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

Scattered-Data Interpolation 157

2 1 1 2

0.2

0.4

0.6

0.8

1.0

2 1 1 2

2

4

6

8

2 1 1 2

0.5

1.0

1.5

2.0

2.5

Gaussian Tri-harmonic Thin-plate spline

e

−

kxk

2

2c

2

kxk

3

kxk

2

ln kxk

Figure 10.8: Radial functions.

Since A is a square matrix, the unknowns c can be solved using a

standard numerical solver.

A one-dimensional example of RBF interpolation is shown in

Figure 10.7 (bottom). Compared to Shepard’s interpolation (Fig-

ure 10.6), the RBF yields functions interpolating the same input

data but that are not as wavy. This advantage is amplified in the

2D example in Figure 10.3, where the RBF interpolation result is

shown on the right.

There are many other radial function candidates ...