ImfChromaticities.cpp

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//-----------------------------------------------------------------------------
//
//	CIE (x,y) chromaticities, and conversions between
//	RGB tiples and CIE XYZ tristimulus values.
//
//-----------------------------------------------------------------------------

#include <ImfChromaticities.h>

namespace Imf {


Chromaticities::Chromaticities (const Imath::V2f &red,
                const Imath::V2f &green,
                const Imath::V2f &blue,
                const Imath::V2f &white)
:
    red (red),
    green (green),
    blue (blue),
    white (white)
{
    // empty
}


Imath::M44f
RGBtoXYZ (const Chromaticities chroma, float Y)
{
    //
    // For an explanation of how the color conversion matrix is derived,
    // see Roy Hall, "Illumination and Color in Computer Generated Imagery",
    // Springer-Verlag, 1989, chapter 3, "Perceptual Response"; and
    // Charles A. Poynton, "A Technical Introduction to Digital Video",
    // John Wiley & Sons, 1996, chapter 7, "Color science for video".
    //

    //
    // X and Z values of RGB value (1, 1, 1), or "white"
    //

    float X = chroma.white.x * Y / chroma.white.y;
    float Z = (1 - chroma.white.x - chroma.white.y) * Y / chroma.white.y;

    //
    // Scale factors for matrix rows
    //

    float d = chroma.red.x   * (chroma.blue.y  - chroma.green.y) +
          chroma.blue.x  * (chroma.green.y - chroma.red.y) +
          chroma.green.x * (chroma.red.y   - chroma.blue.y);

    float Sr = (X * (chroma.blue.y - chroma.green.y) -
            chroma.green.x * (Y * (chroma.blue.y - 1) +
        chroma.blue.y  * (X + Z)) +
        chroma.blue.x  * (Y * (chroma.green.y - 1) +
        chroma.green.y * (X + Z))) / d;

    float Sg = (X * (chroma.red.y - chroma.blue.y) +
        chroma.red.x   * (Y * (chroma.blue.y - 1) +
        chroma.blue.y  * (X + Z)) -
        chroma.blue.x  * (Y * (chroma.red.y - 1) +
        chroma.red.y   * (X + Z))) / d;

    float Sb = (X * (chroma.green.y - chroma.red.y) -
        chroma.red.x   * (Y * (chroma.green.y - 1) +
        chroma.green.y * (X + Z)) +
        chroma.green.x * (Y * (chroma.red.y - 1) +
        chroma.red.y   * (X + Z))) / d;

    //
    // Assemble the matrix
    //

    Imath::M44f M;

    M[0][0] = Sr * chroma.red.x;
    M[0][1] = Sr * chroma.red.y;
    M[0][2] = Sr * (1 - chroma.red.x - chroma.red.y);

    M[1][0] = Sg * chroma.green.x;
    M[1][1] = Sg * chroma.green.y;
    M[1][2] = Sg * (1 - chroma.green.x - chroma.green.y);

    M[2][0] = Sb * chroma.blue.x;
    M[2][1] = Sb * chroma.blue.y;
    M[2][2] = Sb * (1 - chroma.blue.x - chroma.blue.y);

    return M;
}


Imath::M44f
XYZtoRGB (const Chromaticities chroma, float Y)
{
    return RGBtoXYZ (chroma, Y).inverse();
}


} // namespace Imf