Parallel searching for 3D-objects

Abstract

The major problem in three-dimensional geometric applications such as the computation of arbitrary polyhedra intersections is the great diversity of possible configurations of geometric objects. Thus, even seemingly straightforward operations often require an enormous number of floating-point computations. This problem can be alleviated by an appropriate preprocessing of the objects involved. For this purpose, we suggest tetrahedronizing geometric objects and organizing the tetrahedra in a topological B ^*- Tree. The topological B^*-Tree can function both as an index and as an object data structure and is thus ideally suited for a wide spectrum of geometric applications. Furthermore, it can easily be used to support parallel algorithms. Parallel search algorithms can only be efficient if the data is very evenly distributed among the available parallel resources. For this purpose, we have developed a geometric hashing method extended by a special control mechanism. Using the topological B^*-Tree to support preprocessing of geometric objects leads to a significant reduction in the number of required floating-point operations and therefore in execution lime.