Lecture 20 Advanced topics in differential geometry 20.1 Geodesics In this section we study the computation of shortest path between two points on free-form surfaces [14, 11 20.1.1 Motivation ship design robot motion planning · terrain navigation installation of underwater cable 20.1.2 Definition . t: Unit tangent vector of C at P n: Unit normal vector of c at p N: Unit surface normal vector of s at P u: Unit vector perpendicular to t in the tangent plane defined by n x tLecture 20 Advanced topics in differential geometry 20.1 Geodesics In this section we study the computation of shortest path between two points on free-form surfaces [14, 11]. 20.1.1 Motivation • ship design • robot motion planning • terrain navigation • installation of underwater cable 20.1.2 Definition • t: Unit tangent vector of C at P • n: Unit normal vector of C at P • N: Unit surface normal vector of S at P • u: Unit vector perpendicular to t in the tangent plane defined by N × t. 2