TetFusion: an algorithm for rapid tetrahedral mesh simplification

This paper introduces an algorithm for rapid progressive simplification of tetrahedral meshes: TetFusion. We describe how a simple geometry decimation operation steers a rapid and controlled progressive simplification of tetrahedral meshes, while also taking care of complex mesh-inconsistency problems. The algorithm features a high decimation ratio per step, and inherently discourages any cases of self-intersection of boundary, element-boundary intersection at concave boundary-regions, and negative volume tetrahedra (flipping). We achieved rigorous reduction ratios of up to 98% for meshes consisting of 827,904 elements in less than 2 minutes, progressing through a series of level-of-details (LoDs) of the mesh in a controlled manner. We describe how the approach supports a balanced re-distribution of space between tetrahedral elements, and explain some useful control parameters that make it faster and more intuitive than 'edge collapse'-based decimation methods for volumetric meshes. Finally, we discuss how this approach can be employed for rapid LoD prototyping of large time-varying datasets as an aid to interactive visualization.