In Conclusion

By now, you have seen how the NURBS equations can be used to create a wide variety of surfaces. The examples in this chapter serve to introduce several different classes of surfaces that can serve as starting points. In most cases, that's all they are. For instance, you might model a character's head by starting with a surface of revolution, creating a sphere, and then manipulating individual control points to create the facial features. The application might be quite different, but the math is exactly the same.

This chapter concludes all the NURBS material. You now have several tools available to you. At this point, I'd recommend taking some time to experiment with different shapes and trying to solidify your understanding of how everything works. Here are some important things to remember from this chapter.

Ruled surfaces are created when you interpolate between two or more shape curves. This can be done in the context of the basic NURBS framework or you could reformulate the code to specifically deal with ruled surfaces.
Surfaces of revolution are created when you rotate a profile shape about an axis. The result is a shape that is symmetric about the axis of rotation with a varying cross section.
Swept surfaces are created when you sweep a shape curve along a path curve. This allows you to create shapes that are not symmetric about an axis, but have a constant cross section.
The potential downside of a swept surface is that it does not bend as the path curve bends. If you need it to bend, use a skinned surface.
A skinned surface is very similar to a swept surface. The difference is that the cross section is aligned with the tangent vector of the path curve. This forces the final surface to bend as the shape bends.
You can create more flexible skinned and swept surfaces by introducing a third NURBS curve as the path curve. First, use the path curve to position the control points of the surface. Then, use those control points to create the actual surface.