Point-based Tetrahedral Mesh Simplification with Intersection-Free Surface Mesh Simplification

Simplification of tetrahedral meshes is an important tool to decrease the complexity of these datasets. Many visualization systems need the simplified version of a mesh to be fully interactive. This paper presents a rapid tetrahedral simplifier that works in three steps. First, the border of the tetrahedral mesh is simplified. Second, the interior of the mesh is point sampled such that the resulting point cloud contains the most important points. Third, the point cloud is tetrahedralized and constrained to the simplified border. Such a sequence of global operations exceeds the limitations of a sequence of local operations like edge collapses. The point sampling is steered by both a field and a space error such that direct volume renderings as well as isosurfaces are well approximated. For the border simplification, we present a triangle mesh simplifier that ensures an intersectionfree border after is has finished. It can be easily integrated into existing triangle mesh simplification software that is based on edge collapses or vertex contraction. We construct a hierarchy of bounding boxes which is used at simplification time to early reject intersection tests.