A History of Curves and Surfaces in CAGD

This chapter outlines the history of the major developments in the area of curves and surfaces as they entered the area of computer aided geometric design (CAGD). The term “CAGD” was coined by R. Barnhill and R. Riesenfeld in 1974 when they organized a conference on that topic at the University of Utah. CAGD deals with the construction and representation of free-form curves, surfaces, or volumes. The earliest recorded use of curves in a manufacturing environment goes back to early AD Roman times for the purpose of shipbuilding. Shipbuilding connection was the earliest use of constructive geometry to define free-form shapes. Another early influential development for CAGD was the advent of numerical control (NC) in the 1950s. The chapter reveals that curves were employed by draftsmen for centuries; the majority of these curves were circles, but some were free-form. It defines French curves as wooden curves consisting of pieces of conies and spirals. The chapter also discusses the generalization of the concept of splines to surfaces.