An interpolating 4-point C2 ternary non-stationary subdivision scheme with tension control

Authors:
C. Beccari;G. Casciola;L. Romani
Affiliations:
Department of Mathematics, University of Bologna, P.zza di Porta San Donato 5, 40127 Bologna, Italy;Department of Mathematics, University of Bologna, P.zza di Porta San Donato 5, 40127 Bologna, Italy;Department of Mathematics, University of Bologna, P.zza di Porta San Donato 5, 40127 Bologna, Italy
Venue:
Computer Aided Geometric Design
Year:
2007

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Abstract

In this paper we present a non-stationary 4-point ternary interpolatory subdivision scheme which provides the user with a tension parameter that, when increased within its range of definition, can generate C^2-continuous limit curves showing considerable variations of shape. As a generalization we additionally propose a locally-controlled C^2-continuous subdivision scheme, which allows a different tension value to be assigned to every edge of the original control polygon.