This paper describes algorithms using Groebner basis techniques for pa
rameterizing algebraic space curves. It is shown that the Groebner bas
is of the ideal of a non-singular rational space curve of degree n in
general position, taken with respect to an appropriate elimination ord
er, has n + 1 elements whose degrees and structure can be precisely de
scribed. The space curve can be parameterized by taking a birational p
rojection to the plane and parameterizing the resulting plane curve. T
he Groebner basis just described contains all the information necessar
y to deal with the singularities introduced by projection, so that exp
licit calculations relating to these singularities can be avoided. The
modifications necessary to take care of the cases of a singular space
curve, or a curve not in general position, are given. An appendix ske
tches a proof of the result that the projection of a non-singular rati
onal, non-planar space curve from any point is birational. (C) 1997 Pu
blished by Elsevier Science B.V.