0. Overview

Bézier curves are a method of designing polynomial curve segments when you want to control their shape in an easy way. Bézier curves make sense for any degree, but we'll concentrate on cubic ones, the most important case. (``Bézier'' = ``Bay zee ay''.)

To specify a cubic Bézier curve, you give four points, called control points. The first and last are on the curve; the middle two may not be. When you change the control points, the shape of the curve changes. It is helpful to indicate the control points by connecting them with line segments to form the ``control polygon'' (although this is not a polygon in the usual sense, as it is not closed). Some examples are shown in Figure .

Figure: Some Bézier curves

book/08dir/examples.eps

It does not matter which end you consider to be the first and which the last; you get the same points for the curve either way. Observe that the curve is tangent to the first and last ``legs'' of the control polygon.