Geodesic paths and periodic geodesics on polyhedral surfaces: computation and applications

as being locally optimal.

From this property, we propose an iterative method to compute
a geodesic path between two vertices in a finite number of
iterations. On the surface, we consider a face sequence,
compute the shortest path within and update it around pivot
vertices, where the computed path is not locally optimal as
path on the surface.

Extensions to periodic geodesics, to subdivision surfaces
will be mentionned and we will see a few applications.