Parallel Manipulations of Octrees and Quadtrees

Octrees offer a powerful means for representing and manipulating 3-D objects. This paper presents an implementation of octree manipulations using a new approach on a shared memory architecture. Octrees are hierarchical data structures used to model 3-D objects. The manipulation of these data structures involves performing independent computations on each node of the octree. Octrees are much easier to deal with than other forms of representations used to model 3-D objects especially where extensive manipulations are involved. When these operations are distributed among multiple processing elements (PEs) and executed simultaneously, a significant speedup may be achieved. Manipulations such as a complement, a union, an intersection and other operations such as finding the volume and centroid which this paper describes are implemented on the Sequent Balance multiprocessor. In this approach the PEs are allocated dynamically, resulting in a uniform load balancing among them. The experimental results presented illustrate the feasibility of the approach. Although this evaluation has been originally done for shared memory machines, it will provide insight for the evaluation on other architectures.