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Zbl 1037.65024
Hassan, M. F.; Dodgson, N. A.
Ternary and three-point univariate subdivision schemes. (English)
[A] Cohen, Albert (ed.) et al., Curve und surface fitting, Saint-Malo 2002. Fifth international conference on curves and surfaces, Saint-Malo, France, June 27 -- July 3, 2002. Brentwood, TN: Nashboro Press. Modern Methods in Mathematics, 199-208 (2003). ISBN 0-9728482-1-5/hbk

Summary: A family of interpolating 3-point ternary subdivision schemes is shown to exist and have $C^1$-continuity. A family of interpolating 4-point ternary subdivision schemes is shown to exist and have $C^2$-continuity. An approximating 3-point ternary scheme has been found and shown to have $C^2$ continuity. An approximating 3-point binary scheme is derived and shown to have $C^3$ continuity. The generating function formalism is used to analyze the continuity properties of these schemes. These are compared with the established schemes.

MSC 2000:: *65D18 Computer graphics and computational geometry

Keywords: $C^1$-continuity; $C^2$ continuity; subdivision schemes; ternary scheme; binary scheme; generating function

Cited in: Zbl 1235.65011 Zbl 1205.65107 Zbl 1116.65019

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