A Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics, and Image Processing

152 Scattered-Data Interpolation

Before moving on to multiple data points, we give an alternative

interpretation of linear interpolation, which will be used in the

rest of the chapter to motivate other approaches. Observe that

the right-hand side of equation (10.1) is a sum of two terms, each

being a linear function of p. We denote these two functions as

f

1

(p) and f

2

(p), and plot them in color in Figure 10.4(b). The

sum of these two functions, which are line segments themselves, is

the final interpolating segment.

To interpolate between more than two data points, we can lin-

early interpolate between every two successive points, and connect

the resulting ...