% affiliation.
\institute[UWA]% (optional) {Universities of Western Australia}
-{Supervisors: Tim French, Rowan Davies}
+{Supervisors: Tim French, Rowan Davies \\ Colleagues: David Gow}
\date[CSS 2009]{\today} % change the actual date
%\titlegraphic{\includegraphics[width=3cm]{./Logos/WAMSI.png}}
\end{frame}
+\begin{frame}
+\begin{itemize}
+ \item Vector graphics scale better than raster graphics
+\end{itemize}
+ \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}
+\end{frame}
+
\begin{frame}
\frametitle{Is there a zoom limit?}
\centering
-\includegraphics{../figures/koch1.pdf}
+\includegraphics{../figures/koch.pdf}
\end{frame}
\section{Floating Point}
\begin{itemize}
\item SVG, PostScript, PDF specify IEEE-754 \emph{single} floating point number representations
\item Range of values: $\approx 3 \times 10^{-38} \to 3 \times 10^{+38}$
+ \item Bigger than size of Universe?
+\end{itemize}
+\end{frame}
+
+\begin{frame}
+\frametitle{Floating Point Definition}
+\begin{itemize}
\item Rough Floating Point Definition\footnote{IEEE-754 is more complicated}:
\begin{align}
\end{align}
\item $m$ and $E$ are encoded in a \emph{fixed length} string of bits
\item Floating Point $\approx$ Scientific Notation for computers
-
\end{itemize}
\end{frame}
\frametitle{Visualisation of Floats II}
\begin{itemize}
\item Difference between successive floats
+ \item Further from origin $\implies$ less precision
\end{itemize}
\centering
\includegraphics[width=0.8\textwidth]{../figures/floats_diff.pdf}
\begin{frame}
\frametitle{Precision is limited}
+ \begin{itemize}
+ \item Eg: Fox scaled to width of $\approx 10^{-6}$ viewed at zoom of $\approx 10^{8}$
+ \item (Outline should look like images in first slide)
+ \end{itemize}
\centering
\includegraphics[width=0.8\textwidth]{../figures/fox-vector_highzoom1.png}
\end{frame}
+
\begin{frame}
\frametitle{Structure of Vector Graphics}
\begin{itemize}
\includegraphics[width=0.5\textwidth]{../figures/fox-vector_face_with_bezbounds.png}
\end{frame}
+\begin{frame}
+\frametitle{Vector Graphics Viewer Features}
+\begin{itemize}
+ \item GPU (OpenGL) or CPU (custom) rendering
+ \item Import SVG into current View location
+ \item Control through scripts (Python) or Qt4 GUI
+\end{itemize}
+\centering
+\includegraphics[width=0.4\textwidth]{../figures/controlpanel_screenshot.png}
+
+\end{frame}
+
\begin{frame}
\frametitle{Viewing Vector Graphics}
\end{frame}
+\begin{frame}
+ \frametitle{Quantitative Results}
+ \begin{itemize}
+ \item Invariance of grid of lines after scaling
+ \end{itemize}
+ \centering
+ \includegraphics[width=0.8\textwidth]{../figures/cumulative_error_grid.pdf}
+\end{frame}
+
+
\section{Demonstration}
\begin{itemize}
\item Implement more of the SVG standard
\item Trial alternative number representations
- \item Allow for saving and loading SVGs with arbitrary precision
+ \item Allow for saving and loading
+ \item Optimisations, eg: clip objects that are not visible
+ \item Compile for Windows (MinGW)
\end{itemize}
\end{frame}
-%\section{References}
+
\begin{frame}
- \frametitle{References \& More information}
+ \frametitle{Acknowledgements}
\begin{itemize}
\item Work on SVG viewer collaborative with David Gow
\begin{itemize}
\item See David Gow's presentation about Quadtrees
\end{itemize}
+ \item Supervisors: Tim French and Rowan Davies
+ \end{itemize}
+\end{frame}
+%\section{References}
+\begin{frame}
+ \frametitle{References \& More information}
+ \begin{itemize}
\item Muller et al, \emph{Handbook of Floating Point Arithmetic},
\item Hearn, Baker \emph{Computer Graphics}
\item Kahan et al, \emph{IEEE-754} (1985 and 2008 revision)
\end{frame}
%\section{Questions}
-
-
\begin{frame}
-\frametitle{Q: Why not just increase \\ floating point precision?}
-\begin{itemize}
- \item Any fixed precision format will still give inexact results
- \item Eg: Accuracy of rendering a grid
-\end{itemize}
+\frametitle{Q: Why not just increase float precision?}
+ \begin{itemize}
+ \item GPU uses singles anyway
+ \item Can use CPU for bounds transforms
+ \item But eventually lose precision for any \emph{fixed} precision float
+ \end{itemize}
+ \centering
+ \includegraphics[width=0.8\textwidth]{{../figures/loss_of_precision_grid_0.5}.pdf}
\end{frame}
\begin{frame}
+
\frametitle{Q: Arbitrary precision floats?}
\begin{align}
X &= m \times 2^{E}
\end{align}
\begin{itemize}
\item $m$ and $E$ are of arbitrary size
- \item Implemented by MPFR or GMP
+ \item Implemented by MPFR (based on GMP)
\item Difficulties:
\begin{itemize}
\item Need to manually set precision (size) of $m$
\frac{1}{3} &= 0.3333333333333333333333 \text{ ... } \times 10^0
\end{align}
\item How do you choose when to increase precision?
+ \item GMP Rational implementation automatically increases size, but MPFR floats do not
\end{itemize}
\end{itemize}
\end{frame}
\end{frame}
+\begin{frame}
+ \frametitle{Quantitative?}
+% \begin{figure}[H]
+ \centering
+ \includegraphics[width=0.4\textwidth]{../figures/grid_0_1e-6.png}
+ \includegraphics[width=0.4\textwidth]{../figures/{grid_0.5_1e-6}.png} \\
+ \includegraphics[width=0.4\textwidth]{../figures/grid_1_1e-6.png}
+ \includegraphics[width=0.4\textwidth]{../figures/grid_2_1e-6.png}
+ %\caption{Effect of applying \eqref{view-transformation} to a grid of lines seperated by 1 pixel \\
+ %a) Near origin (denormals) b), c), d) Increasing the exponent of $(v_x,v_y)$ by 1}\label{grid-precision}
+%\end{figure}
+
+
+\end{frame}
+
+\begin{frame}
+ \frametitle{Bresenham and Wu}
+ \centering
+ \includegraphics[width=0.5\textwidth]{../figures/line1.pdf}
+ \includegraphics[width=0.5\textwidth]{../figures/line2.pdf}
+\end{frame}
+
+\begin{frame}
+ \frametitle{Bonus: IEEE-754 on GPUs}
+ \begin{itemize}
+ \item Inconsistent behaviour of calculations on different GPUs
+ \item {\small Eg: $x^2 + y^2 < 1$ (shading a circle) zoomed in on the edge.}
+ \end{itemize}
+ \centering
+ \includegraphics[width=0.4\textwidth]{../figures/gpufloats.pdf}
+\end{frame}
\end{document}
git.ucc.asn.au / ipdf / sam.git / blobdiff
UCC git Repository :: git.ucc.asn.au