  In this paper, we consider enumeration of geodesics on a polyhedron, where a
geodesic means locally-shortest path between two points. Particularly, we
consider the following preprocessing problem: given a point $s$ on a polyhedral
surface and a positive real number $r$, to build a data structure that enables,
for any point $t$ on the surface, to enumerate all geodesics from $s$ to $t$
whose length is less than $r$. First, we present a naive algorithm by removing
the trimming process from the MMP algorithm (1987). Next, we present an
improved algorithm which is practically more efficient on a non-convex
polyhedron, in terms of preprocessing time and memory consumption. Moreover, we
introduce a single-pair geodesic graph to succinctly encode a result of
geodesic query. Lastly, we compare these naive and improved algorithms by some
computer experiments.
