Proposed extension of PNG Color Tutorial to explain how to use cHRM
draft 1.0.0 (2000-Mar-07-Tue)
Adam M. Costello
http://www.nicemice.net/amc/

This proposal would add factual information to the color tutorial in the
PNG 1.2 spec, but would not add any recommendations.

Section 14.7 (Characterizing computer monitors) currently ends with:

      Usually, the first thing a program will do is convert the cHRM
      chromaticities into relative XYZ space.

I propose extending this section to tell how this can be done, because
it's far from obvious:

      Usually, the first thing a program will do is convert the cHRM
      chromaticities into relative XYZ space, which can be done as
      follows.  Denote the values from the cHRM chunk by xw, yw, xr, yr,
      xg, yg, xb, yb.  The values zw, zr, zg, zb can be inferred from:

         z = Z / (X + Y + Z) = 1 - x - y

      Let m be a matrix containing the xyz coordinates of the three
      phosphors:

             xr xg xb
         m = yr yg yb
             zr zg zb

      A column vector W containing the relative XYZ coordinates of white
      can be calculated as:

             Xw   Xr + Xg + Xb   xw/yw
         W = Yw = Yr + Yg + Yb = yw/yw
             Zw   Zr + Zg + Zb   zw/yw

      A matrix M containing the relative XYZ coordinates of the three
      phosphors can be calculated as:

             Xr Xg Xb         1
         M = Yr Yg Yb = m * ( 1 transpose(invert(m) W) )
             Zr Zg Zb         1

      Here * means simply multiply corresponding entries, not matrix
      multiplication.

      If you need only the Y values (for converting to greyscale), this
      simplifies to:

         Yr   yr
         Yg = yg * (invert(m) W)
         Yb   yb

      For convenience, here are the relative XYZ values corresponding
      to the CCIR 709 primaries and D65 white point (the same
      chromaticities used by sRGB):

         Xr = 0.412391   Xg = 0.357584   Xb = 0.180481
         Yr = 0.212639   Yg = 0.715169   Yb = 0.072192
         Zr = 0.019331   Zg = 0.119195   Zb = 0.950532

For consistency, I suggest rewording the end of section 14.9 (Converting
between RGB and XYZ):

old:

              R        X
              G = invM Y
              B        Z

           where invM is the inverse of the matrix M.

new:

              R             X
              G = invert(M) Y
              B             Z


End of proposal.