ABSTRACT
This chapter discusses a number of representations for free-form curves. The most important ones for computer graphics are: Cardinal splines use a set of cubic pieces to interpolate control points. They are generally preferred to interpolating polynomials because they are local and easier to evaluate. Bezier curves approximate their control points and have many useful properties and associated algorithms. For this reason, they are popular in graphics applications. B-spline curves represent the curve as a linear combination of B-spline functions. They are general and have many useful properties such as being bounded by their convex hull and being variation diminishing. B-splines are often used when smooth curves are desired. The chapter uses different mechanisms for combining polynomial pieces: using independent polynomial pieces for different ranges of the parameter and blending together piecewise polynomial functions.
