Complete subdivision algorithms, I: Intersection of Bezier curves

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

Abstract

We give the first complete subdivision algorithm for the intersection of two Bezier curves F, G, possibly with tangential intersections. Our approach to robust subdivision algorithms is based on geometric separation bounds, and using a criterion for detecting non-crossing intersection of curves. Our algorithm is adaptive, being based only on exact bigfloat computations. In particular, we avoid manipulation of algebraic numbers and resultant computations. It is designed to be competitive with current algorithms on "nice" inputs. All standard algorithms assume F, G to be relatively prime - our algorithm needs a generalization of this.

Original languageEnglish (US)
Title of host publicationProceedings of the Twenty-Second Annual Symposium on Computational Geometry 2006, SCG'06
Pages217-226
Number of pages10
StatePublished - Sep 4 2006
Event22nd Annual Symposium on Computational Geometry 2006, SCG'06 - Sedona, AZ, United States
Duration: Jun 5 2006Jun 7 2006

Publication series

NameProceedings of the Annual Symposium on Computational Geometry
Volume2006

Other

Other22nd Annual Symposium on Computational Geometry 2006, SCG'06
CountryUnited States
CitySedona, AZ
Period6/5/066/7/06

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Keywords

  • Bezier curves
  • Computational geometry
  • Curve intersection
  • Exact geometric computation
  • Robust numerical algorithms
  • Subdivision method

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics

Cite this

Yap, C. K. (2006). Complete subdivision algorithms, I: Intersection of Bezier curves. In Proceedings of the Twenty-Second Annual Symposium on Computational Geometry 2006, SCG'06 (pp. 217-226). (Proceedings of the Annual Symposium on Computational Geometry; Vol. 2006).