Parallel display of objects represented by linear octrees

The storage, display, and manipulation of three dimensional volumetric information requires large amounts of computing resources, both in terms of memory, and processing power. Most existing serial algorithms that display 3-D objects on a 2-D screen are found to be too slow to process the large amounts of volume data in a reasonable time. Hence, one way to increase the performance of the display algorithm is to process individual volume elements (voxels) in parallel. The first part of this paper presents a brief over view of the linear octree data structure which represents 3-D objects by an eight-way branching tree, while the second part focusses on the parallel display of such objects. We have shown that, for an object represented by a linear octree and enclosed in a 2ⁿ×2ⁿ×2ⁿ universe, the maximum number of voxels that can be processed in parallel is 3ⁿ, and the maximum number of time steps required to display such an object is 4ⁿ. This paper presents a set of formulae which identify the processing element (PE) as well as the time step in which a given linear octree node is processed. Similarly, a procedure which determines the locational code of a linear octree node which must be processed by a given PE, at some specific time step, is presented, along with a strategy for determining whether a PE is active or idle