# Color and Colorimetry – Part 8

The derivation of the famous CIE horseshoe was explained in the previous part in terms of a re-mapping or distortion of rg color space. The derivation is somewhat abstract because the uses of color science go far beyond the applications in broadcasting. However it is equally possible to describe CIE color space from a more television-centered point of view.

Figure 1 - The RGB cube has a Black - White axis where R = G = B on which there are only brightness changes. Any plane orthogonal to that grey scale axis must represent constant brightness.

Figure 2 - At a), the plane of R + G + B = 1 is a constant brightness plane with an achromatic point in the center where the Black - White axis intersects. At b), the color matching experiments require the plane of constant brightness to extend outside the RGB cube, so the human gamut can be drawn on it.

Figure 3 - The RGB to XYZ matrix has the effect of turning the RGB axes inward so the human gamut fits within the XYZ cube.

Figure 4 - The constant brightness plane is projected onto the XY plane to obtain the familiar color horseshoe.

Figure 5 - MacAdam ellipsoids show how the HVS has non-constant ability to distinguish between hues and saturations. Note that the ellipsoids have various sizes and major axes in various directions, which the XYZ mapping does not account for.

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