understanding HSL to RGB color space conversion algorithm -


i've read hsl rgb algorithm in wikipedia. understand , can convert using it. came upon algorithm here, , math "explained" here.

the algorithm is:

//h, s , l input range = 0 ÷ 1.0 //r, g , b output range = 0 ÷ 255  if ( s == 0 ) {     r = l * 255    g = l * 255    b = l * 255 } else {    if ( l < 0.5 ) var_2 = l * ( 1 + s )    else           var_2 = ( l + s ) - ( s * l )     var_1 = 2 * l - var_2     r = 255 * hue_2_rgb( var_1, var_2, h + ( 1 / 3 ) )    g = 255 * hue_2_rgb( var_1, var_2, h )    b = 255 * hue_2_rgb( var_1, var_2, h - ( 1 / 3 ) ) }  hue_2_rgb( v1, v2, vh )             //function hue_2_rgb {    if ( vh < 0 ) vh += 1    if( vh > 1 ) vh -= 1    if ( ( 6 * vh ) < 1 ) return ( v1 + ( v2 - v1 ) * 6 * vh )    if ( ( 2 * vh ) < 1 ) return ( v2 )    if ( ( 3 * vh ) < 2 ) return ( v1 + ( v2 - v1 ) * ( ( 2 / 3 ) - vh ) * 6)    return ( v1 ) }

i've tried following math can't figure it. how work?

the first part if ( s == 0 ) case there no saturation means it’s shade of grey. set luminance, set rgb grey scale level , done.

if not case, need perform tricky part:

we shall use var_1 , var_2 temporary values, making code more readable.

so, if luminance smaller 0.5 (50%) var_2 = luminance x (1.0 + saturation. if luminance equal or larger 0.5 (50%) var_2 = luminance + saturation – luminance x saturation. that's else part of:

if ( l < 0.5 ) var_2 = l * ( 1 + s ) else           var_2 = ( l + s ) - ( s * l )

then do:

var1 = 2 x luminance – var_2

which going useful later.

now need 3 temporary variables each color channel, far hue conserned. red, add 0.333 (h + (1/3) in code), green nothing, , blue, subtract 0.333 (h + (1/3)). temporaty value called vh (value hue) in hue_2_rgb().

now each color channel treated separetely, 3 function calls. there 4 formulas can applied color channel. every color channel should "use" 1 formula.

which one? depends on value of hue (vh).

by way, value of vh must normalized, if it's negative add 1, or if it's greater 1, subtract 1 it, vh lies in [0, 1].

  1. if 6 x vh smaller 1, color channel = var_1 + (var_2 – var_1) x 6 x vh
  2. if 2 x vh smaller 1, color channel = var_2
  3. if 3 x vh smaller 2, color channel = var_1 + (var_2 – var_1) x (0.666 – vh) x 6
  4. else, color channel = var_1

for r = 255 * hue_2_rgb( var_1, var_2, h + ( 1 / 3 ) ), color channel red, named r in code.


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