Verified convex hull and distance computation for octree-encoded objects

Authors:
Eva Dyllong;Wolfram Luther
Affiliations:
Institute of Computer Science and Interactive Systems, University of Duisburg-Essen, Germany;Institute of Computer Science and Interactive Systems, University of Duisburg-Essen, Germany
Venue:
Journal of Computational and Applied Mathematics - Special issue: Scientific computing, computer arithmetic, and validated numerics (SCAN 2004)
Year:
2007

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Abstract

This paper discusses algorithms for computing verified convex hull and distance enclosure for objects represented by axis-aligned or unaligned octrees. To find a convex enclosure of an octree, the concept of extreme vertices of boxes on its boundary has been used. The convex hull of all extreme vertices yields an enclosure of the object. Thus, distance algorithms for convex polyhedra to obtain lower bounds for the distance between two octrees can be applied. Since using convex hulls makes it possible to avoid the unwanted wrapping effect that results from repeated decompositions, it also opens a way to dynamic distance algorithms for moving objects.