  Let $(M,g)$ be a Riemannian manifold with boundary. We show that knowledge of
the length of each geodesic, and where pairwise intersections occur along the
corresponding geodesics allows for recovery of the geometry of $(M,g)$
(assuming $(M,g)$ admits a Riemannian collar of a uniform radius). We call this
knowledge the 'stitching data'. We then pose a boundary measurement type
problem called the 'delayed collision data problem' and apply our first result
about the stitching data to recover the geometry from the collision data (with
some reasonable geometric restrictions on the manifold).
