Bezier Curves Defined in Parametric Terms

In Conclusion

The bulk of this chapter was actually more about the general rendering framework than it was about Bezier surfaces. This is because moving from curves to surfaces really doesn't require all that much new information. The next chapters will concentrate on the specifics of the other surface representations, but the basic concepts and application will remain very much the same. For that reason, it makes sense to review the points of this chapter before moving on.

• Surfaces are built upon the same concepts as curves. The biggest difference is that the parametric space is now 2D.

• Like curves, the position on a surface is the weighted sum of the control points where the influence of each point is determined by the basis functions. For a surface, you use basis functions in both dimensions.

• The normal vector for any given point on the surface can be computed as the cross product of two vectors that are tangent to the surface at that point. Conveniently, you can use partial derivatives to get the tangents in the u and v directions.

• All of the samples use diffuse lighting, which is computed as the dot product of the normal vector and the opposite of the light direction.

• All of the surface applications use the same basic 3D framework.

• All of the surface applications use the same basic format for the vertex and index buffers.