Dyadic C2 Hermite interpolation on a square mesh

Authors:
Serge Dubuc;Bin Han;Jean-Louis Merrien;Qun Mo
Affiliations:
Département de mathématiques et de statistique, Université Montréal, Montréal, Québec, Canada;Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada;INSA de Rennes, Rennes cedex, France;Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada
Venue:
Computer Aided Geometric Design
Year:
2005

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Abstract

For prescribed values of a function and its partial derivatives of orders 1 and 2 at the vertices of a square, we fit an interpolating surface. We investigate two families of solutions provided by two Hermite subdivision schemes, denoted H D2 and H R2. Both schemes depend on 2 matrix parameters, a square matrix of order 2 and a square matrix of order 3. We exhibit the masks of both schemes. We compute the Sobolev smoothness exponent of the general solution of the Hermite problem for the most interesting schemes H D2 and H R2 and we get a lower bound for the Hölder smoothness exponent. We generate a C2 interpolant on any semiregular rectangular mesh with Hermite data of degree 2.