Monotone and Convex C ¹ Hermite Interpolants Generated by a Subdivision Scheme

Abstract. We propose C¹ Hermite interpolants generated by the general subdivision scheme introduced by Merrien [17] and satisfying monotonicity or convexity constraints. For arbitrary values and slopes of a given function f at the end-points of a bounded interval, which are compatible with the contraints, the given algorithms construct shape-preserving interpolants. Moreover, these algorithms are quite simple and fast as well as adapted to CAGD. We also give error estimates in the case of interpolation of smooth functions.

Authors and Affiliations

1. INSA de Rennes 20 av. des Buttes de Coësmes, CS 14315 35043 Rennes Cedex France jean-louis.merrien@insa-rennes.fr, FR

   Merrien

2. INSA de Rennes 20 av. des Buttes de Coësmes, CS 14315 35043 Rennes Cedex France paul.sablonniere@insa-rennes.fr, FR

   Sablonnière

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