Extending Curves to Patch Surfaces

 Download CD Content

Overview

Chapter 3 introduced Bezier curves as an example of parametric curves that are based on a set of basis functions. Bezier curves are far more flexible than the polynomial curves discussed in Chapter 1, but they are still subject to many limitations. This chapter introduces B-splines (short for "basis" splines). These curves are also based on a set of basis functions, but they are far more flexible than Bezier curves. They are also more complicated, but I will show you some straightforward ways to deal with them based on the following topics:

• The building blocks of a B-spline

• Generating the basis functions

• Different types of knot vectors

• Controlling the parameters of a B-spline

• Closed B-splines

• Finding the derivatives of the basis functions

• Drawing B-splines