Eigen这个库，早在研究生阶段的时候，就用到烂了，因为三维的图形算法经常要涉及到求解稀疏矩阵。然而工作一年都没碰到Eigen，突然今天要用到求解稀疏矩阵最小二乘方程组，变得有点陌生了，惭愧，因此简单记录一下，以便日后重新复制粘贴修改使用。
#include "Eigen/Sparse"typedef Eigen::SparseMatrix<double> SparseMatrixType;#include <vector>using namespace std;vec CDepthRegression::Get_LightDirection(){vec light;int fn = m_mesh->faces.size();typedef Eigen::Triplet<double> T;std::vector<T> tripletList;//稀疏矩阵的元素for (int i = 0; i < fn;i++){const TriMesh::Face &f = m_mesh->faces[i];vec v0 = m_mesh->vertices[f[0]];vec v1 = m_mesh->vertices[f[1]];vec v2 = m_mesh->vertices[f[2]];vec facenormal = (v2 - v1) CROSS(v0 - v2);facenormal = normalize(facenormal);for (int j = 0; j < 3;j++){tripletList.push_back(T(i,j, facenormal[j]));}}SparseMatrixType Ls(fn, 3);//矩阵的宽高Ls.setFromTriplets(tripletList.begin(), tripletList.end());//从Triplet中构建稀疏矩阵//最小二乘解超静定方程组SparseMatrixType ls_transpose = Ls.transpose();SparseMatrixType LsLs = ls_transpose* Ls;Eigen::VectorXd RHSPos;//超静定方程组右边RHSPos.resize(fn);RHSPos.setZero();for (int i = 0; i < fn;i++){float I = m_mesh->face_color[i];RHSPos[i] = I;}Eigen::SimplicialCholesky<SparseMatrixType>MatricesCholesky(LsLs);Eigen::VectorXd xyzRHS = ls_transpose*RHSPos;Eigen::Vector3d xyz = MatricesCholesky.solve(xyzRHS);return vec(xyz[0],xyz[1], xyz[2]);}
