Linear subdivision schemes for the refinement of geometric objects

Nira Dyn*

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review

5 Scopus citations

Abstract

Subdivision schemes are efficient computational methods for the design, representation and approximation of surfaces of arbitrary topology in ℝ3. Subdivision schemes generate curves/surfaces from discrete data by repeated refinements. This paper reviews some of the theory of linear stationary subdivision schemes and their applications in geometric modelling. The first part is concerned with "classical" schemes refining control points. The second part reviews linear subdivision schemes refining other objects, such as vectors of Hermite-type data, compact sets in ℝn and nets of curves in ℝ3. Examples of various schemes are presented.

Original languageEnglish
Pages1201-1226
Number of pages26
StatePublished - 2006
Event25th International Congress of Mathematicians, ICM 2006 - Madrid, Spain
Duration: 22 Aug 200630 Aug 2006

Conference

Conference25th International Congress of Mathematicians, ICM 2006
Country/TerritorySpain
CityMadrid
Period22/08/0630/08/06

Keywords

  • Approximation order
  • Arbitrary topology
  • Compact sets
  • Curves
  • Geometric modelling
  • Nets of curves
  • Nets of points
  • Refinements
  • Smoothness
  • Subdivision schemes
  • Surfaces

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