Computer-Aided Design of 3-D Objects Using Polar Spline Representations

Abstract

In recent years there has been considerable interest in systems for the computer-aided design of three dimensional objects. An essential ingredient of such a system is a method for constructing mathematical representations of 3-D surfaces. The method should have the following properties: (1.1) the mathematical representation of any object should depend only on a finite number of parameters which can be stored in a digital computer; (1.2) the representation should be such that perspective views (or 3-D views) of the object can be rapidly generated; (1.3) the representation of any object should depend on a finite number (1.3) of control parameters in such a way that the user can interactively modify these parameters to alter the shape of the object in a controlled fashion.