An application of color graphics to the display of surface curvature

Abstract

In developing a mathematical representation for a surface, designers currently must use line drawing graphics to examine the curvature of a line in a plane, a two-dimensional analysis. By combining a result from differential geometry with the use of color raster graphics, the method described in this paper provides a means for the designer to examine surface curvature, a three-dimensional analysis. In particular, a formulation for the Gaussian and average curvatures is given and it is shown how these indicate the presence or absence of protrusions, hollows, etc. in a surface, i.e., how, where, and by how much the surface curves. Showing a fourth variable, curvature in this case, over a three-dimensional surface is difficult, if not impossible with traditional line drawing computer graphics. The method described solves this problem by using color as a fourth dimension. Examples are given, including both known shapes (torus) and automotive parts (hood, fender).