Curves and Surfaces for CAGD, 5th Edition

2

Introductory Material

2.1 Points and Vectors

When a designer or stylist works on an object, he or she does not think of that object in very mathematical terms. A point on the object would not be thought of as a triple of coordinates, but rather in functional terms: as a corner, the midpoint between two other points, and so on. The objective of this book, however, is to discuss objects that are defined in mathematical terms, the language that lends itself best to computer implementations. As a first step toward a mathematical description of an object, one therefore defines a coordinate system in which it will be described analytically.

The space in which we describe our object does not possess a preferred coordinate system—we have to define ...