ABSTRACT
Geodesics are the analog, for surfaces of the straight lines in the good old Euclidean geometry. While the first concept of geodesics is ubiquitous in Computer Science, with all its ramifications and applications, being essentially identified in the common conception with the famous Dijkstra algorithm, geodesics as straightest curves are generally forgotten, even though it is this avatar of theirs that human beings use in day to day life. The formula above also demonstrates that the notion of geodesics as straightest lines is an extrinsic one, since it depends on the normal, i.e. on the manner the surface is realized in Euclidean space. Thus geodesic torsion measures the deviation from the curve torsion due to its being embedded in a surface, where the deviation is measured by the rate of change of the angle between the curve and surface normals.
