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 find the value of the function at points x¼1.5, y¼0.6, and z¼1.85.

The point p ¼ [x y z]T ¼ [1:5 0:6 1:85]T is inside the cube with vertices n000 n001 n010 n011 n100 n101 n110 n111 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.

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TABLE 6.4 Example of a Uniformly Sampled 3-D LUT y KANS f O 2 1 1 1 2000 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 20 1 0001112220001 1 1 2 2 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 2 3 4 1 5 7 8 3 0 4 3 2 3 21 37 0126 201 1 22 2 2 2 2 8 9 2 5 6 4 222 2223 2 2 2 3 8 6 Moll 1001 P --- Mo10 11 111 101 M110 M10 1000 Moo 100 FIGURE 6.8 Eight vertices of the cube surrounding the point p.