Quality Tetrahedral Mesh Smoothing via Boundary-Optimized Delaunay Triangulation

Area of Science:

• Computational geometry
• Mesh generation and processing
• Computer-aided design

Background:

• Optimal Delaunay triangulation (ODT) effectively improves tetrahedral mesh quality.
• ODT's limitation: it only moves inner vertices, failing to address boundary issues.
• Degenerate triangles on boundaries degrade mesh quality and simulation accuracy.

Purpose of the Study:

• To introduce boundary-optimized Delaunay triangulation (B-ODT) for comprehensive tetrahedral mesh smoothing.
• To address the limitations of ODT in handling boundary mesh quality.
• To develop a volume-preserving and feature-preserving mesh optimization technique.

Main Methods:

• Repositioning both inner and boundary vertices using an analytical minimization approach.
• Minimizing the error between a paraboloid function and its piecewise linear interpolation.
• Adapting the algorithm to preserve sharp features present in the original mesh.

Main Results:

• B-ODT successfully smooths tetrahedral meshes by optimizing boundary vertices.
• The method guarantees volume preservation during mesh smoothing.
• The algorithm demonstrates adaptability in preserving sharp geometric features.

Conclusions:

• B-ODT offers an integrated solution for improving tetrahedral mesh quality, including boundaries.
• The proposed method enhances mesh quality while maintaining geometric integrity and volume.
• B-ODT provides a robust approach for tetrahedral mesh optimization in various applications.