Degree constrained tree embedding into points in the plane

Given a set N = {p₁,...,p_n} of n points in general position in the plane, and a positive integral n-vector d = (d₁,...,d_n) satisfying ∑ⁿ_i=1d_i=2n - 2, can we construct a tree on N, such that the degree of point p_i is d_i and none of the (n - 1) line segments connecting two points corresponding to endpoints of an edge intersect each other (except possibly at its endpoints)? We give a simple proof of the existence of such a tree in any instance and propose an algorithm polynomial on n for constructing one.