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Ternary and three-point univariate subdivision schemes. (English) Zbl 1037.65024
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 (ISBN 0-9728482-1-5/hbk). Modern Methods in Mathematics, 199-208 (2003).
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:
65D18Computer graphics, image analysis, and computational geometry