author Sam Moore Wed, 30 Apr 2014 16:56:11 +0000 (00:56 +0800) committer Sam Moore Wed, 30 Apr 2014 16:56:11 +0000 (00:56 +0800)
Wasted a lot of time with that vector/raster image example (didn't I say I was going to take it out?? Why do I do these things??)
Anyway, I won't let actual sane descriptions of what I've done get in the way of my ongoing over extended metaphor commit messages.

---

After a terrible battle that lasted more than a day and a night, the skeleton overcame Captain Obvious and ate his flesh.
The skeleton incorporated the flesh into its essence and continued on its way, but after a time the flesh began to rot.

"This is mildly annoying" thought the skeleton (using the brain of Captain Obvious), "but I guess it is better than nothing"

However soon parts of the skeleton were dropping off. "If I don't find some sentence structure soon this will end very badly",
thought the skeleton (using the half of its brain that was still working). "Some citations would be nice too" it added.

 chapters/Background.tex patch | blob | history chapters/Conclusion.tex patch | blob | history chapters/Progress.tex patch | blob | history figures/fox-raster.png [new file with mode: 0644] patch | blob figures/fox-vector.pdf [new file with mode: 0644] patch | blob figures/fox-vector.svg [new file with mode: 0644] patch | blob figures/fox.pdf [deleted file] patch | blob | history figures/fox.png [deleted file] patch | blob | history figures/fox.svg [deleted file] patch | blob | history thesis.pdf patch | blob | history

index 751dbe9..700a8b9 100644 (file)
\chapter{Literature Review}\label{Background}

-This chapter will \rephrase{review the literature. It will also include some figures created by us from our test programs to aid with conceptual understanding of the literature.}
+This chapter will \rephrase{review the literature. It will also include some figures created by us from our test programs to aid with conceptual understanding of the literature.} A paper by paper summary of the literature is also available at: \\ \url{http://szmoore.net/ipdf/documents/LiteratureNotes.pdf}.

-\rephrase{TODO: Decide exactly what figures to make, then go make them; so far I have some ideas for a few about Floating Point operations, but none about the other stuff}.
+\rephrase{TODO: If I want to link to the Paper by Paper summary it will need a bit of rewriting}.

\rephrase{TODO: Actually (re)write this entire chapter}.
-\rephrase{????: Do I really want to make this go down to} \verb/\subsubsection/

-A paper by paper summary of the literature is also available at: \\ \url{http://szmoore.net/ipdf/documents/LiteratureNotes.pdf}.
+\rephrase{TODO: Un dot point ify}

+\rephrase{TODO: Citations}

-\rephrase{TODO: Actually make that readable or just remove the link}.
+\rephrase{TODO: Make less terrible}

-\section{Document Formats}

-Since mankind climbed down from the trees... \rephrase{plagiarism alert!}
+\rephrase{TODO: Reconsider sections (do I really want to make this go down to} \verb/\subsubsection/?)

-\subsection{Vector Graphics vs Raster Graphics}
+\rephrase{TODO: :-(}

-Raster Graphics: Stores the exact pixels as they would appear on a device. Causes obvious issues with scaling. Lowest level representation of a document.

-Vector Graphics: Stores relative position of primitives - scales better. BUT still can't scale forever. Vector Graphics must be rasterised before being drawn on most display devices.
+\section{Vector Graphics vs Raster Graphics}

