Delaunay meshes simplification with multi-objective optimisation and fine tuning

Abstract

3D meshes simplification plays an important role in many industrial domains. The two goals of Delaunay mesh simplification are maintaining high geometric fidelity and reducing mesh complexity. However, they are conflicting and cannot solved by gradient. Such limitation prevents existing Delaunay mesh simplification to obtain a small enough number of vertices and promising fidelity at the same time. To address these issues, this paper proposes an evolutionary multi-objective approach for Delaunay mesh simplification. Firstly, the authors replace the previous fixed error-bound threshold by the designed adaptive segment-specific thresholds. Secondly, a constrained simplification is performed through a series of edge collapses that satisfy both Delaunay and error constraints. Next, the non-dominated sorting genetic algorithm II (NSGA-II) is employed to solve the multi-objective problem to search for the optimal trade-off threshold sequences. Finally, a fine-tuning method is designed to further enhance the geometric fidelity of the simplified mesh. Experimental results demonstrate that the authors’ method consistently achieves a satisfactory balance between the approximation error and number of vertices, outperforming existing state-of-the-art methods.