-\rephrase{Woah, an entire page with only one citation ham fisted in after I had written the rest... and the ``actually writing it'' phase of the Lit Review is off to a great start.}
-
-\newlength\imageheight
-\newlength\imagewidth
-\settoheight\imageheight{\includegraphics{figures/fox-raster.png}}
-\settowidth\imagewidth{\includegraphics{figures/fox-raster.png}}
-
-%Height: \the\imageheight
-%Width: \the\imagewidth
-
-
-\begin{figure}[H]
- \centering
- \includegraphics[scale=0.7528125]{figures/fox-vector.pdf}
- \includegraphics[scale=0.7528125]{figures/fox-raster.png}
- \caption{Original Vector and Raster Images}\label{vector-vs-raster}
-\end{figure} % As much as I hate to break up the party, these fit best over the page (at the moment)
-\begin{figure}[H]
- \centering
- \includegraphics[scale=0.7528125, viewport=210 85 280 150,clip, width=0.45\textwidth]{figures/fox-vector.pdf}
- \includegraphics[scale=0.7528125, viewport=0 85 70 150,clip, width=0.45\textwidth]{figures/fox-raster.png}
- \caption{Scaled Vector and Raster Images}\label{vector-vs-raster-scaled}
-\end{figure}
-
-\section{Rendering Vector Images}
-
-Throughout Section \ref{vector-vs-raster-graphics} we were careful to refer to ``modern'' display devices, which are raster based. It is of some historical significance that vector display devices were popular during the 70s and 80s, and so algorithms for drawing a vector image directly without rasterisation exist. An example is the shading of polygons which is somewhat more complicated on a vector display than a raster display\cite{brassel1979analgorithm, lane1983analgorithm}.
-
-All modern displays of practical interest are raster based. In this section we explore the structure of vector graphics in more detail, and how different primitives are rendered.
-
-\rephrase{After the wall of citationless text in Section \ref{vector-vs-raster-graphics} we should probably redeem ourselves a bit here}
-
-\subsection{Bezier Curves}
-
-The bezier curve is of vital importance in vector graphics.
-
-\rephrase{Things this section lacks}
-\begin{itemize}
- \item Who came up with them (presumably it was a guy named Bezier)
- \item Flesh out how they evolved or came into use?
- \item Naive algorithm
- \item De Casteljau Algorithm
-\end{itemize}
-
-Recently, Goldman presented an argument that Bezier's could be considered as fractal in nature, a fractal being the fixed point of an iterated function system\cite{goldman_thefractal}. Goldman's proof depends upon a modification to the De Casteljau Subdivision algorithm. Whilst we will not go the details of the proof, or attempt comment on its theoretical value, it is interesting to note that Goldman's algorithm is not only worse than the De Casteljau algorithm upon which it was based, but it also performs worse than a naive Bezier rendering algorithm. Figure \ref{bezier-goldman} shows our results using implementations of the various algorithms in python.
-
-\begin{figure}[H]
- \centering
- \includegraphics[width=0.7\textwidth]{figures/bezier-goldman.png}
- \caption{Performance of Bezier Subdivision Algorithms}\label{bezier-goldman}
-\end{figure}
-
-\rephrase{Does the Goldman bit need to be here? Probably NOT. Do I need to check very very carefully that I haven't made a mistake before saying this? YES. Will I have made a mistake? Probably.}
-
-
-\subsection{Shapes}
-Shapes are just bezier curves joined together.
-
-\subsubsection{Approximating a Circle Using Cubic Beziers}
-
-An example of a shape is a circle. We used some algorithm on wikipedia that I'm sure is in Literature somewhere
-\cite{citationneeded} and made a circle. It's in my magical ipython notebook with the De Casteljau stuff.
-
-\subsection{Text}
-Text is just Bezier Curves, I think we proved out point with the circle, but maybe find some papers to cite\cite{citationneeded}