During his stay at Purdue University (USA) in 1987-89, Prof Wolter developed algorithms for the computation of geodesics and curvature lines on Riemannian manifolds.
Those algorithms were implemented under the name "Project Riemann" with the support of a US Army Office of Research grant by student assistants Steve Cuthin, Tom Hausman, Bret Johnson, Scott Goehring and Jim Lambers. After developing a first LISP version of the algorithms using Cornell math routines, the whole software was re-implemented in C, sporting a function parser and graphical 3D output. The software package can compute geodesics and curvature lines on algebraic and some classes of non-algebraic surfaces in three-dimensional Euclidean space.
Download source code (archive with C code that compiles on Linux systems).