Feature-preserving surface mesh smoothing via suboptimal Delaunay triangulation

Area of Science:

• Computer Graphics
• Computational Geometry
• Numerical Analysis

Background:

• Surface meshes are crucial in various fields, but their quality (e.g., angle quality) can degrade.
• Existing methods for mesh smoothing may be computationally expensive or compromise feature preservation.

Purpose of the Study:

• To present a novel method for triangular surface mesh smoothing.
• To improve mesh angle quality and reduce noise while preserving sharp features.

Main Methods:

• Extending optimal Delaunay triangulation (ODT) to surface meshes.
• Solving a quadratic optimization problem to minimize interpolation error.
• Deriving a suboptimal problem for a faster, accurate solution.

Main Results:

• The method significantly improves angle quality of surface meshes.
• It effectively removes noise without losing sharp features like edges and corners.
• The suboptimal approach offers a fast and accurate alternative to the optimal solution.

Conclusions:

• The proposed mesh smoothing technique enhances both quality and feature preservation.
• It provides an efficient and accurate solution for surface mesh processing.
• The method demonstrates strong performance across various experimental tests.