ABSTRACT
The problem of constructing or reconstructing continuous curves from a small set of sample points arises in a great many applications. Creating a curve that passes through these points is called interpolation. In this chapter we shall explore some basic issues in interpolation, and we shall contrast global interpolation approaches such as Lagrange interpolation to piecewise parametric polynomial interpolation. Our main motivating application will be the simulation of spatial trajectories. As in the previous chapter, we shall also consider a specific computational problem, in this case that of efficiently rendering or evaluating space curves represented as piecewise parametric polynomials.
