Optimizing Mesh Simplification: A Newton-Based Approach to Quadratic Error Metrics.

Mesh simplification is an important task in the fields of computer graphics and 3D model processing. However, the traditional quadratic error measurement method may lead to the loss of geometric features, abnormal topological changes, and even unstable results in the simplified model. To solve these problems, this paper proposes an improved quadratic error measurement method based on Newton's method. As an iterative optimization algorithm, Newton's method is known for its fast convergence speed and high accuracy and is particularly suitable for solving problems involving quadratic error metric matrices. This method also fully considers the influence of different simplified vertices on the mesh simplification results. By using the Euclidean distance metric, the simplified vertices with the smallest error from the original vertices are selected, thereby making the details of the simplified model closer to the original model. Experimental results show that the quadratic error measurement method based on Newton's method can more effectively retain the detailed features of the original model at the same simplified scale. What is even more encouraging is that this method performs well when handling model simplifications with different curvature characteristics, while the simplification results are more stable. This provides strong support for further research in the field of 3D model simplification.