-Vector Graphics formats may contain more information than is shown on the display device; Raster Graphics always contain as much or less pixel information than is shown.
+\newlength\imageheight
+\newlength\imagewidth
+\settoheight\imageheight{\includegraphics{figures/fox-raster.png}}
+\settowidth\imagewidth{\includegraphics{figures/fox-raster.png}}
+
+%Height: \the\imageheight
+%Width: \the\imagewidth
+
+\rephrase{TODO: Distinguish between Raster Formats and the Rasterisation of an image (which may or may not be in a raster format)}
+
+
+\subsubsection{Raster Graphics}
+\begin{itemize}
+       \item Bitmap --- array of colour information for pixels
+       \item Exact pixels in a similar format to how they would appear on a (modern) display device.
+       \begin{itemize}
+               \item Also similar to how they would be stored by a camera or scanner
+               \item \rephrase{Is it misleading to say 2D array? Pixels are actually stored in a 1D array, but conceptually it's nicer to say 2D}
+               \item \rephrase{For that matter, should it described as 3D (3rd dimension = colour)?}
+       \end{itemize}
+       \item Lowest level representation of a document
+       \item Issues with scaling; values of extra pixels must be calculated
+       \item Not convenient to edit; ill suited to text
+\end{itemize}
+
+
+\subsubsection{Vector Graphics}
+\begin{itemize}
+       \item Stores relative position of primitives - scales better
+       \item In particular, \emph{edges} of lines can be zoomed without becomming jagged; sometimes (somewhat misleadingly) described as infinitely sharp''
+       \item Vector Graphics must be rasterised before being drawn on most display devices.
+       \item Still can't scale forever due to use of fixed size floats
+\end{itemize}
+
+\subsubsection{Resolution and Raster Graphics}
+\begin{itemize}
+       \item DPI = dots (pixels) per inch differs per display device - a rastered image looks different on different display devices
+       \item PostScript/PDF use 72 points per inch; this means a rasterised image will look the same in all pdf viewers regardless of the display.
+       \item Tex uses 72.27 points per inch (?)
+       \item The vector image was rastered at 96 points per inch
+       \item Hence, have to scale by 72.27/96 = 0.7528125 to get the vector and rastered version to look exactly the same in the pdf
+\end{itemize}

-\rephrase{Captain Obvious strikes again!} \\
-Figure \ref{fox} shows an example of scaling. The top image is a vector graphics drawing which has been scaled. The bottom image was a raster image of the original drawing which has then been scaled by the same amount. Scaling in = interpolation/antialiasing/just scale the pixels depending on the viewer and scale; scaling out = blurring of pixels by averaging of neighbours. If you are viewing this document in a PDF viewer you can try it yourself! Otherwise, welcome to the 21st century.

\begin{figure}[H]
\centering
-       \includegraphics[width=0.5\textwidth]{figures/fox.pdf}
-       \includegraphics[width=0.5\textwidth]{figures/fox.png}
-       \caption{Scaling of Vector and Raster Graphics}\label{fox}
+
+       \includegraphics[scale=0.7528125]{figures/fox-vector.pdf}
+       \includegraphics[scale=0.7528125]{figures/fox-raster.png}
+       \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{Scaling of vector and Raster Graphics}\label{vector-vs-raster}
\end{figure}
-\rephrase{I am torn as to whether to use a Fox or Rabbit or Rox here}.

-\subsection{Document Format Categories}

-Main reference: Pixels or Perish\cite{hayes2012pixels}
+Figure \ref{vector-vs-raster} shows a vector image (left) which has been rasterised (right). At the original scale the two foxes should appear to be mirror images\footnote{If I've worked out the scaling to account for dpi differences between inkscape and latex/pdf correctly}. When the scale is increased, the edges of the vector image remain sharp, whilst the raster image begins to appear jagged. PDF viewers will typically use antialiasing to smooth the edges of a scaled bitmap, causing the image to appear blurred.\footnote{In the Atril Document Viewer 1.6.0 this image will only be antialiased at zoom levels $\leq 125\%$}.

