An Improved Physically-Based Surface Triangulation Method

2025-08-07

AI Summary

To address the high computational cost and slow convergence of bubble meshing on complex curved surfaces, this paper proposes an efficient triangulation method integrating conformal mapping with bubble dynamics. The method first flattens the surface onto the plane via conformal parameterization, optimizes bubble arrangement and generates a Delaunay mesh in the planar domain, then maps the result back to the original surface. Crucially, it decouples bubble count optimization from geometric relaxation, enabling significant acceleration. The approach naturally supports local size control, curvature-adaptive refinement, and dynamic remeshing. Experimental results demonstrate over 70% reduction in computation time, substantially improving both efficiency and mesh quality for disk-topology surfaces. This advancement extends the applicability of bubble meshing to complex geometry modeling and simulation preprocessing tasks.

Technology Category

• Machine Learning: Learning with Manifolds
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

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

Problem

• Improving bubble meshing for faster surface triangulation
• Reducing computational costs in complex surface triangulation
• Enhancing local size control and curvature adaptation

Innovation

• Uses conformal mapping to flatten surfaces
• Optimizes bubble control for faster convergence
• Separates relaxation to reduce computation time