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Abstract: Dyadic C2 Hermite interpolation on a square mesh

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Serge Dubuc, Bin Han, Jean-Louis Merrien and Qun Mo

## 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 H\"{o}lder smoothness exponent. We generate a $C^2$
interpolant on any semiregular rectangular mesh with Hermite data
of degree 2.

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