openmesh 用矩陣法映射到圓盤

#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;
}