Smoothness of Subdivision Surfaces with Boundary

Henning Biermann, Sara Grundel, Denis Zorin

Research output: Contribution to journalArticle

Abstract

Subdivision rules for meshes with boundary are essential for practical applications of subdivision surfaces. These rules have to result in piecewise C<sup>ℓ</sup>-continuous boundary limit curves and ensure C<sup>ℓ</sup>-continuity of the surface itself. Extending the theory of Zorin (Constr Approx 16(3):359–397, 2000), we present in this paper general necessary and sufficient conditions for C<sup>ℓ</sup>-continuity of subdivision schemes for surfaces with boundary, and specialize these to practically applicable sufficient conditions for <sup>C1</sup>-continuity. We use these conditions to show that certain boundary rules for Loop and Catmull–Clark are in fact C<sup>1</sup> continuous.

Original languageEnglish (US)
JournalConstructive Approximation
Volume42
Issue number1
DOIs
StatePublished - Aug 1 2015

Fingerprint

Subdivision Surfaces
Smoothness
Subdivision Scheme
Sufficient Conditions
Subdivision
Mesh
Necessary Conditions
Curve

Keywords

  • Boundary rules
  • C<sup>1</sup>-analysis
  • Catmull–Clark
  • Characteristic maps
  • Loop
  • Subdivision algorithms

ASJC Scopus subject areas

  • Mathematics(all)
  • Analysis
  • Computational Mathematics

Cite this

Smoothness of Subdivision Surfaces with Boundary. / Biermann, Henning; Grundel, Sara; Zorin, Denis.

In: Constructive Approximation, Vol. 42, No. 1, 01.08.2015.

Research output: Contribution to journalArticle

Biermann, Henning ; Grundel, Sara ; Zorin, Denis. / Smoothness of Subdivision Surfaces with Boundary. In: Constructive Approximation. 2015 ; Vol. 42, No. 1.
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