C1 analysis of some 2D subdivision schemes refining point-normal pairs with the circle average

This article continues the investigation started in Lipovetsky and Dyn (2016) on subdivision schemes refining 2D point-normal pairs, obtained by modifying linear subdivision schemes using the circle average. While in Lipovetsky and Dyn (2016) the convergence of the Modified Lane–Riesenfeld algorithm...

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Bibliographic Details
Published in:Computer aided geometric design 2019-02, Vol.69, p.45-54
Main Authors: Lipovetsky, Evgeny, Dyn, Nira
Format: Article
Language:English
Subjects:
2D curve design
Circle average
Modified 4-Point scheme
Modified Lane–Riesenfeld algorithm
Smoothness analysis by proximity
Subdivision of 2D point-normal pairs
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Summary:This article continues the investigation started in Lipovetsky and Dyn (2016) on subdivision schemes refining 2D point-normal pairs, obtained by modifying linear subdivision schemes using the circle average. While in Lipovetsky and Dyn (2016) the convergence of the Modified Lane–Riesenfeld algorithm and the Modified 4-Point schemes is proved, here we show that the curves generated by these two schemes are C1. •Further investigations of subdivision schemes refining point-normal pairs based on the circle average.•Deriving more properties of the circle average.•Showing C1 smoothness of two modified schemes with the circle average.•Conjecturing C1 smoothness for a wider class of modified subdivision schemes.
ISSN:0167-8396
1879-2332
DOI:10.1016/j.cagd.2019.01.001