Computer-aided definition, manipulation and depiction of objects composed of spheres

Abstract

As previously demonstrated by Badler and O'Rourke, a variety of 3-D objects can be defined conveniently as collections of spheres-having various sizes and positions in 3-D space and possibly intersecting. This paper is an elaboration on the technique, describing methods of constructing and manipulating such objects and, most particularly, a method of achieving realism in rendering the picture-even though, for reasons of efficiency, computation is performed as if everything were 2-dimensional, with depth ordering.Pictorial realism results from three features of the overall method: roundedness of the basic picture plane images of individual spheres, pictorial merging of 3-dimensionally intersecting spheres (which are very likely intended as parts of the same object), and pictorial separation of spheres whose images overlap but which lie at significantly different depths in 3-space. Separation is achieved by a black line and resembles the lines traditionally found in cartoon cel animation; merging is accomplished by arranging, in effect, for every sphere image to be transparent to the brighter parts of images of other spheres of the same color.The system lends itself well to construction and manipulation of objects defined by geometry and mathematical transformations; it also serves well in construction and depiction of organic forms which arise and/or are modified by random growth and rules of contingency. Several examples of pictorial results are presented.