Consistent Mesh Partitioning using Tetrahedral Meshes

This thesis presents partitioning techniques which classify a volumetric mesh into difierent regions while preserving the mesh connectivity (consistency). A mesh is partitioned by applying a plane partitioning technique which is geometrically exact, and a novel approach for approximate partitioning where triangular surface meshes are used as partitioning shapes. In both methods, the propagation of intersection points to adjacent faces is performed by using a hash table. The subdivision of the plane partitioning technique relies on existing methods while the shape partitioning algorithm requires an extension of these subdivision methods to identify correct partitions and handle multiple intersection points per edge. Therefore, a subdivision technique is introduced which splits tetrahedra in an iterative way. In order to partition the volumetric mesh after splitting, a strategy is introduced which assigns subdivided and initial tetrahedra to the corresponding region in a robust way. A labeled hierarchical mesh model is used which is able to store consecutive partitioning operation, and to perform an e–cient boundary extraction for visualization. A known problem of subdivision algorithms is the generation of badly shaped tetrahedra due to subdivision. In order to avoid degenerated primitives, several optimization and node snapping techniques are presented. Finally, the problem of °oating point roundofi errors, which can cause inconsistency, is covered in the thesis as well. Index words: partition, consistency, shape partitioning, plane partitioning, tetrahedral mesh, subdivision, mesh optimization, degeneracies, °oating point errors