Monotone and convex C-1 Hermite interpolants generated by an adaptive subdivision scheme

Creating interpolants preserving the monotonicity and/or the convexity of a rbitrary data on a bounded interval is a basic problem in CAGD. In order to solve it, we use C-1 interpolants on [0, 1] defined by the subdivision alg orithm introduced by Merrien [3], which depends on two parameters ce and 3. For any system {y(0), y(0)', y(1), (y)1 '} of boundary data at the ends of [0, 1], we show the existence of pairs (alpha, beta), where beta is an ele ment of [- 1, 0] and alpha = beta /4(1-beta), for which the construction of monotone or convex interpolants is always possible and we describe the two corresponding algorithms. (C) 2001 Academie des sciences/Editions scientif iques et medicales Elsevier SAS.