Abstract
An investigation of surface and solid modeling using a single unbounded algebraic function for objects requiring free form surfaces is discussed. The purpose of this investigation is to determine if a single closed algebraic function can be effectively used to represent objects. Curve fitting techniques are developed. Surfaces using implicit algebraic functions are developed using the techniques of revolution about an axis and extrusion along a curve segment. Infinite extrusions of a planar cross section along an axis of the form y = f(x) are developed. The boolean operators of union, intersection, and difference are developed using the defining function form of algebraic functions. All of the operations have been accomplished in algebra using polynomial multiplication, addition, and subtraction. Examples of all the operations are presented.
