ABSTRACT
This chapter focuses on the differential geometry of surfaces, which only represents the central part of any introductory course in Differential Geometry, it also provides most of the essential theoretical tools essential in Graphics, CAGD and Imaging. The first such result viewpoint relates shows how to compute the curvature of a curve obtained by sectioning the surface by a non-normal plane; thus showing that the choice of normal sections is, indeed, truly restrictive. But first, let us introduce a new definition that will allow us to formulate the theorem in question in a simple form. All curves on the surface S, having the same tangent vector at p, have the same normal curvature; The normal curvature is the curvature of the curve obtained by sectioning the surface S with the normal plane through p. Clearly the second definition is simpler to handle, thus one would expect both notions to be at least equally important.
