ABSTRACT
Interpolating spline equations are calculated using coordinates of points along their paths. However, non-interpolating splines do not pass through all their control points. For such splines a separate set of techniques are needed to calculate their equations. This chapter introduces the concept of blending functions and how these functions are used to derive equations for hybrid splines, which pass through only a subset of their control points or where conditions other than control points are used for deriving their equations. Specifically, the chapter deals with the Hermite spline, Cardinal spline, Catmull–Rom spline, and Bezier spline. For Bezier splines both the quadratic and cubic variants have been discussed along with Bernstein polynomials used to formulate their blending functions. As before, the theoretical concepts are followed by numerical examples, MATLAB codes and graphical plots for visualization. The chapter ends with a discussion how one spline type can be converted to another.
