Non-Obtuse Remeshing with Centroidal Voronoi Tessellation

Area of Science:

• Computational geometry
• Computer graphics
• Numerical analysis

Background:

• Meshing algorithms are crucial for simulations and visualizations.
• Existing methods often produce poor-quality meshes with acute or obtuse angles.
• Centroidal Voronoi Tesselation (CVT) is a common technique for mesh generation.

Purpose of the Study:

• To develop a novel remeshing algorithm that generates high-quality meshes.
• To specifically avoid triangles with small (acute) and large (obtuse) angles.
• To improve upon the state-of-the-art in mesh generation techniques.

Main Methods:

• The proposed algorithm is an extension of Centroidal Voronoi Tesselation (CVT).
• A penalty term is added to the CVT formulation to penalize short Voronoi edges.
• The CVT term inherently helps in avoiding small angles.

Main Results:

• The novel algorithm successfully avoids generating triangles with acute and obtuse angles.
• Significant improvements in remeshing quality were observed compared to existing methods.
• The enhanced CVT approach leads to better mesh quality.

Conclusions:

• The developed remeshing algorithm offers superior quality by controlling triangle angles.
• This method provides a robust solution for generating high-quality meshes.
• The approach demonstrates potential for various applications requiring accurate mesh generation.