Curvature continuous corner cutting
Additional information
Authors
Hormann K.,
Mancinelli C.
Type
Journal Article
Year
2024
Language
English
Abstract
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.
Keywords
Subdivision, Corner cutting, Curvature continuity
Journal
Computer aided geometric design
Volume
114
Number ( Month )
102392
Diffusion
License
CC BY
Visibility
Public
Status open access
Hybrid
