In this paper we study relations between normal curves and geodesic curves on triangulated smooth surfaces. Based on a curvature measure for normal curves, we define normal geodesics and build a semi discrete curvature flow under which normal geodesics converge to classical geodesic curves and vice versa, each geodesic in the classic differential geometric sense can be approximated by a sequence of normal geodesics under the defined flow. We give experimental results for the approximation of geodesics on both synthetic as well as on meshes generated from point clouds obtained by sampling of real data.
