Parallel computation of discrete geodesics and its applications - Le, Tien Hung (2017)
Computing geodesics on meshes is a classical problem in computational and differential geometry. It measures the length of the local shortest path with minimum curvature along the surface between two points. Previous studies have documented many important properties of geodesics, such as being a distance metric, locally isotropic and invariant to isometric transformation. With those properties, geodesic distance could be considered as a more general deﬁnition of Euclidean distance. Thus, it plays an important role in constructing various algorithms, solving many real-world problems and developing countless applications in a wide range of ﬁelds, including computer graphic, digital geometric processing, computer vision and image processing, etc.