Three-Dimensional Control of Color Management Systems - Control of Color Imaging Systems: Analysis and Design - page 386

be used to extract the nominal CMYK values for a given x value. The Euclidean norm
(

D E a * ) is computed for each iteration. Tables 7.11 and 7.12 show an example of
the D E a * convergence numbers for 101 colors, each with 10 iterations. If the D E a *

numbers are close to zero (or close to a prede ned threshold value, e.g., 0.05) after

steady state is reached, then those colors are considered inside the printer gamut.
If the D E a * numbers are larger than the threshold value, then we can say that those

colors are out-of-gamut. In Table 7.12, color numbers 77

- 100 are out-of-gamut.

Color numbers 0 - 76 are considered as being inside the gamut.

TABLE 7.11
Example Illustrating the Convergence of a Ray between x 0 ¼ [L 0 ¼50, a 0 ¼0,
b 0 ¼0] and x c ¼ [L c ¼80, a c ¼50, b c ¼30] for Colors between 0 and 50
Iteration# Best CMYK

Color# L * a * b * 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 C M Y K

0 50.00 0.00 0.00 8.22 2.77 0.94 0.30 0.09 0.03 0.01 0.00 0.00 0.00 87.86 70.74 70.26 98.23

1 50.30 0.50 0.30 8.17 2.79 0.94 0.30 0.10 0.04 0.01 0.01 0.00 0.00 86.40 72.45 70.67 97.30

2 50.60 1.00 0.60 7.97 2.74 0.88 0.29 0.11 0.04 0.01 0.01 0.00 0.00 86.21 75.18 71.86 95.88

3 50.90 1.50 0.90 8.49 2.93 0.94 0.33 0.12 0.04 0.02 0.01 0.00 0.00 84.60 76.62 72.17 94.94

4 51.20 2.00 1.20 7.99 2.70 0.89 0.33 0.13 0.05 0.02 0.01 0.00 0.00 84.93 79.85 73.70 93.29

5 51.50 2.50 1.50 7.94 2.72 0.94 0.35 0.13 0.04 0.02 0.01 0.00 0.00 83.59 81.40 74.18 92.27

6 51.80 3.00 1.80 8.06 2.69 0.95 0.35 0.13 0.05 0.02 0.01 0.00 0.00 83.53 83.71 75.79 90.57

7 52.10 3.50 2.10 8.04 2.80 1.02 0.37 0.15 0.07 0.03 0.01 0.01 0.00 82.56 85.22 76.62 89.15

8 52.40 4.00 2.40 7.85 2.75 1.02 0.43 0.20 0.09 0.04 0.02 0.01 0.00 82.34 87.32 78.14 87.17

9 52.70 4.50 2.70 8.08 2.86 1.12 0.49 0.22 0.11 0.05 0.02 0.01 0.01 81.75 89.12 79.34 85.37

10 53.00 5.00 3.00 7.67 2.74 1.19 0.55 0.26 0.13 0.07 0.03 0.02 0.01 82.43 91.73 81.68 82.63

11 53.30 5.50 3.30 8.20 2.97 1.29 0.60 0.29 0.15 0.07 0.04 0.02 0.01 80.97 92.71 82.04 81.36

12 53.60 6.00 3.60 7.77 3.00 1.36 0.64 0.32 0.16 0.08 0.04 0.02 0.01 81.21 94.93 83.75 78.81

13 53.90 6.50 3.90 8.21 3.26 1.46 0.70 0.35 0.18 0.09 0.05 0.02 0.01 80.25 96.27 84.57 77.09

14 54.20 7.00 4.20 7.66 3.18 1.49 0.73 0.38 0.19 0.09 0.04 0.02 0.01 80.03 98.05 85.94 74.98

15 54.50 7.50 4.50 8.20 3.43 1.59 0.80 0.39 0.18 0.08 0.04 0.02 0.01 78.59 98.88 86.43 73.79

16 54.80 8.00 4.80 7.90 3.48 1.65 0.80 0.36 0.16 0.07 0.03 0.02 0.01 78.06 100.30 87.51 72.00

17 55.10 8.50 5.10 7.68 3.49 1.73 0.79 0.36 0.17 0.08 0.04 0.02 0.01 77.35 101.59 88.33 70.29

18 55.40 9.00 5.40 7.39 3.49 1.67 0.75 0.37 0.18 0.09 0.05 0.02 0.01 77.53 103.29 89.70 67.88

19 55.70 9.50 5.70 7.63 3.60 1.66 0.75 0.36 0.18 0.09 0.05 0.02 0.01 75.82 103.94 89.89 66.82

20 56.00 10.00 6.00 7.46 3.65 1.64 0.79 0.38 0.19 0.09 0.05 0.02 0.01 76.52 106.15 91.63 63.92

21 56.30 10.50 6.30 7.61 3.66 1.66 0.80 0.39 0.19 0.09 0.05 0.02 0.01 75.39 107.26 92.18 62.38

22 56.60 11.00 6.60 7.18 3.37 1.55 0.73 0.35 0.17 0.08 0.03 0.01 0.01 75.09 108.90 93.10 60.26

23 56.90 11.50 6.90 7.40 3.39 1.54 0.71 0.31 0.12 0.05 0.02 0.01 0.00 74.04 110.08 93.64 58.93

24 57.20 12.00 7.20 7.13 3.29 1.51 0.64 0.25 0.10 0.04 0.01 0.01 0.00 73.74 111.73 94.61 57.14

25 57.50 12.50 7.50 7.33 3.31 1.48 0.57 0.23 0.09 0.04 0.01 0.01 0.00 72.72 112.84 95.15 55.74

26 57.80 13.00 7.80 7.05 3.09 1.26 0.49 0.19 0.07 0.03 0.01 0.00 0.00 72.56 114.43 96.15 53.79

27 58.10 13.50 8.10 6.60 2.94 1.15 0.45 0.18 0.07 0.03 0.01 0.00 0.00 72.09 115.83 96.97 52.04

28 58.40 14.00 8.40 6.82 2.99 1.16 0.45 0.17 0.07 0.03 0.01 0.00 0.00 71.06 116.89 97.41 50.65

29 58.70 14.50 8.70 7.00 2.98 1.15 0.44 0.17 0.06 0.03 0.01 0.00 0.00 70.12 118.01 97.91 49.20

30 59.00 15.00 9.00 6.22 2.63 1.01 0.40 0.16 0.07 0.03 0.01 0.00 0.00 70.30 119.75 99.02 46.91

31 59.30 15.50 9.30 6.21 2.51 0.99 0.40 0.16 0.07 0.03 0.01 0.00 0.00 69.38 120.76 99.51 45.39

32 59.60 16.00 9.60 6.46 2.53 1.02 0.41 0.16 0.06 0.03 0.01 0.00 0.00 68.64 121.90 100.13 43.76

33 59.90 16.50 9.90 6.59 2.61 1.04 0.42 0.16 0.06 0.03 0.01 0.00 0.00 67.48 122.81 100.52 42.45

( continued )