Constrained Remeshing Using Evolutionary Vertex Optimization

Abstract

We propose a simple yet effective method to perform surface remeshing with hard constraints, such as bounding approximation errors and ensuring Delaunay conditions. The remeshing is formulated as a constrained optimization problem, where the variables contain the mesh connectivity and the mesh geometry. To solve it effectively, we adopt traditional local operations, including edge split, edge collapse, edge flip, and vertex relocation, to update the variables. Central to our method is an evolutionary vertex optimization algorithm, which is derivative-free and robust. The feasibility and practicability of our method are demonstrated in two applications, including error-bounded Delaunay mesh simplification and error-bounded angle improvement with a given number of vertices, over many models. Compared to state-of-the-art methods, our method achieves higher remeshing quality.