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Parallel Display of Objects Represented by Linear Octrees
January 1995 (vol. 6 no. 1)
pp. 79-85

Abstract—The storage, display, and manipulation of three dimensional volumetrique information requires a 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 overview of the linear octree [6] 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 $2^n\times2^n\times2^n$ universe, the maximum number of voxels that can be processed in parallel is $3^n$, and the maximum number of time steps required to display such an object is $4^n$. 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.

Index Terms—Linear octree, octree, parallel 3-D display, back-to-front projections, volume rendering.

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Djaffer Ibaroudene, Raj Acharya, "Parallel Display of Objects Represented by Linear Octrees," IEEE Transactions on Parallel and Distributed Systems, vol. 6, no. 1, pp. 79-85, Jan. 1995, doi:10.1109/71.363409
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