The refinability of the four point scheme

Authors:
I. P. Ivrissimtzis;N. A. Dodgson;M. F. Hassan;M. A. Sabin
Affiliations:
University of Cambridge, Computer Laboratory, William Gates Building, JJ Thomson Avenue, Cambridge CB3 0FD, UK;University of Cambridge, Computer Laboratory, William Gates Building, JJ Thomson Avenue, Cambridge CB3 0FD, UK;University of Cambridge, Computer Laboratory, William Gates Building, JJ Thomson Avenue, Cambridge CB3 0FD, UK;Numerical Geometry Ltd., 26 Abbey Lane, Lode, Cambridge CB5 9EP, UK
Venue:
Computer Aided Geometric Design
Year:
2002

Citing 3
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Abstract

Let C be the curve constructed using the 4-point scheme on an initial control point set S. We prove that, in general, C is not invariant under any refinement of S except the refinement by one or more steps of the 4-point scheme itself. We outline the proofs of similar results holding for more general interpolatory subdivision schemes.