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An interpolating 4-point \(C^2\) ternary stationary subdivision scheme. (English) Zbl 0984.68167

Summary: A novel 4-point ternary interpolatory subdivision scheme with a tension parameter is analyzed. It is shown that for a certain range of the tension parameter the resulting curve is \(C^{2}.\) The role of the tension parameter is demonstrated by a few examples. There is a brief discussion of computational costs.

MSC:

68U05 Computer graphics; computational geometry (digital and algorithmic aspects)
65D05 Numerical interpolation
41A15 Spline approximation
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References:

[1] Deslauriers, G.; Dubuc, S., Symmetric iterative interpolation processes, Constr. Approx., 5, 49-68 (1989) · Zbl 0659.65004
[2] Doo, D.; Sabin, M., Behaviour of recursive division surfaces near extraordinary points, Computer-Aided Design, 10, 356-360 (1978)
[3] Dubuc, S., Interpolation through an iterative scheme, J. Math. Anal. Appl., 114, 185-204 (1986) · Zbl 0615.65005
[4] Dyn, N., Subdivision schemes in computer-aided geometric design, (Light, W., Advances in Numerical Analysis, Vol. 2 (1992), Clarendon Press), 36-104 · Zbl 0760.65012
[5] Dyn, N.; Levin, D.; Gregory, J. A., A 4-point interpolatory subdivision scheme for curve design, Computer Aided Geometric Design, 4, 257-268 (1987) · Zbl 0638.65009
[6] Hassan M.F., Dodgson N.A., 2001. Ternary and 3-point univariate subdivision schemes. University of Cambridge, Computer Laboratory Technical Report No. 520; Hassan M.F., Dodgson N.A., 2001. Ternary and 3-point univariate subdivision schemes. University of Cambridge, Computer Laboratory Technical Report No. 520 · Zbl 1037.65024
[7] Kobbelt, L., \(3\)-Subdivision, SIGGRAPH 00 Conference Proceedings (2000)
[8] Warren J., t.a. Subdivision methods for geometric design. Unpublished manuscript; Warren J., t.a. Subdivision methods for geometric design. Unpublished manuscript
[9] Weissman, A., A 6-point interpolatory subdivision scheme for curve design, M.Sc. Thesis (1990), Tel-Aviv University
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