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Durham University

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Publication details for Dr Ioannis Ivrissimtzis

Hassan, Mohamed, Ivrissimtzis, Ioannis, Dodgson, Neil & Sabin, Malcolm (2002). An interpolating 4-point C2 ternary stationary subdivision scheme. Computer Aided Geometric Design 19(1): 1-18.

Author(s) from Durham


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 C2. The role of the tension parameter is demonstrated by a few examples. There is a brief discussion of computational costs.


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 Unpublished manuscript.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