Computing geodesics on discrete surfaces

Abstract

Geodesics are shortest paths between two points on a surface. In smooth differential geometry, various methods of finding geodesics on surfaces exist. These methods are not the same methods used in discrete differential geometry since there exists a difference between a smooth surface and a discrete one. Two methods for computing discrete geodesics are presented in this project. One uses a graph to compute the geodesic and another one solves the differential equation. Implementing these two algorithms to a triangle mesh of a sphere, the outputs were different in the accuracy, complexity, length, and uniqueness.