Interactive volume visualization (i.e., the visualization of scalar data defined on volumetric meshes in real time) is not only difficult to achieve for large meshes but it is also complicated by particular geometric features of volumetric meshes, e.g., non-uniform cells, non-convex boundaries, or visibility cycles.

This thesis addresses several of these geometric features and their unpleasant consequences with respect to direct volume visualization, which is one of the most successful techniques for interactive volume visualization. In order to overcome, or at least alleviate, these difficulties, several new algorithmic solutions are presented: pre-integrated cell projection and hardware-assisted ray casting for non-uniform meshes, edge collapses in non-convex meshes, cell sorting and cell projection for non-convex and cyclic meshes, as well as texture-based pre-integrated volume rendering, topology-guided downsampling, and adaptive volume textures for non-simplicial volumetric meshes (i.e., non-tetrahedral meshes).

As this work cannot cover all geometrically unpleasant features of volumetric meshes, particular emphasis is put on a description of the development of the proposed algorithms. In fact, most of the presented techniques are (or may be interpreted as) generalizations, adaptations, or extensions of existing methods. The intention of explaining these origins is to motivate new solutions for those geometrically unpleasant features of meshes that were out of the scope of this work.