Generalizing Swept and Skinned Shapes

In Conclusion

The relatively short length of this chapter is indicative of the fact that surfaces are relatively simple extensions of the concepts you should already know. In the next chapter, I will provide the same explanations for NURBS surfaces before moving on to different kinds of surfaces in Chapter 10, "More NURBS Surfaces." Before I get too far ahead of myself , let me review:

• B-spline surfaces are just extensions of B-spline curves into a second parametric dimension.

• The same advantages of B-spline curves apply to B-spline surfaces. You get more control over the shape and the degree of the surface.

• The u and v directions are each controlled by their own knot vectors and can be of different degrees.

• You can simplify the calculations if you use the knot vector to decide whether or not a given control point affects a given point on the surface.