Interpolation of Multidimensional Functions - Control of Color Imaging Systems: Analysis and Design - page 255

Example 6.3

Consider a system with three inputs, x, y, and z, and one output, f. The LUT
representing the function is given in Table 6.4. Use trilinear interpolation to nd

the value of the function at points x ¼ 1.5, y¼ 0.6, and z ¼ 1.85.

[xyz] T 85] T is inside the cube with vertices The point p ¼ ¼ [1 : 50 : 61 :

½ , as shown in Figure 6.8. The

coordinates of these nodes and the corresponding values of the function f are
given in Table 6.5.

n 000 n 001 n 010 n 011 n 100 n 101 n 110 n 111

TABLE 6.4
Example of a Uniformly Sampled 3-D LUT

x 012012012012012012012012012
y 000111222000111222000111222
z 000000000111111111222222222
f 234157830432321378925643863

n 011

n 11

n 1

n 111

n 001

n 0 1

p

n 101

n 010

n 10

n 110

n 0

n 000

n 00

n 100

FIGURE 6.8 Eight vertices of the cube surrounding the point p.

TABLE 6.5
LUT for Example 6.3

n 000 n 001 n 010 n 011 n 100 n 101 n 110 n 111

x 1 1 1 1 2 2 2 2

y 0 0 1 1 0 0 1 1

z 1 2 1 2 1 2 1 2

f 3 2 2 4 2 5 1 3