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Algorithmica

, Volume 9, Issue 6, pp 518–533 | Cite as

Computing the intersection-depth of polyhedra

  • David Dobkin
  • John Hershberger
  • David Kirkpatrick
  • Subhash Suri
Article

Abstract

Given two intersecting polyhedraP, Q and a directiond, find the smallest translation ofQ alongd that renders the interiors ofP andQ disjoint. The same problem can also be posed without specifying the direction, in which case the minimum translation over all directions is sought. These are fundamental problems that arise in robotics and computer vision. We develop techniques for implicitly building and searching convolutions and apply them to derive efficient algorithms for these problems.

Key words

Intersection Minkowski sum Plane sweep Ray shooting Polyhedral hierarchy 

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Copyright information

© Springer-Verlag New York Inc 1993

Authors and Affiliations

  • David Dobkin
    • 1
    • 2
  • John Hershberger
    • 3
  • David Kirkpatrick
    • 4
  • Subhash Suri
    • 5
  1. 1.Department of Computer SciencePrinceton UniversityUSA
  2. 2.Bell Communications ResearchMorristownUSA
  3. 3.DEC Systems Research CenterPalo AltoUSA
  4. 4.Department of Computer ScienceUniversity of British ColumbiaVancouverCanada
  5. 5.Bell Communications ResearchMorristownUSA

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