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 de Montréal, C.P. 6128 Succursale Centre-ville, Montréal, Québec, Canada H3C 3J7;Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1;INSA de Rennes, 20 av. des Buttes de Coësmes, CS 14315, 35043 Rennes cedex, France;Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1

  • 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 HD^2 and HR^2. 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 HD^2 and HR^2 and we get a lower bound for the Holder smoothness exponent. We generate a C^2 interpolant on any semiregular rectangular mesh with Hermite data of degree 2.