+Various ways to end this section:
\begin{enumerate}
-       \item DOM - eg: HTML/XMLish - defined in terms of elements that can contain other elements
-       \item Programming Language - eg: PostScript - programmer (or program) produces a program that is interpreted
-       \item Combination - eg: Javascript with HTML/XML - Program is interpreted that modifies the DOM.
+       \item \rephrase{It should be obvious that documents containing text must use the vector graphics format, and so the remainder of this chapter will concentrate on the latter}.
+       \item \rephrase{As can be seen in Figure \ref{fox}, if we were to decide to pursue infinite precision'' in raster graphics we would be shooting ourselves in both feet and then the face before we even started. The rest of this chapter will concentrate on vector graphics.}
+       \item \rephrase{You can't have infinite precision in raster graphics by definition, therefore we no longer care about them in this report.}
+       \item \rephrase{This report being in a vector format is a clue that we only care about vector formats}.
+\end{enumerate}
+
+\section{Primitives in Vector Graphics Formats (and how they are Rendered)}
+
+\subsection{Bezier Curves}
+\rephrase{I did an ipython notebook on this in February, but I forgot all of it}
+
+\subsection{Text}
+Text is just Bezier Curves
+
+\subsection{Shapes}
+Shapes are just bezier curves joined together.
+
+\subsection{Other Things}
+We don't really care about other things (ie: Colour gradients etc) in this report.
+
+\section{Document Representations}
+
+\rephrase{The file format can be either human readable\footnote{For some definition of human and some definition of readable} or binary\footnote{So, our viewer is basically a DOM style but stored in a binary format}. Can also be compressed or not. Here we are interested in how the document is interpreted or traversed in order to produce graphics output.}
+
+
+
+\subsection{Interpreted Model}
+
+\rephrase{Did I just invent that terminology or did I read it in a paper? Is there actually existing terminology for this that sounds similar enough to Document Object Model'' for me to compare them side by side?}
+
+\begin{itemize}
+       \item This model treats a document as the source code program which produces graphics
+       \item Arose from the desire to produce printed documents using computers (which were still limited to text only displays).
+       \item Typed by hand or (later) generated by a GUI program
+       \item PostScript --- largely supersceded by PDF on the desktop but still used by printers\footnote{Desktop pdf viewers can still cope with PS, but I wonder if a smartphone pdf viewer would implement it?}
+       \item \TeX --- Predates PostScript! {\LaTeX } is being used to create this very document and until now I didn't even have it here!
\begin{itemize}
-               \item The lines are becomming increasingly blurred between 1. and 2.
-               \item In the case of Javascript/HTML, a special DOM element \verb/<canvas>/ allows even lower level manipulation of graphics.
+               \item I don't really want to go down the path of investigating the billion steps involved in getting \LaTeX into an actually viewable format
+               \item There are interpreters (usually WYSIWYG editors) for \LaTeX though
+               \item Maybe if \LaTeX were more popular there would be desktop viewers that converted \LaTeX directly into graphics
\end{itemize}
-\end{enumerate}
+       \item Potential for dynamic content, interactivity; dynamic PostScript, enhanced Postscript

-Can be either human readable\footnote{For some definition of human and some definition of readable} or binary\footnote{So, our viewer is basically a DOM style but stored in a binary format}
+       \item Scientific Computing --- Mathematica, Matlab, IPython Notebook --- The document and the code that produces it are stored together
+       \item Problems with security --- Turing complete, can be exploited easily
+\end{itemize}

-\subsection{Modern Graphics Formats}
+\subsection{Crippled Interpreted Model}

-PostScript: Not actually widely used now, but PDF is basically the same thing.
-PDF: A way for adobe to make money
-SVG: Based on the DOM model, vector format
-BMP,PNG,GIF: Are these even worth mentioning?
+\rephrase{I'm pretty sure I made that one up}

-HTML: With the evolution of JavaScript and CSS, this has actually become a competitive document format; it can display much more complex dynamic content than eg: PDF.
+\begin{itemize}
+       \item PDF is PostScript but without the Turing Completeness
+       \item Solves security issues, more efficient
+\end{itemize}

-Web based documents still suffer from precision issues (JavaScript is notorious for its representation of everything, even integers, as floats, so you get rounding errors even with integer maths), and it also has other limitations (requires reasonably skilled programmer to create Javascript and/or a disgusting GUI tool that auto generates 10000 lines to display a button (I have seen one of these)). \rephrase{Hate on javascript a bit less maybe.}
+\subsection{Document Object Model}

