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Octree Representation of Objects in Arbitrary Motion J. Weng and N. Ahuja An algorithm is presented that updates the octree of a three-dimensional object after the object has undergone arbitrary rotation and translation. The algorithm moves each of the black leaves and then adds the subtree corresponding to the displaced black leaf. It uses a computationally efficient method to detect the intersections of moved blocks with octree tessellation. On the average, the space and time complexities of the algorithm are both bounded by O(Kn), where K is the number of nodes in the source tree and n is the logarithm of the side length of the universe space. The quantization errors are prevented from accumulating by the maintenance of a compact source octree. Each incremental displacement is performed with respect to the source tree. Full Text: NA |