**Abstract:** Let $\Delta$ be an arbitrary regular triangulation
of a simply connected compact polygonal domain $\Omega\subset\RR^2$ and
let $S_q^1(\Delta)$ denote the space of bivariate polynomial splines of
degree $q$ and smoothness $1$ with respect to $\Delta$. We develop an algorithm
for constructing point sets admissible for Lagrange interpolation by $S_q^1(\Delta)$
if $q\ge4$. In the case $q=4$ it may be necessary to slightly modify $\Delta$,
but only if exeptional constellations of triangles occur. Hermite interpolation
schemes are obtained as limits of the Lagrange interpolation sets.

**Preprint version available:** pdf

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