-Algorithms for shading on vector displays involved drawing equally spaced lines in the region with endpoints defined by the boundaries of the region\cite{brassel1979analgorithm}. Apart from being unrealistic, these techniques required a computationally expensive sorting of vertices\cite{lane1983analgorithm}.
+In the ``painter's model'' as described by the SVG standard the ``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 $(r_T/a_T, g_T/a_T, b_T/a_T)$.