TABLE OF CONTENTS In this chapter, we cover the basics of cubic B zier curves. These are the "bread-and-butter" curves of most commercial systems, ranging from CAD/CAM to Graphic Design. While higher order curves are also used, the basic principles are easily explored using this simple curve type. Figure 3.1 shows several B zier curves which were generated using PostScript language.
Most people know about curves from calculus. There, a curve is a function such as
plotted in Sketch 22.
That sketch does not show the function y = 2 x ? 2 x 2; it shows its graph. The graph is a set of points
From calculus, we know that there is a horizontal tangent where 
, in our example at x = .
A parametric curve is a more complicated concept, and not all facts from calculus carry over in a straightforward way.
We already encountered a parametric curve in Section 2.1; there, we were dealing with straight lines in parametric form:
This is the straight line through the points a and b.
In general, a parametric curve is of the form
In the straight line example, both f and g are linear functions. For a general parametric curve, they can be any kind of function. Just as we discussed for parametric lines in Section 2.1, the domain of a...
