O. Davydov and G. Nürnberger, Interpolation by \$C^1\$ splines of degree \$q\ge4\$ on triangulations, J. Comput. Appl. Math. 126 (2000), 159-183.

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.

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