public bool Invert(out tMat3x3 result)
{
result = default;
// calculate the minors for the first row
var minor00 = this[1, 1] * this[2, 2] - this[1, 2] * this[2, 1];
var minor01 = this[1, 2] * this[2, 0] - this[1, 0] * this[2, 2];
var minor02 = this[1, 0] * this[2, 1] - this[1, 1] * this[2, 0];
// calculate the determinant
var determinant = this[0, 0] * minor00 +
this[0, 1] * minor01 +
this[0, 2] * minor02;
// check if the input is a singular matrix (non-invertable)
// (note that the epsilon here was arbitrarily chosen)
if (determinant > -0.000001f && determinant < 0.000001f)
{
return(false);
}
// the inverse of inMat is (1 / determinant) * adjoint(inMat)
var invDet = 1.0f / determinant;
result[0, 0] = invDet * minor00;
result[0, 1] = invDet * (this[2, 1] * this[0, 2] - this[2, 2] * this[0, 1]);
result[0, 2] = invDet * (this[0, 1] * this[1, 2] - this[0, 2] * this[1, 1]);
result[1, 0] = invDet * minor01;
result[1, 1] = invDet * (this[2, 2] * this[0, 0] - this[2, 0] * this[0, 2]);
result[1, 2] = invDet * (this[0, 2] * this[1, 0] - this[0, 0] * this[1, 2]);
result[2, 0] = invDet * minor02;
result[2, 1] = invDet * (this[2, 0] * this[0, 1] - this[2, 1] * this[0, 0]);
result[2, 2] = invDet * (this[0, 0] * this[1, 1] - this[0, 1] * this[1, 0]);
return(true);
}
/// <summary>
/// Convert a linear sRGB color to an sRGB color
/// </summary>
public static tMat3x3 CalcColorSpaceConversion_RGB_to_XYZ
(
tVec2 red_xy, // xy chromaticity coordinates of the red primary
tVec2 green_xy, // xy chromaticity coordinates of the green primary
tVec2 blue_xy, // xy chromaticity coordinates of the blue primary
tVec2 white_xy // xy chromaticity coordinates of the white point
)
{
tMat3x3 pOutput = new tMat3x3();
// generate xyz chromaticity coordinates (x + y + z = 1) from xy coordinates
tVec3 r = new tVec3(red_xy.X, red_xy.Y, 1.0f - (red_xy.X + red_xy.Y));
tVec3 g = new tVec3(green_xy.X, green_xy.Y, 1.0f - (green_xy.X + green_xy.Y));
tVec3 b = new tVec3(blue_xy.X, blue_xy.Y, 1.0f - (blue_xy.X + blue_xy.Y));
tVec3 w = new tVec3(white_xy.X, white_xy.Y, 1.0f - (white_xy.X + white_xy.Y));
// Convert white xyz coordinate to XYZ coordinate by letting that the white
// point have and XYZ relative luminance of 1.0. Relative luminance is the Y
// component of and XYZ color.
// XYZ = xyz * (Y / y)
w.X /= white_xy.Y;
w.Y /= white_xy.Y;
w.Z /= white_xy.Y;
// Solve for the transformation matrix 'M' from RGB to XYZ
// * We know that the columns of M are equal to the unknown XYZ values of r, g and b.
// * We know that the XYZ values of r, g and b are each a scaled version of the known
// corresponding xyz chromaticity values.
// * We know the XYZ value of white based on its xyz value and the assigned relative
// luminance of 1.0.
// * We know the RGB value of white is (1,1,1).
//
// white_XYZ = M * white_RGB
//
// [r.x g.x b.x]
// N = [r.y g.y b.y]
// [r.z g.z b.z]
//
// [sR 0 0 ]
// S = [0 sG 0 ]
// [0 0 sB]
//
// M = N * S
// white_XYZ = N * S * white_RGB
// N^-1 * white_XYZ = S * white_RGB = (sR,sG,sB)
//
// We now have an equation for the components of the scale matrix 'S' and
// can compute 'M' from 'N' and 'S'
pOutput.SetCol(0, r);
pOutput.SetCol(1, g);
pOutput.SetCol(2, b);
pOutput.Invert(out tMat3x3 invMat);
tVec3 scale = invMat * w;
pOutput[0, 0] *= scale.X;
pOutput[1, 0] *= scale.X;
pOutput[2, 0] *= scale.X;
pOutput[0, 1] *= scale.Y;
pOutput[1, 1] *= scale.Y;
pOutput[2, 1] *= scale.Y;
pOutput[0, 2] *= scale.Z;
pOutput[1, 2] *= scale.Z;
pOutput[2, 2] *= scale.Z;
return(pOutput);
}