-\subsection{Precision Limitations}
+\begin{itemize}
+       \item DOM = Tree of nodes; node may have attributes, children, data
+       \item XML (SGML) is the standard language used to represent documents in the DOM
+       \item XML is plain text
+       \item SVG is a standard for a vector graphics language conforming to XML (ie: a DOM format)
+\end{itemize}
+
+\subsection{Blurring the Line --- Javascript}
+
+\begin{itemize}
+       \item The document is expressed in DOM format using XML/HTML/SVG
+       \item A Javascript program is run which can modify the DOM
+       \item At a high level this may be simply changing attributes of elements dynamically
+       \item For low level control there is canvas2D and even WebGL which gives direct access to OpenGL functions
+       \item Javascript can be used to make a HTML/SVG interactive
+       \begin{itemize}
+               \item Overlooking the fact that the SVG standard already allows for interactive elements...
+       \end{itemize}
+       \item Javascript is now becoming used even in desktop environments and programs (Windows 8, GNOME 3, Cinnamon, Game Maker Studio) ({\bf shudder})
+       \item There are also a range of papers about including Javascript in PDF Pixels or Perish'' being the only one we have actually read\cite{hayes2012pixels}
+       \begin{itemize}
+               \item I have no idea how this works; PDF is based on PostScript... it seems very circular to be using a programming language to modify a document that is modelled on being a (non turing complete) program
+               \item This is yet more proof that people will converge towards solutions that work'' rather than those that are optimal or elegant
+               \item I guess it's too much effort to make HTML look like PDF (or vice versa) so we could phase one out
+       \end{itemize}
+\end{itemize}
+
+
+
+
+\section{Precision Limitations of Modern Documents}
+
+\rephrase{All this is very interesting and provides important context, but it is not actually directly related to the problem of infinite precision which we are going to try and solve}.
+
+\subsection{Limitations Imposed By Standards}
+\begin{itemize}
+       \item Implementations of PostScript and PDF must by definition restrict themselves to IEEE binary32 single precision'' floating point number representations in order to conform to the standards\cite{plrm, pdfref17}.
+       \item Implementations of SVG are by definition required to use IEEE binary32 as a {\bf minimum}. High Quality'' SVG viewers are required to use at least IEEE binary64.\cite{svg2011-1.1}
+\end{itemize}
+
+
+\subsection{Limitations Imposed By Graphics APIs and/or GPUs}
+
+It's not really the standard's fault (although they could specify double); they specify IEEE because underlying hardware must use IEEE.
+
+\begin{itemize}
+       \item Internal representations are GPU dependent\cite{hillesland2004paranoia}
+       \item OpenGL standards specify: binary16, binary32, binary64
+       \item OpenVG aims to become a standard API for SVG viewers but it uses binary32 and may be {\bf worse} internally\cite{rice2008openvg}
+\end{itemize}
+
+\subsection{Limitations Imposed By CPU}
+
+Even if we don't use the GPU, CPU's are restricted in their representation of floating point numbers by the IEEE standard.
+
+\rephrase{AND THUS WE FINALLY GET TO THE POINT}

\section{Representation of Numbers}

-Although this project has been motivated by a desire for more flexible document formats, the fundamental source of limited precision in vector document formats such as PDF and PostScript is the use of floating point numbers to represent the coordinates of vertex positions. In particular, implementations of PostScript and PDF must by definition restrict themselves to IEEE binary32 single precision'' floating point number representations in order to conform to the standards\cite{plrm, pdfref17}.
+Although this project has been motivated by a desire for more flexible document formats, the fundamental source of limited precision in vector document formats is the restriction to IEEE floating point numbers for representation of coordinates.
+
+Whilst David Gow will be focusing on structures \rephrase{and the use of multiple coordinate systems} to represent a document so as to avoid or reduce these limitations\cite{proposalGow}, the focus of our own research will be \rephrase{increased precision in the representation of real numbers so as to get away with using a single global coordinate system}.

