  We study geodesics in the complete family of nonexpanding impulsive
gravitational waves propagating in spaces of constant curvature, that is
Minkowski, de Sitter and anti-de Sitter universes. Employing the continuous
form of the metric we prove existence and uniqueness of continuously
differentiable geodesics (in the sense of Filippov) and use a C^1-matching
procedure to explicitly derive their form.
