That ratio seems to say, that “hue begins after white”?
That is, when the common part (white) is removed.
I’m not entirely sure what that means, but I think the answer is “yes” for (I stress) the simple arithmetical systems. If we add the same constant k
to all three channels (k
can be negative), the ratio becomes:
( (mid + k) - (min + k) )
-------------------------
( (max + k) - (min + k) )
(mid + k - min - k)
= -------------------
(max + k - min - k)
(mid - min)
= -----------
(max - min)
… so the ratio is unchanged, so the hue is unchanged.
Given the two conditions I mentioned above, the first condition tells us which of the six segments in the hue circle we are in. The boundaries of the segments are: red, yellow, green, cyan, blue, magenta and back to red. For example, if red is the maximum channel and green is the middle channel, the hue is somewhere in the segment between red and yellow.
Suppose RGB values (R,G,B) are in the range [0,1]. We can subtract the minimum value from all three channels without changing hue. So now the mimimum is zero. Then we can divide all channels by the maximum without changing hue, so the maximum is now at 1.0. In our example, the blue channel is zero, and the red channel is one, and green is somewhere between zero and one: the RGB values are (1, G’, 0).
The middle channel then gives the angular distance of this hue to one of the boundaries. If green is zero, the hue is red. If green is one, the hue is yellow. For other values of green, the hue is orange or reddish-yellow or yellowish-red or whatever.