Editing HSL and HSV (section)

===== HSV to RGB alternative =====

Given a color with hue <math>H \in [0^\circ,360^\circ]</math>, saturation <math>S=S_V \in [0,1]</math>, and value <math>V \in [0,1]</math>, first we define function :
: <math>f(n) = V - VS \max(0, \min(k, 4-k, 1))</math>
where <math>k,n \in \mathbb R_{\geq 0}</math>  and:
: <math>k = \left(n+\frac{H}{60^\circ}\right) \bmod 6</math>

And output R,G,B values (from <math>[0,1]^3</math>) are:
: <math>(R,G,B) = (f(5), f(3), f(1))</math>

Above alternative equivalent formulas allow shorter implementation. In above formulas the <math>a\bmod b</math> returns also fractional part of module e.g. the formula <math> 7.4 \bmod 6 = 1.4</math>. The values of <math>k \in \mathbb R \land k \in [0,6)</math>.  The base shape
: <math>t(n,H) = T(k) = \max(0, \min(k, 4-k, 1))</math> 
is constructed as follows: <math>t_1 = \min(k,4-k)</math> is "triangle" for which non-negative values starts from k=0, highest point at k=2 and "ends" at k=4, then we change values bigger than one to one by <math>t_2 = \min(t_1,1) = \min(k,4-k,1)</math>, then change negative values to zero by <math>t = \max(t2,0)</math> – and we get (for <math>n=0</math>) something similar to green shape from Fig. 24 (which max value is 1 and min value is 0). The R,G,B functions of {{mvar|H}} use this shape transformed in following way: modulo-shifted on {{mvar|X}} (by {{mvar|n}}) (differently for R,G,B) scaled on {{mvar|Y}} (by <math>-VS</math>) and shifted on {{mvar|Y}} (by {{mvar|V}}). We observe following shape properties(Fig. 24 can help to get intuition about this):
: <math>t(n,H) = 1-t(n+3,H)</math>
: <math>\min(t(n,H), t(n+2,H), t(n+4,H)) = 0</math>
: <math>\max(t(n,H), t(n+2,H), t(n+4,H)) = 1</math>