H is the same
for HSV and HSL. We won't give the equations here; you can find them in
efg's
HSV lab report. Expressed in degrees (0360º) for any nonzero
x,
H = 0 for Red (x,0,0); 60º for Yellow (x,x,0),
120º for Green (0,x,0) (illustrated below), 180º for Cyan
(0,x,x), 240º for Blue (0,0,x), and 300º
for Magenta (x,0,x). H can also be represented on a scale
of 0 to 1.
Assume R, G, and B can have
values between 0 and 1. Let W = min(R,G,B) = the gray component.
HSV (HSB)

HSL (HLS)

V = max(R,G,B)

L = (V+W)/2

S_{HSV} = (VW)
/ V

S_{HSL} = (VW)
/ (V+W) = (VW) / (2L) ; L <= 0.5
S_{HSL} = (VW)
/ (2VW) = (VW) / (22L) ; L > 0.5

Any color with R, G,
or B = 1 has V = 1.
Maximum saturation occurs
when W = 0.

A bright, fully saturated
color (max(R,G,B) = V = 1; min(R,G,B) = W = 0; S_{HSV} = S_{HSL}
= 1) must have L = 0.5. L = 1 corresponds to pure white.

V,
L, and S illustrated for H = 0.333 (120º; Green)

HSV: Best representation
of saturation

HSL: Best representation
of lightness

V,
L, and H illustrated for S = 1 (maximum saturation)



The Y, C, and M bands
are much narrower than the R, G, and B bands. I'm not sure why; I suspect
it results from specific properties of HSL and HSV (where V = max(R,G,B)
rather than, say, mean(R,G,B).). Y, C, and M appear brighter than R, G,
and B at similar V and L levels because both V and L are related to max(R,G,B).

Some
interesting relationships
(1) For W = min(R,G,B) =
0 (no gray; maximum saturation), S_{HSL} = S_{HSV}
= 1 ; L = V / 2 ; L <= 0.5.
(2) For V = max(R,G,B) =
1 and S_{HSL} = 1, L = 1(S_{HSV }/ 2) ; S_{HSV
}=
(1L) / 2; L >= 0.5

These relationships
imply that (1) the bottom half of the HSL LH plot for S=1 (above, right)
is identical to the HSV VH plot for S=1 (above, left), and (2) the top
half of the HSL SH plot is identical to an HSV SH plot for V=1 (not shown),
i.e., the HSL LH plot (above, right) combines two HSV plots.

All saturation equations
have VW in the numerator; they differ in denominator scaling. In both
representations, S is a measure of relative saturation. S is 0 when
W = V (R = G = B; neutral gray); S = 1 when W is at its minimum allowable
value for a given value of V or L. For HSV, W = 0 when S = 1.
For HSL with L <= 0.5,
maximum saturation takes place when W = 0; S_{HSL} = (VW) / (V+W)
= 1. When L > 0.5, W must be greater than 0. Maximum saturation takes place
when W = 2LV takes its minimum value, W_{min}. In this case
V = 1, so W_{min} = 2L1. S_{HSL} = (VW) / (2VW) = (12L+1)
/ (212L+1) = 1.
V and L don't correspond
with perceived luminance; for example, blue and gray or white with the
same V or L values would have very different luminance. The PAL luminance
signal, Y = 0.30R + 0.59G + 0.11B, corresponds more closely to perceived
luminance. 