Exploring subdivision surfaces

The Catmull–Clark Subdivision Surface algorithm was invented by some of the very talented engineers at Pixar. It has been a very important innovation in the 3D industry, as it provides you with a way in which to make models look smoother. This is achieved by taking input geometry and dividing all of the polygons into smaller polygons. Then, the spacing between the vertices of these new polygons is averaged to create a smooth result.

This algorithm works especially well with quadrilaterals. Each quad can be divided vertically and horizontally at the same time, which turns a single quad into a small grid of four quads. This algorithm can be repeated for multiple levels of subdivision. A second iteration on a quad will result in 16 small quads in a very clean grid pattern, as you can view in the following diagram:

Figure 5.16 – A quad with various levels of subdivision

Generally, two levels of the subdivision are...