Computer Graphics

University of California - Berkeley

Agressive Tetrahedral Mesh Improvement


We present a tetrahedral mesh improvement schedule that usually creates meshes whose worst tetrahedra have a level of quality substantially better than those produced by any previous method for tetrahedral mesh generation or mesh clean-up. Our goal is to aggressively optimize the worst tetrahedra, with speed a secondary consideration. Mesh optimization methods often get stuck in bad local optima (poor-quality meshes) because their repertoire of mesh transformations is weak. We employ a broader palette of operations than any previous mesh improvement software. Alongside the best traditional topological and smoothing operations, we introduce a topological transformation that inserts a new vertex (sometimes deleting others at the same time). We describe a schedule for applying and composing these operations that rarely gets stuck in a bad optimum. We demonstrate that all three techniques—smoothing, vertex insertion, and traditional transformations—are substantially more effective than any two alone. Our implementation usually improves meshes so that all dihedral angles are between 31o and 149o, or (with a different objective function) between 23o and 136o.


Bryan Matthew Klingner and Jonathan Richard Shewchuk. "Agressive Tetrahedral Mesh Improvement". In Proceedings of the 16th International Meshing Roundtable, pages 3–23, Seattle, Washington, October 2007.

Supplemental Material

Stellar: A Tetrahedral Mesh Improvement Program

Software to improve tetrahedral meshes so that their worst tetrahedra have high quality, making them more suitable for finite element analysis.

Animation of Mesh Improvement

Download Example Meshes