Efficient distance calculation using the spherically-extended polytope (S-tope) model

An object representation scheme which allows fast Euclidean distance calculation is presented. The object model extends the polytope model by representing objects as the convex hull of a finite set of spheres. Objects with rounded surfaces can be represented with far fewer vertices than would be required with the polytope model. An algorithm for calculating distances between objects is developed which is linear in the total number of spheres specifying the two objects. To determine the efficiency of the distance computation algorithms, a program was written and tested using randomly generated objects with varying numbers of vertices