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 R 0 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 R o 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
Publication statusPublished - 2009
Event25th Annual Symposium on Computational Geometry, SCG'09 - Aarhus, Denmark
Duration: Jun 8 2009Jun 10 2009

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

  • Computational Mathematics
  • Geometry and Topology
  • Theoretical Computer Science

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) https://doi.org/10.1145/1542362.1542423