Robust Minkowski sums of polyhedra via controlled linear perturbation

Victor Milenkovic, Elisha Sacks, Min Ho Kyung

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Abstract

We present a new approach, called controlled linear perturbation (CLP), to the robustness problem in computational geometry and demonstrate it on Minkowski sums of polyhedra. The robustness problem is how to implement real RAM algorithms accurately and efficiently using computer arithmetic. Large errors can occur when predicates are assigned inconsistent truth values because the computation assigns incorrect signs to the associated polynomials. CLP enforces consistency by performing a small input perturbation, which it computes using differential calculus. CLP enables us to compute Minkowski sums via convex convolution, whereas prior work uses convex decomposition, which has far greater complexity. Our program is fast and accurate even on inputs with many degeneracies.

Original languageEnglish (US)
Title of host publicationProceedings - 14th ACM Symposium on Solid and Physical Modeling, SPM'10
Pages23-30
Number of pages8
DOIs
StatePublished - Oct 25 2010
Event14th ACM Symposium on Solid and Physical Modeling, SPM'10 - Haifa, Israel
Duration: Sep 1 2010Sep 3 2010

Publication series

NameProceedings - 14th ACM Symposium on Solid and Physical Modeling, SPM'10

Other

Other14th ACM Symposium on Solid and Physical Modeling, SPM'10
CountryIsrael
CityHaifa
Period9/1/109/3/10

Keywords

  • Perturbation methods
  • Robust computational geometry

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Algebra and Number Theory
  • Geometry and Topology

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  • Cite this

    Milenkovic, V., Sacks, E., & Kyung, M. H. (2010). Robust Minkowski sums of polyhedra via controlled linear perturbation. In Proceedings - 14th ACM Symposium on Solid and Physical Modeling, SPM'10 (pp. 23-30). (Proceedings - 14th ACM Symposium on Solid and Physical Modeling, SPM'10). https://doi.org/10.1145/1839778.1839782