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Approximating CSG trees of moving objects

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Abstract

A discussion of the relationship between two solid representation schemes is presented: CSG trees and recursive spatial subdivision exemplified by the bintree, a generalization of the quadtree and octree. Detailed algorithms are developed and analyzed for evaluating CSG trees by bintree conversion. These techniques are shown to enable the addition of the time dimension and motion to the approximate analysis of CSG trees. This facilitates the solution of problems such as static and dynamic interference detection. A technique for projecting across any dimension is also shown. For “well-behaved” CSG trees the execution time of the conversion algorithm is directly related to the spatial complexity of the object represented by the CSG tree (i.e., as the resolution increases, it is asymptotically proportional to the number of bintree nodes and does not depend on the size or form of the CSG tree representation). The set of well-behaved CSG trees include all trees that define multidimensional polyhedra in a manner that does not give rise to tangential intersections at CSG tree nodes.

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Authors and Affiliations

  1. Computer Science Department, University of Maryland, 20742, College Park, MD, USA

    Hanan Samet & Markku Tamminen

Authors
  1. Hanan Samet
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  2. Markku Tamminen
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Additional information

This is an expanded version of a paper titled “Bintrees, CSG Trees, and Time” which appeared inProceedings of the SIGGRAPH '85 Conference, San Francisco (July 1985), pp. 121–130. This work was supported in part by the National Science Foundation under Grants DCR-83-02118 and IRI-88-02457 and in part by the Finnish Academy

Deceased on August 5, 1989

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Samet, H., Tamminen, M. Approximating CSG trees of moving objects. The Visual Computer 6, 182–209 (1990). https://doi.org/10.1007/BF02341044

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