Hierarchical meshes for volume data

An algorithm for adaptive refinement of 3D meshes is presented. This algorithm can be applied for the generation of mesh hierarchies used for efficient volume visualization algorithms, e.g. iso-surface extraction or direct volume rendering, as well as for multilevel finite element computations. The aim was to construct an algorithm which generates as few congruence classes as possible. The main idea is to work with consistent partitions of the domain into tetrahedra and octahedra. The refinement consists of regular refinement rules which produce per element type one congruence class. In the case of local mesh refinement, for generating consistent subdivisions a temporary (virtual) closure is done based on suitable irregular refinement rules.