-Whilst David Gow will be focusing on how to structure a document format so as to avoid or reduce these limitations\cite{proposalGow}, the focus of our own research will be \rephrase{NUMBERS}.
+\subsection{The IEEE Standard}

\subsection{Floating Point Number Representations}

@@ -93,6 +225,19 @@ The most a result can be rounded in conversion to a floating point number is the

\rephrase{Even though that paper that claims double is the best you will ever need because the error can be as much as the size of a bacterium relative to the distance to the moon}\cite{} \rephrase{there are many cases where increased number of bits will not save you}.\cite{HFP}

+\subsection{Examples of Precision Related Errors in Floating Point Arithmetic}
+
+\subsection{Relate This to the Sorts of Maths Done By Document Formats}
+
+\subsection{Techniques for Arbitrary Precision Arithmetic}
+
+\begin{itemize}
+       \item Fast2SUM for summation (and multiplication).
+       \item Guard digits.
+       \item Other techniques
+       \item Hardware techniques that improve speed (which may be beneficial because you can get away with higher precision in hardware)
+       \item Anything you can do in hardware you can do in software but it will be slower and have more segmentation faults
+\end{itemize}

\subsection{Alternate Number Representations}

index 8d9620c..22ccc64 100644 (file)
@@ -4,6 +4,22 @@ This report has provided motivation for considering approaches to achieving an i

\section{Acheived Milestones}

-\section{Areas of further Research}
+\section{Areas of further work}
+
+\begin{itemize}
+       \item Continue looking for relevant literature
+       \item Implement all those tests mentioned in Chapter \ref{Introduction}
+       \item \rephrase{Actually identify the techniques I will use} {\bf THIS ONE SHOULD BE DONE BEFORE I HAND IN THE LITERATURE REVIEW!}
+       \item Possible Ultimate Goal: Implement (a subset) of SVG and then show an SVG document that we can render but a browser can't
+       \begin{itemize}
+               \item This means extending our viewer to be able to read (a subset) SVG
+               \item Can already read XML, so this shouldn't actually be too bad
+               \begin{itemize}
+                       \item Emphasis on {\bf subset}
+                       \item (I've seen the SVG standard; I'm talking about implementing the 18 pages under Basic Shapes''. The other 818 pages can complain to someone who cares.)
+               \end{itemize}
+               \item Suggestion to David that he probably won't like (or read): Make his octree structure specifiable as an SVG extension
+       \end{itemize}
+\end{itemize}

\section{Witty Conclusion Goes Here}
index d67e913..808e7c0 100644 (file)
@@ -14,6 +14,14 @@ We wrote a very simple OpenGL 1.1 program to experiment with, and then David Gow

\end{itemize}

+\section{Document Format}
+
+Currently we effectively have a DOM format but with the following non-features:
+\begin{itemize}
+       \item Binary file format (non standard; not XML)
+       \item Only rectangles.
+\end{itemize}
+
\section{Floating Point Number Representations}

\rephrase{I have\footnote{Ok... will have''} some figures that I would prefer to include in Chapter \ref{Background} when I am talking about the papers that inspired them.}
@@ -28,6 +36,8 @@ We wrote a very simple OpenGL 1.1 program to experiment with, and then David Gow

Techniques for dealing with FP numbers can be implemented in software (CPU) or on dedicated hardware (FPU). We are able to run FP arithmetic on arbitrary simulations of FPUs created using VHDL. \rephrase{Hopefully explore this a bit in Chapter \ref{Background}}.

+
+
\section{Version Control}

Git is a distributed version control system widely used in the development of open source software\cite{}. All rescources created for or used by this project have been placed in git repositories on several servers. The repositories are publically accessable at \url{http://git.ucc.asn.au}
diff --git a/figures/fox-raster.png b/figures/fox-raster.png
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diff --git a/figures/fox-vector.pdf b/figures/fox-vector.pdf
new file mode 100644 (file)
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diff --git a/figures/fox-vector.svg b/figures/fox-vector.svg
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