Correct formula for determining the hue of a CIE L*a*b* color

Question

EasyRGB gives the following formula for determining the hue (and chroma) of a CIE L*a*b* color:

var_H = arc_tangent( CIE-b*, CIE-a* )  //Quadrant by signs

if ( var_H > 0 ) var_H = ( var_H / PI ) * 180
else             var_H = 360 - ( abs( var_H ) / PI ) * 180

CIE-L* = CIE-L*
CIE-C* = sqrt( CIE-a* ^ 2 + CIE-b* ^ 2 )
CIE-H° = var_H

However, it gives the formula below on this page (used by the Delta CMC algorithm):

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 )
}

To worsen matters, this Wikipedia page states the following:

CIELUV can also be expressed in cylindrical form (CIELCH), with the chromaticity components replaced by correlates of chroma and hue.

One could conclude that this means that CIE L*a*b* should be first converted to CIE L*u*v* before the hue can be determined.

Can anyone shed any light on this?

Answer 1

Convert orthogonal coordinates a, b to polar coordinates C, h

 C = sqrt (a * a + b * b)
 h = arctan (b/a)

C is the chroma, h is the hue angle.