Shading: fitting a smooth intensity surface

Abstract

Visual realism in computer-generated images is an important goal for many computer applications. However, a tradeoff exists between the degree of realism achieved and the time required to generate an image. Thus efficient algorithms for generating realistic images are being actively investigated. Shading is one graphical technique for rendering more realistic images of 3D objects. However, the most widely used algorithm, Gouraud shading, suffers from the Mach band effect, a perceptual phenomenon that reduces realism. Gouraud shading also handles specular reflection poorly. The next most popular algorithm, Phong shading, generally reduces Mach banding and captures specular highlights, though at great computational expense. Bishop and Weimer improved the efficiency of Phong shading, but their algorithm introduces approximation error and is still significantly slower than Gouraud shading. A new algorithm is proposed which takes an innovative approach to shading 3D objects. A smooth intensity surface is generated with a known surface-fitting technique, Powell-Sabin quadratic interpolation. The intensity surface is generated at a modest cost using the Cendes-Wong formulae and forward differencing. The C 1 surface virtually eliminates Mach banding.