Now consider Figure 13-8 on the following page which provides a different graphical representation of the preceding discussion based on well-accepted spectral color matching experiments. This figure only displays r and g values for the visible spectrum. Any point on the curve corresponds to a spectral frequency, and subtracting the sum of a point’s r and g coordinate values from 1.0 provides the corresponding b value. Note that all g values are equal to or greater than zero but that r has negative values.

Figure 13-8 is useful because it predicts the result obtained by blending any two light sources. Simply find their corresponding points on or inside the curve and draw a line between the two points. The result’s corresponding point will be located on the line positioned between the two points. The point’s distance between the two original lights is a function of the radiance of each light. If three lights are mixed, then the triangle formed by the points corresponding to the source lights encloses all color combinations the three lights can construct—called the color gamut.

Referencing Figure 13-7, the curves for the red, green, and blue lights are useful in predicting what resulting chromaticity would result when shining a specific light source on a specific object. The effort involved multiplying the source’s spectral power distribution with the object spectral reflectance curve separately with each of the three chromaticity coordinate curves in Figure 13-7. The area under each of the three curves was calculated (using mathematical integration) and the three values comprised the resulting chromaticity.

Figure 13-8  Spectral horseshoe chromaticity diagram

As confusing as this might sound, it was even more difficult to perform in 1931 using hand calculators because of the existence of negative numbers in the calculations. So, rather than use the NPL primaries, the CIE decided in 1931 to use the imaginary lights indicated in Figure 13-9 referred to as X, Y, and Z. After affine transformation distortion magic, Figure 13-10 illustrates the corresponding chromaticity coordinates and Figure 13-11 associates colors with the coordinates and is referred to as the CIE XYZ chromaticity diagram. Note that all curve values are positive, assisting the tireless calculator operators.

Figure 13-9  Z,Y, and Z diagram

Figure 13-10  Chromaticity coordinates

Figure 13-11  CIE XYZ chromaticity diagram

Like the other previous perceptual spaces, the CIE XYZ space is not a perceptually uniform space. Within its three-dimensional coordinate system, it begins its descent to the xy surface as a gleaming white spot. It assumes a potato shape and descends with a plop, leaving its characteristic horseshoe print on the xy plane. While its exterior is brightly adorned, its xy plane print represents the space’s maximum range. Other z values cross sections cover less area. Looking down on the space from above provides the generally accepted color areas Figure 13-11 illustrates.

The CIE XYZ space is useful because it predicts the resulting chromaticity that results from mixing two chromaticities (Figure 13-12). By extension, it also shows the gamut that results from source primary selections (Figure 13-13), intuitively proving that no combination of source primaries can generate all chromaticities. As an example, it correctly indicates the difficulty of producing 500 nm wavelengths from typical primaries. Finally, when the white point is known, it provides an easy way to calculate the dominant wavelength of any chromaticity.

Figure 13-12  Chromaticity resulting from mixing two chromaticities

Figure 13-13  Chromaticity resulting from mixing three colors

RGB/HSV/HLS/HSI Color Model Conversion Routines

Appendix B contains several color space conversion routines from the VESAPCX.C program.