  Given a non-rational real space curve and a tolerance $\epsilon>0$, we
present an algorithm to approximately parametrize the curve. The algorithm
checks whether a planar projection of the space curve is $\epsilon$-rational
and, in the affirmative case, generates a planar parametrization that is lifted
to an space parametrization. This output rational space curve is of the same
degree as the input curve, both have the same structure at infinity, and the
Hausdorff distance between them is always finite.
