DESCRIBING SURFACES

This paper continues our work on visual representations of 2-dimensional surfaces. The theoretical component of our work is a study of classes of surface curves as a source of constraint on the surface on which they lie, and as a basis for describing it. We analyze bounding contours, surface intersections, lines of curvature, and asymptotes. Our experimental work investigates whether the information suggested by our theoretical study can be computed reliably and efficiently. We demonstrate algorithms that compute lines of curvature of a (Gaussian smoothed) surface; determine planar patches and umbilic regions; extract axes of surfaces of revolution and tube surfaces. This paper is concerned with the geometrical basis of such a representation. In particular, a set of curves are isolated that lie upon the surface and enjoy a global property, for example being planar. The structure of the representation is currently under development.