The paper presents an algorithm for optimizing triangular meshes to fit a set of 3D data points while maintaining the same topological type. The goal is to produce a mesh with fewer vertices that closely represents the data. The optimization is achieved by minimizing an energy function that balances geometric fit and vertex reduction. The energy function consists of three components: distance energy, representation energy, and a spring energy term. The algorithm involves an inner continuous minimization over vertex positions and an outer discrete minimization over simplicial complexes. The method is effective for surface reconstruction from unorganized points and mesh simplification, producing meshes with well-shaped features and reduced complexity. The paper also discusses related work and future research directions, including the use of more advanced optimization techniques to improve convergence and avoid local minima.The paper presents an algorithm for optimizing triangular meshes to fit a set of 3D data points while maintaining the same topological type. The goal is to produce a mesh with fewer vertices that closely represents the data. The optimization is achieved by minimizing an energy function that balances geometric fit and vertex reduction. The energy function consists of three components: distance energy, representation energy, and a spring energy term. The algorithm involves an inner continuous minimization over vertex positions and an outer discrete minimization over simplicial complexes. The method is effective for surface reconstruction from unorganized points and mesh simplification, producing meshes with well-shaped features and reduced complexity. The paper also discusses related work and future research directions, including the use of more advanced optimization techniques to improve convergence and avoid local minima.