**Abstract:** By using the algorithm of Nürnberger & Riessinger,
we construct Hermite interpolation sets for spaces of bivariate splines
$S_q^r(\Delta^1)$ of arbitrary smoothness defined on the uniform type triangulations.
It is shown that our Hermite interpolation method yields optimal approximation
order for $q \geq 3.5 r +1$. In order to prove this, we use the concept
of weak interpolation and arguments of Birkhoff interpolation.

**Preprint version available:** pdf

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