-Basic vector primitives composed of B{\'e}ziers may be rendered using only integer operations, once the starting and ending positions are rounded to the nearest pixel.
+The literature discussed in Chapter \ref{Background} is primarily concerned with the rendering process for graphical primitives, namely outlines defined by B\'{e}zier curves. We have seen that basic vector primitives composed of B{\'e}ziers may be rendered using only integer operations, once the starting and ending positions are rounded to the nearest pixel.
However, a complete document will contain many such primitives which in general cannot all be shown on a display at once. A ``View'' rectangle can be defined to represent the size of the display relative to the document. To interact with the document a user can change this view through scaling or translating with the mouse.
However, a complete document will contain many such primitives which in general cannot all be shown on a display at once. A ``View'' rectangle can be defined to represent the size of the display relative to the document. To interact with the document a user can change this view through scaling or translating with the mouse.
-Moving the mouse\footnote{or on a touch screen, swiping the screen} by a distance $(\Delta x, \Delta y)$ relative to the size of the view should translate it by the same amount\cite{}:
+Moving the mouse (or on a touch screen, swiping the screen) by a distance $(\Delta x, \Delta y)$ relative to the size of the view should translate it by the same amount:
\end{align}
The effect of this transformation is that, measured relative to the view rectangle, the distance of primitives with coordinates $(x, y)$ to the point $(x_0, y_0)$ will decrease by a factor of $s$. For $s < 1$ the operation is ``zooming out'' and for $s > 1$, ``zooming in''.
\end{align}
The effect of this transformation is that, measured relative to the view rectangle, the distance of primitives with coordinates $(x, y)$ to the point $(x_0, y_0)$ will decrease by a factor of $s$. For $s < 1$ the operation is ``zooming out'' and for $s > 1$, ``zooming in''.