Chapter 5 - Improvement For Line and Plane Fitting

[RicoJia]

"我们使用快速的 SVD 分解，仅计算 A 矩阵 SVD 结果的最后一列。"....

This is used in both line and plane fitting. For example, the code is here

Eigen::JacobiSVD svd(A, Eigen::ComputeThinV);
plane_coeffs = svd.matrixV().col(3);

On my machine, it turns out that Eigen::SelfAdjointEigenSolver is 2x faster, possibly because it only operates on an nxn symmetric matrices, whereas SVD works on mxn general matrices:

  Eigen::MatrixXf ATA = A.transpose() * A;   // Compute A^T A

  Eigen::SelfAdjointEigenSolver<Eigen::MatrixXf> solver(ATA);   // Efficient for symmetric matrices

  if (solver.info() != Eigen::Success) {
      throw std::runtime_error("Eigen decomposition failed!");
  }

  return {solver.eigenvalues(), solver.eigenvectors()};

I understand that it's the method that the book uses, so I'm happy to leave this as a comment instead of a PR. Well, please feel free to close if this makes sense 😊 @gaoxiang12