OpenGL Programming Guide

Appendix CThe OpenGL Utility Library

Polygon Tessellation

As discussed in "Describing Points, Lines, and Polygons," OpenGL can directly display only simple convex polygons. A polygon is simple if the edges intersect only at vertices, there are no duplicate vertices, and exactly two edges meet at any vertex. If your application requires the display of simple nonconvex polygons or of simple polygons containing holes, those polygons must first be subdivided into convex polygons before they can be displayed. Such subdivision is called tessellation. GLU provides a collection of routines that perform tessellation. Note that the GLU tessellation routines can't handle nonsimple polygons; there's no standard OpenGL method to handle such polygons.

Since tessellation is often required and can be rather tricky, this section describes the GLU tessellation routines in detail. These routines take as input arbitrary simple polygons that might include holes, and they return some combination of triangles, triangle meshes, and triangle fans. You can insist on only triangles if you don't want to have to deal with meshes or fans. If you care about performance, however, you should probably take advantage of any available mesh or fan information.

The Callback Mechanism
The Tessellation Object
Specifying Callbacks
Describing the Polygon to Be Tessellated

OpenGL Programming Guide