# CS788 Assignment 1: Written problems

	Billy Biggs
97049311
wbiggs@uwaterloo.ca


# Problem 2: sRGB Conversion Matrix

The colour primaries used are defined in xyY space.

 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:

# Problem 3: sRGB Matching Functions

The matching functions are created by converting the xbar, ybar and zbar quantities to sRGB-space.
 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.