Chromaticity Color Spaces
=========================

Images often represent color using three channels: (R, G, B) - red, green, and blue. For this document, we assume the range of each channel is [0.0, 1.0].

Normalized Chromaticity
-----------------------

Formulas
^^^^^^^^

Output (r, g, b)
   :(1.0, 0.0, 0.0): 100% red
   :(0.0, 1.0, 0.0): 100% green
   :(0.0, 0.0, 1.0): 100% blue

Output (r, g)
   :(1.0, 0.0): 100% red
   :(0.0, 1.0): 100% green
   :(0.0, 0.0): 100% blue (implied)

Normalized RG/RGB
"""""""""""""""""

.. math::

   r = \frac{R}{R+G+B} \\
   g = \frac{G}{R+G+B} \\
   b = \frac{B}{R+G+B} \\
   \\
   r+g+b = 1

Normalized RG/RGB White-Point
"""""""""""""""""""""""""""""

.. math::

   R = 1 \\
   G = 1 \\
   B = 1 \\
   \\
   r = \frac{R}{R+G+B} \\
   g = \frac{G}{R+G+B} \\
   b = \frac{B}{R+G+B} \\
   \\
   r+g+b = 1

.. code-block:: none

   float3 RGBtoChromaticityRGB(float3 Color)
   {
      // Optimizes 2 ADD instructions into 1 DP3 instruction.
      float SumRGB = dot(Color, 1.0);
      float3 Chromaticity = saturate(Color / SumRGB);
      // Output the chromaticity's white point if the divisor is 0.0.
      // Prevents undefined behavior when dividing by 0.
      Chromaticity = (SumRGB == 0.0) ? float3(1.0 / 3.0) : Chromaticity;
      return Chromaticity;
   }

Spherical Chromaticity
----------------------

This section introduces a color space that represents chromaticity using angles.

Precision Loss in RG Chromaticity
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

A significant drawback of RG chromaticity is precision loss. All possible values map to a right triangle, effectively halving the precision in integer buffers.

Spherical chromaticity encodes data that utilizes the entire RG8 range by calculating angles between the color channels.

.. code-block:: none

   /*
      This code is based on the algorithm described in the following paper:
      Author(s): Joost van de Weijer, T. Gevers
      Title: "Robust optical flow from photometric invariants"
      Year: 2004
      DOI: 10.1109/ICIP.2004.1421433
      Link: https://www.researchgate.net/publication/4138051_Robust_optical_flow_from_photometric_invariants
   */

   float2 RGBtoSphericalRG(float3 Color)
   {
      const float HalfPi = 1.0 / acos(0.0); // 1 / (pi/2) = 2 / pi

      // Precalculate (x*x + y*y)^0.5 and (x*x + y*y + z*z)^0.5
      float L1 = length(Color.rg);
      float L2 = length(Color.rgb);

      float2 Angles = 0.0;
      Angles[0] = (L1 == 0.0) ? 1.0 / sqrt(2.0) : Color.g / L1;
      Angles[1] = (L2 == 0.0) ? 1.0 / sqrt(3.0) : L1 / L2;

      return saturate(asin(abs(Angles)) * HalfPi);
   }