Simplification of Unstructured Tetrahedral Meshes by Point-Sampling

by
Louis Bavoil

Advised by
Claudio Silva

Tetrahedral meshes are widely used in scientific computing for representing three-dimensional scalar, vector, and tensor fields. Their size and complexity limit the performance of many visualization algorithms, making it hard to achieve interactive visualization. The use of simplified models is one way to enable the real-time exploration of these datasets. In this paper, we propose a novel technique for simplifying large unstructured meshes. Most current techniques simplify the geometry of the mesh using edge collapses. Our technique simplifies the underlying scalar field directly by segmenting the original scalar field into two pieces: the boundary of the original domain and the interior samples of the scalar field. We then simplify each piece separately, taking into account proper error bounds. Finally, we combine the simplified domain boundary and scalar field into a complete, simplified mesh that can be visualized with standard unstructured-data visualization tools. Our point-sampling has the advantage of being much faster than edge-collapse-based approaches. Furthermore, it is particularly suitable for aggressive simplification while maintaining high quality renderings. Experiments show that isosurfaces and volume renderings of meshes produced by our technique have few noticeable visual artifacts.