ABSTRACT
The visual appearance of 3D models representing all kinds of objects is dictated by the properties of their surfaces with color being the most important. Often the surface of a model is constructed by building it up from a series of primitive shapes. A polygon with three sides (a triangle) is the simplest form of primitive shape. In chapter 2 other simple primitives like the sphere were discussed. Today in computer-aided design (CAD) application programs more complex surface shapes referred to as patches have proved popular. These include Be´zier and NURBS (non-uniform rational B-spline) patches which have curved edges and continuously varying internal curvature. A model can usually be accurately represented by combining a lot fewer of these more sophisticated surface shapes. Whether using primitive polygons or curved patches to describe a model there are advantages and disadvantages. The simplest polygon is fast to render and easy to manipulate; the more complex patches usually give a better approximation to the original object, especially if it has many curved parts. Occasionally, it is a matter of personal preference which sort of patch to use. For example, a cube is modeled just as effectively with triangular polygons as it is with Be´zier patches. Figure 3.1 shows the famous Utah teapot in polygonal and Be´zier patch form.
