Fast Spheres

Abstract

A new method for generating sphere-like images, using parabolic surfaces delimited by Bresenham s circle- generation algorithm, is presented. In many cases the resultant images are indistinguishable from spheres illuminated from a given single direction. The main form of the algorithm uses first and second integer differences to minimise computation and uses typically not more than one floating-point calculation per sphere. Two variants of the algorithm are given, one optimized for the special case of the light-source being behind the view-point, and one in which values are calculated for a z-buffer hidden-surface algorithm at the same time as the pixel values. The difference formulae can be exploited by differencing hardware or digital signal processors although very little arithmetic, typically five low-weight integer operations, including address calculation operations, is required per pixel on a conventional architecture.