Curves and Surfaces for Computer-Aided Geometric Design

In the late 1950s, hardware became available that allowed the machining of 3D shapes out of blocks of wood or steel.1 These shapes could then be used as stamps and dies for products such as the hood of a car. The bottleneck in this production method was soon found to be the lack of adequate software. In order to machine a shape using a computer, it became necessary to produce a computer-compatible description of that shape. The most promising description method was soon identified to be in terms of parametric surfaces. An example of this approach is provided by Plates I and III: Plate I shows the actual hood of a car; Plate III shows how it is represented internally as a collection of parametric surfaces.