Color delta/comparison math

These are the formulas to calculate color differences. All of them refers to the CIE-L*ab color space.
Each formula is written as a "neutral programming function", easy to be translate in any specific computer language.
We did not post obvious deltas which involve a simple subtraction of two values.

Please keep in mind that implementing complex delta calculation (CMC, 1994, 2000) in your code may involve a lot of attention about the math itself and also the coding syntax.

Delta C*

Delta H*

Delta E*

Delta E 1994

Delta E 2000

Delta CMC

CIE-L*1, CIE-a*1, CIE-b*1          //Color #1 CIE-L*ab values CIE-L*2, CIE-a*2, CIE-b*2          //Color #2 CIE-L*ab values WHT-L, WHT-C                       //Wheight factor xC1 = sqrt( ( CIE-a*1 ^ 2 ) + ( CIE-b*1 ^ 2 ) ) xC2 = sqrt( ( CIE-a*2 ^ 2 ) + ( CIE-b*2 ^ 2 ) ) xff = sqrt( ( xC1 ^ 4 ) / ( ( xC1 ^ 4 ) + 1900 ) ) xH1 = CieLab2Hue( CIE-a*1, CIE-b*1 )   if ( xH1 < 164 || xH1 > 345 ) xTT = 0.36 + abs( 0.4 * cos( dtor(  35 + xH1 ) ) ) else                          xTT = 0.56 + abs( 0.2 * cos( dtor( 168 + xH1 ) ) )   if ( CIE-L*1 < 16 ) xSL = 0.511 else                xSL = ( 0.040975 * CIE-L*1 ) / ( 1 + ( 0.01765 * CIE-L*1 ) )   xSC = ( ( 0.0638 * xC1 ) / ( 1 + ( 0.0131 * xC1 ) ) ) + 0.638 xSH = ( ( xff * xTT ) + 1 - xff ) * xSC xDH = sqrt( ( CIE-a*2 - CIE-a*1 ) ^ 2 + ( CIE-b*2 - CIE-b*1 ) ^ 2 - ( xC2 - xC1 ) ^ 2 ) xSL = ( CIE-L*2 - CIE-L*1 ) / WHT-L * xSL xSC = ( xC2 - xC1 ) / WHT-C * xSC xSH = xDH / xSH Delta CMC = sqrt( xSL ^ 2 + xSC ^ 2 + xSH ^ 2 ) CieLab2Hue( var_a, var_b )          //Function returns CIE-H° value {    var_bias = 0    if ( var_a >= 0 && var_b == 0 ) return 0    if ( var_a <  0 && var_b == 0 ) return 180    if ( var_a == 0 && var_b >  0 ) return 90    if ( var_a == 0 && var_b <  0 ) return 270    if ( var_a >  0 && var_b >  0 ) var_bias = 0    if ( var_a <  0               ) var_bias = 180    if ( var_a >  0 && var_b <  0 ) var_bias = 360    return ( rad2deg( atan( var_b / var_a ) ) + var_bias ) } Top