV(:,1),QIJV(:,2),QIJV(:,3),"<<
//    data.Q.rows()<<","<<data.Q.cols()<<");"<<endl;
//#endif

  // Always do dynamics precomputation so we can hot-switch
  //if(data.with_dynamics)
  //{
    // Build cotangent laplacian
    SparseMatrix<double> Mass;
    //printf("massmatrix()\n");
    massmatrix(V,F,(F.cols()>3?MASSMATRIX_TYPE_BARYCENTRIC:MASSMATRIX_TYPE_VORONOI),Mass);
    //cout<<"MIJV=["<<endl;print_ijv(Mass,1);cout<<endl<<"];"<<
    //  endl<<"M=sparse(MIJV(:,1),MIJV(:,2),MIJV(:,3),"<<
    //  Mass.rows()<<","<<Mass.cols()<<");"<<endl;
    //speye(data.n,Mass);
    SparseMatrix<double> Mass_rep;
    repdiag(Mass,data.dim,Mass_rep);

    // Multiply either side by weights matrix (should be dense)
    data.Mass_tilde = MT * Mass_rep * M;
    MatrixXd ones(data.dim*data.n,data.dim);
    for(int i = 0;i<data.n;i++)
    {
      for(int d = 0;d<data.dim;d++)
      {
        ones(i+d*data.n,d) = 1;
      }
    }
    data.fgrav = MT * (Mass_rep * ones);
    data.fext = MatrixXS::Zero(MT.rows(),1);
    //data.fgrav = MT * (ones);
  //}


  // This may/should be superfluous
  //printf("is_symmetric()\n");
  if(!is_symmetric(data.Q))
  {
    //printf("Fixing symmetry...\n");
    // "Fix" symmetry
    LbsMatrixType QT = data.Q.transpose();
    LbsMatrixType Q_copy = data.Q;
    data.Q = 0.5*(Q_copy+QT);
    // Check that ^^^ this really worked. It doesn't always
    //assert(is_symmetric(*Q));
  }

  //printf("arap_dof_precomputation() succeeded... so far...\n");
  verbose("Number of handles: %i\n", data.m);
  return true;
}