2020/07/06 by Andrew R. Tawfeek, Tawfeek, Andrew R.
Computer Science · Engineering · #3D Shape Modeling and Analysis #Advanced Numerical Analysis Techniques #Computational Geometry and Mesh Generation #FOS: Mathematics #Functional Analysis (math.FA)
paper · pdf · doi:10.48550/arxiv.2007.02864
openalex publication_date 2020/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give an accessible introduction and elaboration on the methods used in obtaining a geodesic, which is the curve of shortest length connecting two points lying on the surface of a function. This is found through computing what's known as the variation of a functional, a "function of functions" of sorts. Geodesics are of great importance with wide applications, e.g. dictating the path followed by aircraft (great-circles), how light travels through space, assist in the process of mapping a 2D image to a 3D surface, and robot motion planning.