The goal of this project is to find applications of advanced differential geometry and singularity theory in computer science and its teaching. The research so far is concentrated on extraction of invariant features of surfaces in three-dimensional space, such as ridges and ravines, investigation of motion of a rigid body under various holonomic and non-holonomic constraints and interpolation in manifolds, in particular, interpolation of rotations. The project resulted in 1994 in 6 published, 2 submitted and 3 accepted papers and a Maple tutoring spreadsheet.