An Improved Physically-Based Surface Triangulation Method

TL;DR

This paper introduces an improved bubble meshing technique that uses conformal mapping and optimized bubble control to significantly reduce computation time and enhance surface triangulation quality for complex geometries.

Contribution

It presents a novel approach combining conformal mapping with bubble meshing to accelerate convergence and improve mesh quality on complex surfaces.

Findings

Computation time reduced by over 70%.

Supports local size control and curvature adaptation.

Enables efficient triangulation of disk topology surfaces.

Abstract

This paper proposes improvements to the physically-based surface triangulation method, bubble meshing. The method simulates physical bubbles to automatically generate mesh vertices, resulting in high-quality Delaunay triangles. Despite its flexibility in local mesh size control and the advantage of local re-meshing, bubble meshing is constrained by high computational costs and slow convergence on complex surfaces. The proposed approach employs conformal mapping to simplify surface bubble packing by flattening the surface onto a plane. Surface triangulation is induced from the planar mesh, avoiding direct bubble movement on the surface. Optimizing bubble quantity control and separating it from the relaxation process accelerates convergence, cutting computation time by over 70%. The enhanced method enables efficient triangulation of disk topology surfaces, supports local size control, curvature adaptation, and re-meshing of discrete surfaces. Keywords: Adaptive triangulation, Surface remeshing, Bubble meshing, Conformal parameterization, Algorithm efficiency