A Remeshing Method via Adaptive Multiple Original-Facet-Clipping and Centroidal Voronoi Tessellation

2025-05-20

AI Summary

To address the challenge in surface remeshing where Centroidal Voronoi Tessellation (CVT) struggles to balance mesh quality and computational efficiency, this paper proposes a curvature-adaptive multi-round primal patch clipping CVT framework. We innovatively quantify local curvature via normal angle deviation, enabling dynamic control of clipping iterations; within the Voronoi–Delaunay framework, we optimize 3D CVT cells while integrating curvature-aware geometric metrics to jointly enhance triangle regularity and vertex uniformity. Experimental results demonstrate that our method achieves significantly lower angular distortion and higher vertex uniformity compared to state-of-the-art approximations, while accelerating exact CVT computation by several-fold. Notably, it is the first approach to realize concurrent optimization of high mesh quality and high computational efficiency in CVT-based surface remeshing.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures

Abstract

CVT (Centroidal Voronoi Tessellation)-based remeshing optimizes mesh quality by leveraging the Voronoi-Delaunay framework to optimize vertex distribution and produce uniformly distributed vertices with regular triangles. Current CVT-based approaches can be classified into two categories: (1) exact methods (e.g., Geodesic CVT, Restricted Voronoi Diagrams) that ensure high quality but require significant computation; and (2) approximate methods that try to reduce computational complexity yet result in fair quality. To address this trade-off, we propose a CVT-based surface remeshing approach that achieves balanced optimization between quality and efficiency through multiple clipping times of 3D Centroidal Voronoi cells with curvature-adaptive original surface facets. The core idea of the method is that we adaptively adjust the number of clipping times according to local curvature, and use the angular relationship between the normal vectors of neighboring facets to represent the magnitude of local curvature. Experimental results demonstrate the effectiveness of our method.

Problem

• Balances mesh quality and computational efficiency in remeshing
• Uses adaptive clipping based on local curvature for optimization
• Improves vertex distribution via curvature-aware Centroidal Voronoi Tessellation

Innovation

• Adaptive multiple original-facet-clipping for curvature adjustment
• Centroidal Voronoi Tessellation optimizes vertex distribution
• Balances remeshing quality and computational efficiency