Curvature continuous corner cutting

Subdivision schemes are used to generate smooth curves by iteratively refining an initial control polygon. The simplest such schemes are corner cutting schemes, which specify two distinct points on each edge of the current polygon and connect them to get the refined polygon, thus cutting off the cor...

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Bibliographic Details
Published in:Computer aided geometric design 2024-11, Vol.114, p.102392, Article 102392
Main Authors: Hormann, Kai, Mancinelli, Claudio
Format: Article
Language:English
Subjects:
Corner cutting
Curvature continuity
Subdivision
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Summary:Subdivision schemes are used to generate smooth curves by iteratively refining an initial control polygon. The simplest such schemes are corner cutting schemes, which specify two distinct points on each edge of the current polygon and connect them to get the refined polygon, thus cutting off the corners of the current polygon. While de Boor (1987) shows that this process always converges to a Lipschitz continuous limit curve, no matter how the points on each edge are chosen, Gregory and Qu (1996) discover that the limit curve is continuously differentiable under certain constraints. We extend these results and show that the limit curve can even be curvature continuous for specific sequences of cut ratios. •Proof that non-uniform corner cutting schemes can generate curvature continuous limit curves.•Corner cutting rules for generating cubic B-splines as limit curves.•Corner cutting rules for generating cubic non-uniform γ-B-splines as limit curves.•Corner cutting rules for generating cubic non-uniform rational γ-B-splines as limit curves.
ISSN:0167-8396
DOI:10.1016/j.cagd.2024.102392