Billy Biggs 97049311 wbiggs@uwaterloo.ca
Red | ||
Green | ||
Blue | ||
White (D65) |
These are the primaries specified by both ITU-R BT.709 and sRGB. Given these chromanicities, we are given a relationship between the coordinates and the values of , , and . For example, the value of any colour can be expressed as a linear combination of the values for , , and individually. Since we can derive those from the chromanicities, we define constants , and to represent the factors of which the chromanicities contribute to the resulting value. To solve these values, I'm using the notation and ideas from the method described in Foley/van Dam.
In order to compute the values of , and , we need a known reference point. For this we will use the D65 white point (black body at 6500K) and use unity luminance () and map this to .
We can now use these to solve for , and by taking the inverse of the following:
We get:
Submitting back, we get the final matrix:
Inverting this we get the desired matrix:
Raw version, relative sensitivity on the y axis, wavelength in nanometers along the x axis. |
Normalized version such that each integral sums to unity. Again, relative sensitivity on the y axis, wavelength in nanometers along the x axis. |