Adaptive error-bounded simplification of Delaunay meshes with multi-objective optimization

Abstract

Delaunay meshes play a critical role in geometry processing for their favorable geometric and numerical properties. However, Delaunay mesh simplification is rather challenging because of the no-differentiable constraint and the two conflicting goals: high geometric fidelity and low mesh complexity. To simultaneously meet these criteria, this paper addresses the Delaunay mesh simplification from an evolutionary multi-objective viewpoint. First, the adaptive segment-specific thresholds replace the previous unique error-bound threshold. Second, we perform constrained simplification by a sequence of edge collapses with Delaunay and error constraints. Finally, the non-dominated sorting genetic algorithm II (NSGA-II) is introduced to search optimal trade-off threshold sequences. Compared with state-of-the-art methods, our method can consistently achieve a satisfactory balance regarding approximation error and the number of vertices.