VRCC-3D+: Qualitative spatial and temporal reasoning in 3 dimensions

Qualitative Spatial Reasoning (QSR) has varying applications in Geographic Information Systems (GIS), visual programming language semantics, and digital image analysis. Systems for spatial reasoning over a set of objects have evolved in both expressive power and complexity, but implementations or usages of these systems are not common. This is partially due to the computational complexity of the operations required by the reasoner to make informed decisions about its surroundings. These theoretical systems are designed to focus on certain criteria, including efficiency of computation, ease of human comprehension, and expressive power. Sadly, the implementation of these systems is frequently left as an exercise for the reader. Herein, a new QSR system, VRCC-3D+, is proposed that strives to maximize expressive power while minimizing the complexity of reasoning and computational cost of using the system. This system is an evolution of RCC-3D; the system and implementation are constantly being refined to handle the complexities of the reasoning being performed. The refinements contribute to the accuracy, correctness, and speed of the implementation. To improve the accuracy and correctness of the implementation, a way to dynamically change error tolerance in the system to more accurately reflect what the user sees is designed. A method that improves the speed of determining spatial relationships between objects by using composition tables and decision trees is introduced, and improvements to the system itself are recommended; by streamlining the relation set and enforcing strict rules for the precision of the predicates that determine the relationships between objects. A potential use case and prototype implementation is introduced to further motivate the need for implementations of QSR systems, and show that their use is not precluded by computational complexity. --Abstract, page iv

Enhanced Automatic Creation of Multi-Purpose Object Hierarchies

Using well-adapted object hierarchies can support the rendering of large scenes in different ways. For instance, the quality of the lighting simulation may be improved, or the computational cost for rendering may be reduced. However, the meaning of ``well-adapted'' depends heavily on the criterion due to which the hierarchy has been constructed. Different applications typically have different demands like low average intersection cost for a ray tracer or grouping objects with similar material properties or surface orientation for hierarchical radiosity. In this paper we propose a new algorithm for the automatic creation of object hierarchies. The hierarchies are constructed by sequentially inserting all scene objects into the hierarchy created so far. By basing the insertion decision on a cost function defined by the user, the method can be guided to create hierarchies tailored to the desired application. The results can be improved significantly by running a global optimization on the completed hierarchy. During this optimization step we perform a re-grouping of the objects in the hierarchy. Any ill-formed groups that were created during the initial algorithm are subject to being eliminated by our global optimization