  Let $B$ be a point robot moving in the plane, whose path is constrained to
forward motions with curvature at most one, and let $P$ be a convex polygon
with $n$ vertices. Given a starting configuration (a location and a direction
of travel) for $B$ inside $P$, we characterize the region of all points of $P$
that can be reached by $B$, and show that it has complexity $O(n)$. We give an
$O(n^2)$ time algorithm to compute this region. We show that a point is
reachable only if it can be reached by a path of type CCSCS, where C denotes a
unit circle arc and S denotes a line segment.
