Fast Intersection-Free Remeshing of Triangular Meshes

Area of Science:

• Computer Graphics
• Computational Geometry
• Geometric Modeling

Background:

• Remeshing algorithms are crucial for generating high-quality triangular meshes.
• Intersection detection during remeshing is a major computational bottleneck.
• Existing methods often struggle with efficiency and mesh quality.

Purpose of the Study:

• To develop a fast and robust intersection-free remeshing technique.
• To significantly improve the efficiency of generating non-intersecting triangular meshes.
• To enhance the quality of generated meshes, avoiding issues like sharp edges and banding.

Main Methods:

• An adaptive method identifies structurally complex regions where intersections are likely.
• Intersection checks are performed selectively only within these identified regions.
• A flip-aware extension mechanism constrains local operations to prevent triangle flipping.
• Adaptive iterative size fields and quasi-geometric size field adjustments are used to improve mesh quality and transitions.

Main Results:

• The proposed method is an order of magnitude faster than traditional approaches.
• It consistently generates higher quality non-intersecting meshes compared to state-of-the-art methods.
• Robustness and efficiency were validated on 5,469 models from the Thingi10K dataset.

Conclusions:

• The adaptive, intersection-free remeshing approach offers significant improvements in speed and quality.
• The method effectively addresses key challenges in triangular mesh generation, including intersections and mesh quality.
• This technique provides a robust and efficient solution for generating high-quality, non-intersecting meshes for various applications.