Mesh Simplification Algorithm Based on the Quadratic Error Metric and Triangle Collapse

Triangular mesh is a commonly used method for representing 3D models. With the continuous development of 3D modeling and scanning technologies, the complexity of the mesh is increasing. The greater the density of the mesh is, the higher the representation quality of the model. However, a higher mesh density also results in greater storage and time costs. Mesh simplification is a basic research topic in the fields of computer graphics and virtual reality. This paper implements a mesh simplification algorithm based on triangle collapse. The algorithm uses a half-edge data structure to record the mesh information, obtains the folding point by minimizing the sum of squares of the spatial distances from the folding point to all adjacent surfaces, and then calculates the folding cost and folding order. The algorithm iteratively folds the triangular faces with the smallest folding costs to achieve mesh simplification. By processing a large number of models, it is proven that the algorithm in this paper can retain the original model features during the simplification process.