Error-Bounded and Feature Preserving Surface Remeshing with Minimal Angle Improvement.

Area of Science:

• Computer Graphics
• Computational Geometry
• Geometric Modeling

Background:

• Surface remeshing is crucial for geometry processing, aiming for geometric accuracy, low complexity, and high-quality elements.
• Existing methods often struggle to balance these competing objectives simultaneously.

Purpose of the Study:

• To develop a surface remeshing algorithm that concurrently addresses geometric fidelity, mesh complexity, and element quality.
• To provide a robust framework for generating high-quality meshes within specified error and angle bounds.

Main Methods:

• A novel optimization framework employing prioritized local operators for greedy mesh refinement.
• Incorporation of local approximation error estimation for runtime efficiency.
• Specialized vertex relocation operators for implicit feature preservation.

Main Results:

• The algorithm successfully generates meshes that are geometrically faithful, with bounded approximation error.
• It achieves a desirable balance between mesh complexity and element quality (minimum interior angle).
• Experimental results demonstrate superior performance compared to state-of-the-art methods, especially for reasonable angle bounds.

Conclusions:

• The proposed surface remeshing algorithm offers a significant advancement in geometry processing.
• It effectively produces high-quality, feature-preserving meshes with improved trade-offs between fidelity, complexity, and element quality.
• The method provides a feasible and efficient solution for demanding remeshing applications.