Algorithm realization and application of geodesic

Geodesic can be described as the shortest distance between two points on a Riemann surface, which plays a pivotal role in differential geometry analysis and has come into widespread use in plenty of fields. This paper derives the parameter geodesic equation on the cylindrical and the spherical surface respectively. Meanwhile, the MATLAB visualization is also applied to provide a distinct illustration of the features of geodesic. In the application of geodesic, taking advantage of Prim's algorithm, the simulation of city network indicates the shortest route between two connected cities. It is hoped that the application of geodesic can be promoted to solve city network issues in regard to minimum engineering costs, shortest routes etc.