Let Δ be an arbitrary regular triangulation of a simply connected compact polygonal domain Ω ⊂ IR² and let S1q (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 S1q (Δ) if q ≥ 4. In the case q
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