Adaptive isotopic approximation of nonsingular curves: The parametrizability and nonlocal isotopy approach

Long Lin, Chee Yap

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

Abstract

We consider domain subdivision algorithms for computing isotopic approximations of nonsingular curves represented implicitly by an equation f (X, Y) = 0. Two algorithms in this area are from Snyder (1992) and Plantinga & Veg- ter (2004). We introduce a new algorithm that combines the advantages of these two algorithms: like Snyder, we use the parametrizability criterion for subdivision, and like Plantinga & Vegter we exploit non-local isotopy. We further extend our algorithm in two important and practical directions: first, we allow subdivision cells to be rectangles with arbitrary but bounded aspect ratios. Second, we extend the input domains to be regions R0 with arbitrary geometry and which might not be simply connected. Our algorithm halts as long as the curve has no singularities in the region, and intersects the boundary of Ro transversally. Our algorithm is also easy to implement exactly. We report on very encouraging preliminary experimental results, showing that our algorithms can be much more efficient than both Plantinga & Vegter's and Snyder's algorithms.

Original languageEnglish (US)
Title of host publicationProceedings of the 25th Annual Symposium on Computational Geometry, SCG'09
Pages351-360
Number of pages10
DOIs
StatePublished - Dec 4 2009
Event25th Annual Symposium on Computational Geometry, SCG'09 - Aarhus, Denmark
Duration: Jun 8 2009Jun 10 2009

Publication series

NameProceedings of the Annual Symposium on Computational Geometry

Other

Other25th Annual Symposium on Computational Geometry, SCG'09
CountryDenmark
CityAarhus
Period6/8/096/10/09

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Keywords

  • Curve approximation
  • Exact numerical algorithms
  • Isotopy
  • Meshing
  • Parametrizability
  • Subdivision algorithms
  • Topological correctness

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Computational Mathematics

Cite this

Lin, L., & Yap, C. (2009). Adaptive isotopic approximation of nonsingular curves: The parametrizability and nonlocal isotopy approach. In Proceedings of the 25th Annual Symposium on Computational Geometry, SCG'09 (pp. 351-360). (Proceedings of the Annual Symposium on Computational Geometry). https://doi.org/10.1145/1542362.1542423