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 -continuity. A family of interpolating 4-point ternary subdivision schemes is shown to exist and have -continuity. An approximating 3-point ternary scheme has been found and shown to have continuity. An approximating 3-point binary scheme is derived and shown to have continuity. The generating function formalism is used to analyze the continuity properties of these schemes. These are compared with the established schemes.
|65D18||Computer graphics, image analysis, and computational geometry|