  Given n general points p_1, p_2,..., p_n in P^r, it is natural to ask when
there exists a curve C \subset P^r, of degree d and genus g, passing through
p_1, p_2,..., p_n. In this paper, we give a complete answer to this question
for curves C with nonspecial hyperplane section. This result is a consequence
of our main theorem, which states that the normal bundle N_C of a general
nonspecial curve of degree d and genus g in P^r (with d >= g + r) has the
property of interpolation (i.e. that for a general effective divisor D of any
degree on C, either H^0(N_C(-D)) = 0 or H^1(N_C(-D)) = 0), with exactly three
exceptions.
