+The emergence of the internet, web browsers, XML/HTML, JavaScript and related technologies has seen a revolution in the ways in which information can be presented digitally, and the PDF standard itself has begun to move beyond static text and figures\cite{hayes2012pixels, barnes2013embedding}. However, the popular document formats are still designed with the intention of showing information at either a single, fixed level of detail, or a small range of levels.
+
+As most digital display devices are smaller than physical paper medium, all useful viewers are able to ``zoom'' to a subset of the document. Vector graphics formats including PostScript and PDF support rasterisation at different zoom levels\cite{plrm, pdfref17}, but the use of fixed precision floating point numbers causes problems due to imprecision either far from the origin, or at a high level of detail\cite{goldberg91whatevery, goldberg1992thedesign}.
+
+We are now seeing a widespread use of mobile computing devices with touch screens, where the display size is typically much smaller than paper pages and traditional computer monitors; it seems that there is much to be gained by breaking free of the restricted precision of traditional document formats.
+
+\section{Aim}
+
+In this project, we will explore the state of the art of current document formats including PDF, PostScript, SVG, HTML, and the limitations of each in terms of precision.
+We will consider designs for a document format allowing graphics primitives at an arbitrary level of zoom with no loss of detail. We will refer to such a document format as ``infinite precision''. A viewer and editor will be implemented as a proof of concept; we adopt a low level, ground up approach to designing this viewer so as to not become restricted by any single existing document format.
+
+\rephrase{New bit} \\
+It is necessary to clarify what we mean by ``infinite'' precision. We do not propose to be able to contain an infinite amount of information within a document. The goal is to be able to render a primitive at the same level of detail it is specified by a document format. For example, the precision of coordinates of primitives drawn in a graphical editor will always be limited by the resolution of the display on which they are drawn, but not by the viewer.
+
+There are many possible applications for documents in which precision is unlimited. Several areas of use include: visualisation of extremely large or infinite data sets; visualisation of high precision numerical computations; digital artwork; computer aided design; and maps.
+
+\section{Methods}
+
+Initial research and software development is being conducted in collaboration with David Gow\cite{proposalGow}. Once a simple testbed application has been developed, we will individually explore approaches for introducing arbitrary levels of precision; these approaches will be implemented as alternate versions of the same software. The focus will be on drawing simple primitives (lines, polygons, circles). However, if time permits we will explore adding more complicated primitives (font glyphs, bezier curves, embedded bitmaps).
+
+At this stage we have identified two possible areas for individual research:
+
+\begin{enumerate}
+
+ \item {\bf Arbitrary Precision real valued numbers} --- Sam Moore
+
+ We plan to investigate the representation of real values to a high or arbitary degree of precision. Such representations would allow for a document to be implemented
+ using a single global coordinate system. However, we would expect a decrease in performance with increased complexity of the data structure used to represent a real value. \rephrase{Both software and hardware techniques will be explored.} We will also consider the limitations imposed by performing calculations on the GPU or CPU.
+
+ Starting points for research in this area are Priest's 1991 paper, ``Algorithms for Arbitrary Precision Floating Point Arithmetic''\cite{priest1991algorithms}, and Goldberg's 1992 paper ``The design of floating point data types''\cite{goldberg1992thedesign}. \rephrase{A more recent and comprehensive text book, ``Handbook of Floating Point Arithmetic''\cite{hfpa}, published in 2010, has also been identified as highly relevant.}
+
+ \item {\bf Local coordinate systems} --- David Gow \cite{proposalGow}
+
+ An alternative approach involves segmenting the document into different regions using fixed precision floats to define primitives within each region. A quadtree or similar data structure could be employed to identify and render those regions currently visible in the document viewer.\rephrase{Say more here?}
+
+\end{enumerate}
+\pagebreak
+We aim to compare these and any additional implementations considered using the following metrics: