ClaudiusMaximus' 2008-01-30

I stumbled across Susan Roberta Curtis' 1982 MSc thesis: Saturation and Luminance Control in Color Image Processing. This defines an LC₁C₂ colour space with some interesting properties that make it more useful than either RGB or YUV.

RGB is a pain at the best of times, but YUV isn't much better. The problem with YUV is that the "constant saturation curve" is not a circle, but a skew ellipse, which makes setting absolute saturation very tricky. This is generally shown best on a vector scope:

The constant saturation curves in the LC₁C₂ colour space seems to be more circular than in YUV, I haven't measured it yet but the results are pleasing. Here's a fragment of GLSL code that sets the saturation of an RGB colour:

   // inputs
   vec3 in;
   float saturation;
   // outputs
   vec3 out;
   // conversion matrices
   mat3 rgb2lcc = mat3(
      0.299,  0.621,  0.080,
      0.498, -0.442, -0.056,
     -0.162, -0.336,  0.498
   );
  mat3 lcc2rgb = mat3(
      1.0,  1.407,  0.0,
      1.0, -0.677, -0.236,
      1.0,  0.0,    1.848
   );
   // saturation bashing
   vec3 lcc1 = in * rgb2lcc;
   float l  = lcc1.x;
   float c1 = lcc1.y;
   float c2 = lcc1.z;
   float sat = saturation/sqrt(c1*c1+c2*c2);
   vec3 lcc2 = vec3(l, sat*c1, sat*c2);
   vec3 out = lcc2 * lcc2rgb;

Next step is to investigate LC₁C₂ more scientifically.

Following on from hypercube (which renders a 4D cube, aka a tesseract), I've been working on hyperx, a generalisation to arbitrary dimensions and structures. To this end, I switched from (very slow) CPU based rendering to (very fast) GPU based rendering. Not all is accelerated so far, but the polygon rasterization is several orders of magnitude faster. To get the colours looking good, I'm using GLSL, with a fragment shader that manipulates the rendered image.

hexeract is a temporary branch of hyperx to experiment with, currently it renders a 6D cube. It's heavily based on the HelloGPGPU example (GLSL version) from GPGPU. Hopefully Pd's Gem package for OpenGL will be fixed so I can used shaders in it - just seems to be a matter of using GLEW in the right way, or not converting GLint to float and losing precision, or something.

Some example output is here: hexeract undergoing 3 orthogonal rotations (3.3MB)

Source code is in SVN:

svn co https://devel.goto10.org/svn/maximus/hyperx/hexeract hexeract

Undecidable :: some old tunes from 2001 that I found on a hard disk image.