Subdivision Algorithms for Ruled Surfaces

Abstract

Recent research has produced results on subdivision in arbitrary manifolds. These results can be applied to the manifold of lines and thus we can create subdivision schemes especially for ruled surfaces. We present different methods for refining discrete models of ruled surfaces: An algorithm combining subdivision and projection to the manifold of lines in Euclidean three-space. A further algorithm combines subdivision for the striction curve with geodesic subdivision in the Euclidean unit sphere. The third method is based on the Denavit-Hartenberg-Method for serial robots. We refine the sequence of motions of the Sannia frame by means of geodesic subdivision in the group of Euclidean motions.