Octree optimization

摘要

Abstract: A number of algorithms search large 3D arrays (computation space) for features of interest. Marching cubes isosurface generation described by Lorenson and Cline is an example. The speed of these algorithms is dependent on the time necessary to find the features of interest in the data and to compute their graphic representation. Efficiently searching for these features is the topic of this paper. The author describes an optimizing search using octrees to divide computation space. When the tree is walked, information stored in the branch nodes is used to prune portions of computation space thus avoiding unnecessary memory references and tests for features of interest. This technique was implemented for marching cubes isosurface generation on computational fluid dynamics data. The code was then adapted to continuing particle traces in multiple-zoned data sets when a trace leaves one zone and enters another. For multiple isosurfaces, numerical experiments indicate a factor of 3.8 - 9.0 overall performance increase, measured by stopwatch; and a factor of 3.9 - 9.9 speedup in calculation times as measured by the UNIX times approximately icron$+2$/ utility. The overhead is a one-time cost of 0.2 - 2.8 times the time to compute an average isosurface and O(n) space with a constant factor less than one, where 'n' is the number of grid points.!