Interpolation by C1 splines of degree q⩾4 on triangulations

Let Δ be an arbitrary regular triangulation of a simply connected compact polygonal domain Ω⊂R2 and let Sq1(Δ) denote the space of bivariate polynomial splines of degree q and smoothness 1 with respect to Δ. We develop an algorithm for constructing point sets admissible for Lagrange interpolation by Sq1(Δ) if q⩾4. In the case q=4 it may be necessary to slightly modify Δ, but only if exceptional constellations of triangles occur. Hermite interpolation schemes are obtained as limits of the Lagrange interpolation sets.