Curves

Abstract

Curves are important in computer graphics for two reasons:

• 1. The main task of computer graphics is to generate realistic-looking images. Most real objects are seen because they reflect light, so the computer has to simulate the way light is reflected from a surface. This requires a mathematical model of the surface of an object and such a model is normally based on a model for a single curve. An understanding of computer graphics should therefore start with curves, continue with surfaces, and include a model of light reflection from a surface.

• 2. Some important graphics problems are two-dimensional and can be solved with curves, without the need for surfaces and light reflection. Examples are computer art (drawing and painting), technical drawing, and computer-aided manufacturing (CAM). Clothes designers, for example, can benefit from a program that can draw general curves and that can later automatically cut material along a given curve. In fact, the fair cubic splines (Section 4.8.7) were originally developed to design and cut insoles and other shoe parts.