TABLE OF CONTENTS 
When the first author worked in the CAD/CAM department of Mercedes-Benz, Germany, he often had to communicate with designers who traditionally have little training in mathematics. A designer thinks in terms such as "fair," "smooth," or "sweet." How can such concepts be incorporated into computer programs? As it turned out, the central concept of any kind of shape description is curvature, and, luckily, it lends itself to a very intuitive understanding.
We will discuss the shape of a curve in local terms, i.e., we will talk about the curve's shape at a particular point x( t). In order to do this, it would be helpful to have a local coordinate system at x( t), thus enabling us to express local curve properties in terms of this system. We will base the construction of such a system on the first and second derivatives of the curve: 
and 
, illustrated in Sketch 69.
Neither of these two derivatives is (in general) of unit length, nor are they orthogonal to each other. Yet we may use them to define our desired coordinate system using normalization and cross products. Our coordinate system will have origin x( t) and three axes
