-Most raster displays are based on an additive red-green-blue colour representation which matches the human eye's response to light\cite{citationneeded}. In 1984, Porter and Duff introduced a fourth colour channel to be used when combining rasterised images called the ``alpha'' channel, analogous to the transparency of a pixel\cite{porter1984compositing}. Elements can be rendered seperately, with the four colour channels of successively drawn elements being combined according to one of several possible operations described by Porter and Duff.
+Colour raster displays are based on an additive red-green-blue $(r,g,b)$ colour representation which matches the human eye's response to light\cite{computergraphics2}. In 1984, Porter and Duff introduced a fourth colour channel for rasterised images called the ``alpha'' channel, analogous to the transparency of a pixel\cite{porter1984compositing}. In compositing models, elements can be rendered seperately, with the four colour channels of successively drawn elements being combined according to one of several possible operations.
+
+In the ``painter's model'' as described by the SVG standard, Porter and Duff's ``over'' operation is used when rendering one primitive over another\cite{svg2011-1.1}.
+Given an existing pixel $P_1$ with colour values $(r_1, g_1, b_1, a_1)$ and a pixel $P_2$ with colours $(r_2, g_2, b_2, a_2)$ to be painted over $P_1$, the resultant pixel $P_T$ has colours given by:
+\begin{align}
+ a_T &= 1 - (1-a_1)(1-a_2) \\
+ r_T &= (1 - a_2)r_1 + r_2 \quad \text{(similar for $g_T$ and $b_T$)}
+\end{align}
+It should be apparent that alpha values of $1$ correspond to an opaque pixel; that is, when $a_2 = 1$ the resultant pixel $P_T$ is the same as $P_2$.
+When the final pixel is actually drawn on an rgb display, the $(r, g, b)$ components are $(r_T/a_T, g_T/a_T, b_T/a_T)$.