Abstract
We show how (now familiar) hierarchical representations of (convex) polyhedra can be used to answer various separation queries efficiently (in a number of cases, optimally). Our emphasis is i) the uniform treatment of polyhedra separation problems, ii) the use of hierarchical representations of primitive objects to provide implicit representations of composite or transformed objects, and iii) applications to natural problems in graphics and robotics.
Among the specific results is an O(log|P|·log|Q|) algorithm for determining the separation of polyhedra P and Q (which have been individually preprocessed in at most linear time).
Supported in part by NSF Grant Number CCR87-00917 and a Guggenheim Fellowship.
Supported in part by Natural Sciences and Engineering Research Council Grant A3583 and a BCASI Fellowship.
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© 1990 Springer-Verlag Berlin Heidelberg
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Dobkin, D.P., Kirkpatrick, D.G. (1990). Determining the separation of preprocessed polyhedra — A unified approach. In: Paterson, M.S. (eds) Automata, Languages and Programming. ICALP 1990. Lecture Notes in Computer Science, vol 443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032047
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DOI: https://doi.org/10.1007/BFb0032047
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