In [G. Nurnberger and Th. Riessinger, numer. Math. 71 (1995), 91-119],
we developed an algorithm for constructing point sets at which unique
Lagrange interpolation by spaces of bivariate splines of arbitrary de
gree and ssmoothness, on uniform type triangulations is possible. Here
, we show that similar Hermite interpolation sets field (nearly) optim
al approximation order. This is shown for differentiable splines of de
gree at least four defined on non-rectangular domains subdivided in un
iform type triangles. Therefore. in practice we use Lagrange configura
tions which are ''close'' to these Hermite configurations. Application
s to data fitting problems and numerical examples are given. (C) 1996
Academic Press, Inc.