converting XYZ color to RGB

Question

color-primary transformations

Does anyone know of any formula for converting a XYZ to an RGB value?

how find rgb from XYZ in this pic?

Solution

There is a simple linear relationship between RGB and XYZ spaces (if you wish you can express this in matrix form in the obvious way): R = 3.2404542*X - 1.5371385*Y - 0.4985314*Z G = -0.9692660*X + 1.8760108*Y + 0.0415560*Z B = 0.0556434*X - 0.2040259*Y + 1.0572252*Z

However, if what you meant is sRGB space, then additional non-linear transformation needs to be applied to each component: R=adj(R), G=adj(G), and B=adj(B). The adj function is defined as follows:

function adj(C) {
  if (Abs(C) < 0.0031308) {
    return 12.92 * C;
  }
  return 1.055 * Math.pow(C, 0.41666) - 0.055;
}

Comments

[beaker]

I'm sure wikipedia does. What research have you done?

[Wyzard]

There's no generic "XYZ to RGB" because "RGB" doesn't have a precise meaning. You need to choose a specific color space that has specific primaries, such as sRGB.

[Manfred Radlwimmer]

There is a lot of math involved. My recommendation would be Bruce Lindbloom's Website. It contains all the formulas, parameters and background knowledge you need to konverta a color from one color space to another.

[Константин Ван]

That matrix is of sRGB, and sRGB is not the only RGB color space.