Blending based corner cutting subdivision scheme for nets of curves

Costanza Conti, Nira Dyn

Research output: Contribution to journalArticlepeer-review

Abstract

We present a new subdivision scheme (BCC-algorithm) for constructing a surface from an initial net of 3D curves, by repeated refinements of nets of curves. This algorithm improves a subdivision scheme for nets of curves (BC-algorithm), proposed in a previous paper, which generalizes the well known Chaikin subdivision scheme refining control points. While the BC-algorithm generates continuous surfaces, the BCC-algorithm generates C1 surfaces. This is achieved by a corner cutting step following each refinement step of the BC-algorithm. The analysis of convergence, smoothness and approximation order of the BCC-algorithm is based on its proximity to the tensor-product Chaikin scheme. A short discussion of boundary rules for the BCC-algorithm is also included. Several numerical examples, illustrating the operation of the BCC-algorithm, with and without boundary rules, are presented. In the examples the advantage of the BCC-algorithm over the tensor-product Chaikin algorithm is evident.

Original languageEnglish
Pages (from-to)340-358
Number of pages19
JournalComputer Aided Geometric Design
Volume27
Issue number4
DOIs
StatePublished - May 2010

Keywords

  • Chaikin scheme
  • Coons transfinite interpolation
  • Corner cutting
  • Proximity
  • Subdivision scheme for nets of curves

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