openmesh 用矩阵法映射到圆盘

#include<iostream>  #include <OpenMesh\Core\IO\MeshIO.hh>  #include <OpenMesh\Core\Mesh\TriMesh_ArrayKernelT.hh>  #include <OpenMesh\Core\Utils\Property.hh>#include <Eigen/Dense>    #include <Eigen/Sparse>#include <map>struct MyTraits : public OpenMesh::DefaultTraits{VertexTraits{int some_additional_index;};};typedef OpenMesh::TriMesh_ArrayKernelT<MyTraits> MyMesh;using namespace std;using namespace Eigen;const double inf = 0.0000001;bool judge(float xx, float yy){//cout << xx - yy << endl;   if ((xx - yy) > -1 * inf && (xx - yy) < inf)return true;return false;}double get_cot(MyMesh::Point t1, MyMesh::Point t2){double p1 = t1.data()[0];double p2 = t1.data()[1];double p3 = t2.data()[0];double p4 = t2.data()[1];double f1 = (p1*p3 + p2*p4);double len_a = powf(t1.data()[0], 2) + powf(t1.data()[1], 2);double len_b = powf(t2.data()[0], 2) + powf(t2.data()[1], 2);double COS = f1 / sqrtf(len_a*len_b);double SIN=sqrtf(1.0-COS*COS);return COS / SIN;}bool solve_eigen(Eigen::SparseMatrix<double>&A, VectorXd&b, VectorXd&x){Eigen::SimplicialLDLT<Eigen::SparseMatrix<double>> solver;solver.compute(A);if (solver.info() != Success){ return false; }x = solver.solve(b);return solver.info() == Success;}int main(){MyMesh mesh;MyMesh mymesh;//mesh.request_vertex_texcoords2D();  if (!OpenMesh::IO::read_mesh(mesh, "meshes/alex.off")){cerr << "can't open the file." << endl;exit(1);}vector<MyMesh::HalfedgeHandle>h_handle;vector<MyMesh::VertexHandle>v_handle;vector<MyMesh::VertexHandle>v_in_handle;map<MyMesh::VertexHandle, int>V_Map;OpenMesh::VPropHandleT<bool>VH_Bool;OpenMesh::VPropHandleT<double>VH_Double;OpenMesh::VPropHandleT<MyMesh::TexCoord2D>VH_TC;OpenMesh::HPropHandleT<bool>HE_bool;//OpenMesh::HPropHandleT<double>mesh.add_property(VH_Bool, "VH_Bool");mesh.add_property(VH_Double, "VH_Double");mesh.add_property(HE_bool, "HE_bool");V_Map.clear();float PAI = acosf(-1.0);float r = 1.0;MyMesh::VertexHandle temp_vh_it;MyMesh::VertexHandle temp_mark;//int dd = 0;  for (MyMesh::VertexIter vh_it = mesh.vertices_begin(); vh_it != mesh.vertices_end(); ++vh_it){if (mesh.is_boundary(*vh_it)){temp_vh_it = *vh_it;break;}}//cout << temp_vh_it.idx() << endl;  //cout << "111111" << endl;  int uu = 0;int break_ll = 0;temp_mark = temp_vh_it;while (1){//if (break_ll == 1)break;  for (MyMesh::VertexOHalfedgeCWIter VOH_it = mesh.voh_cwbegin(temp_vh_it); VOH_it != mesh.voh_cwend(temp_vh_it); ++VOH_it){if (mesh.is_boundary(*VOH_it)){MyMesh::VertexHandle temp_in_v = mesh.to_vertex_handle(*VOH_it);if (mesh.property(VH_Bool, temp_in_v)){ break_ll = 1; break; }h_handle.push_back(*VOH_it);//v_handle.push_back(temp_in_v);temp_vh_it = temp_in_v;mesh.property(VH_Bool, temp_in_v) = true;mesh.property(VH_Bool).set_persistent(true);//uu++;  //cout << uu << endl;  //cout << temp_mark.idx() << " " << temp_vh_it.idx() << endl;  break;}}if (temp_mark == temp_vh_it)break;//cout <<"IDX = "<<temp_vh_it.idx() << endl;  //if (uu == 466)break;  }cout << "222222" << endl;  float sum = 0.0;float temp_sum = 0.0;for (auto it = h_handle.begin(); it != h_handle.end(); it++){MyMesh::VertexHandle VH_it_to = mesh.to_vertex_handle(*it);MyMesh::VertexHandle VH_it_from = mesh.from_vertex_handle(*it);MyMesh::Point P_it_to = mesh.point(VH_it_to);MyMesh::Point P_it_from = mesh.point(VH_it_from);temp_sum = powf(P_it_from.data()[0] - P_it_to.data()[0], 2.0) + powf(P_it_from.data()[1] - P_it_to.data()[1], 2.0) + powf(P_it_from.data()[2] - P_it_to.data()[2], 2.0);temp_sum = sqrt(temp_sum);sum += temp_sum;mesh.property(VH_Double, VH_it_to) = sum;}cout << "333333" << endl;  mesh.request_vertex_texcoords2D();MyMesh::TexCoord2D;for (auto it = mesh.vertices_begin(); it != mesh.vertices_end(); it++){if (mesh.is_boundary(mesh.halfedge_handle(*it))){float arf = (mesh.property(VH_Double, *it)*PAI * 2 / sum);float point_x = cosf(arf)*r;float point_y = sinf(arf)*r;mesh.set_texcoord2D(*it, OpenMesh::Vec2f(point_x, point_y));}else{v_in_handle.push_back(*it);V_Map[*it] = v_in_handle.size() - 1;mesh.set_texcoord2D(*it, OpenMesh::Vec2f(0.0, 0.0));}//cout << (*it).idx() << endl;  }int pp = 0;cout << "Begin computing!!!!" << endl;  int in_size = v_in_handle.size();cout << "In_Point = " << in_size << endl;vector<Eigen::Triplet<double>>A_coefficient;Eigen::SparseMatrix<double> A(in_size, in_size);Eigen::VectorXd U(in_size);Eigen::VectorXd V(in_size);for (int ii = 0; ii < v_in_handle.size(); ii++){MyMesh::VertexHandle temp_v = v_in_handle[ii];double Kij = 0.0;double Kij_U = 0.0;double Kij_V = 0.0;for (auto it = mesh.voh_ccwbegin(temp_v); it != mesh.voh_ccwend(temp_v); it++){                                                 //out in ?//MyMesh::HalfedgeHandle temp_he_handle = mesh.halfedge_handle(*it, 0);MyMesh::HalfedgeHandle temp_he_op_handle = mesh.opposite_halfedge_handle(*it);MyMesh::HalfedgeHandle temp_he_handle_next = mesh.next_halfedge_handle(*it);MyMesh::HalfedgeHandle temp_he_op_handle_next = mesh.next_halfedge_handle(temp_he_op_handle);MyMesh::VertexHandle temp_is_to = mesh.to_vertex_handle(*it);MyMesh::VertexHandle temp_is_from = mesh.from_vertex_handle(*it);MyMesh::VertexHandle temp_is_third = mesh.to_vertex_handle(temp_he_handle_next);MyMesh::VertexHandle temp_is_op_to = mesh.to_vertex_handle(temp_he_op_handle);MyMesh::VertexHandle temp_is_op_from = mesh.from_vertex_handle(temp_he_op_handle);MyMesh::VertexHandle temp_is_op_third = mesh.to_vertex_handle(temp_he_op_handle_next);MyMesh::Point temp1_point = mesh.point(temp_is_to) - mesh.point(temp_is_third);MyMesh::Point temp2_point = mesh.point(temp_is_from) - mesh.point(temp_is_third);double cot1 = get_cot(temp1_point, temp2_point);MyMesh::Point temp1_op_point = mesh.point(temp_is_op_to) - mesh.point(temp_is_op_third);MyMesh::Point temp2_op_point = mesh.point(temp_is_op_from) - mesh.point(temp_is_op_third);double cot2 = get_cot(temp1_op_point, temp2_op_point);double temp_Kij = (cot1 + cot2)/2 ;Kij -= temp_Kij;if (mesh.is_boundary(mesh.to_vertex_handle(*it))){Kij_U -= temp_Kij*mesh.texcoord2D(mesh.to_vertex_handle(*it)).data()[0];Kij_V -= temp_Kij*mesh.texcoord2D(mesh.to_vertex_handle(*it)).data()[1];}else{A_coefficient.push_back(Eigen::Triplet<double>(ii, V_Map[mesh.to_vertex_handle(*it)], temp_Kij));}}U(ii) = Kij_U;V(ii) = Kij_V;A_coefficient.push_back(Eigen::Triplet<double>(ii, ii, Kij));}A.setFromTriplets(A_coefficient.begin(), A_coefficient.end());Eigen::VectorXd x(in_size);Eigen::VectorXd y(in_size);solve_eigen(A,U,x);solve_eigen(A,V,y);for (int ii = 0; ii < x.size(); ii++){mesh.set_texcoord2D(v_in_handle[ii],OpenMesh::Vec2f(x[ii],y[ii]));}/*while (1){int mark_break = 0;pp = 0;for (auto it = mesh.vertices_begin(); it != mesh.vertices_end(); it++){if (mesh.is_boundary(*it))continue;else {float xx_sum = 0.0;float yy_sum = 0.0;float xx_pre = 0.0;float yy_pre = 0.0;float num = 0.0;for (auto v_it = mesh.vv_begin(*it); v_it != mesh.vv_end(*it); v_it++){float xx = mesh.texcoord2D(*v_it).data()[0];float yy = mesh.texcoord2D(*v_it).data()[1];xx_sum += xx;yy_sum += yy;num++;}if (judge(num, 0.0))continue;xx_pre = mesh.texcoord2D(*it).data()[0];yy_pre = mesh.texcoord2D(*it).data()[1];yy_sum /= num;xx_sum /= num;float f_sum = (xx_pre - xx_sum)*(xx_pre - xx_sum) + (yy_pre - yy_sum)*(yy_pre - yy_sum);f_sum = sqrtf(f_sum);if (!judge(f_sum, 0.0)){ mark_break = 1; pp++; }mesh.set_texcoord2D(*it, OpenMesh::Vec2f(xx_sum, yy_sum));}}if (!mark_break)break;//if (pp%1000==0)  //cout << pp << endl;  //if (pp <= 63000)cout << pp << endl;  }*/cout << "Output Answer!!!!" << endl;mesh.property(VH_Bool).set_persistent(true);mesh.property(VH_Double).set_persistent(true);//mesh.release_vertex_texcoords2D();  OpenMesh::IO::Options opt = OpenMesh::IO::Options::VertexTexCoord;if (!OpenMesh::IO::write_mesh(mesh, "gg.off", opt)){cerr << "Can't write the mesh." << endl;cin.get();}cout << "YOU GET THE ANSWER!!!!" << endl;cin.get();return 0;}