author Sam Moore Sun, 12 Oct 2014 20:23:04 +0000 (04:23 +0800) committer Sam Moore Sun, 12 Oct 2014 20:23:04 +0000 (04:23 +0800)
12 files changed:
 figures/view_transformation.pdf [new file with mode: 0644] patch | blob figures/view_transformation_cumulative.pdf [new file with mode: 0644] patch | blob figures/view_transformation_fail.pdf [new file with mode: 0644] patch | blob figures/view_transformation_fail.svg [new file with mode: 0644] patch | blob figures/view_transformation_paths.pdf [new file with mode: 0644] patch | blob figures/view_transformation_paths.svg [new file with mode: 0644] patch | blob presentation/cumulative_float_SHORT.mkv [new file with mode: 0644] patch | blob presentation/float.mkv [new file with mode: 0644] patch | blob presentation/path-Gmprat.mkv [new file with mode: 0644] patch | blob presentation/presentation.nav patch | blob | history presentation/presentation.pdf patch | blob | history presentation/presentation.tex patch | blob | history

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+           id="path9899-8" /></g></g><text
+       xml:space="preserve"
+       style="font-size:9.60000038px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:center;line-height:125%;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#ff0000;fill-opacity:1;stroke:none;font-family:DejaVu Serif;-inkscape-font-specification:DejaVu Serif"
+       x="303.01843"
+       y="-40.359756"
+       id="text12659"
+       sodipodi:linespacing="125%"
+       transform="scale(1,-1)"><tspan
+         sodipodi:role="line"
+         id="tspan12661"
+         x="303.01843"
+         y="-40.359756">Drifting of Paths</tspan></text>
+<text
+       xml:space="preserve"
+       style="font-size:9.60000038000000089px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:center;line-height:125%;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#00ff00;fill-opacity:1;stroke:none;font-family:DejaVu Serif;-inkscape-font-specification:DejaVu Serif"
+       x="78.156982"
+       y="-41.000385"
+       id="text12663"
+       sodipodi:linespacing="125%"
+       transform="scale(1,-1)"><tspan
+         sodipodi:role="line"
+         id="tspan12665"
+         x="78.156982"
+         y="-41.000385">Inserted SVG</tspan></text>
+<text
+       xml:space="preserve"
+       style="font-size:9.60000038px;font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;text-align:center;line-height:125%;letter-spacing:0px;word-spacing:0px;text-anchor:middle;fill:#000000;fill-opacity:1;stroke:none;font-family:DejaVu Serif;-inkscape-font-specification:DejaVu Serif"
+       x="192.18929"
+       y="-17.937672"
+       id="text12686"
+       sodipodi:linespacing="125%"
+       transform="scale(1,-1)"><tspan
+         sodipodi:role="line"
+         id="tspan12688"
+         x="193.71741"
+         y="-17.937672">We only need to transform the Paths with increased precision </tspan></text>
+</g></svg>
\ No newline at end of file
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@@ -3,59 +3,71 @@
-\headcommand {\sectionentry {1}{Motivation \& Background}{4}{Motivation \& Background}{0}}
+\headcommand {\sectionentry {3}{Vector Graphics Viewer}{10}{Vector Graphics Viewer}{0}}
+\headcommand {\sectionentry {5}{Arbitrary Precision Rationals}{15}{Arbitrary Precision Rationals}{0}}
index 9021d5a..955ca05 100644 (file)
Binary files a/presentation/presentation.pdf and b/presentation/presentation.pdf differ
index 7d5494b..8b4108c 100644 (file)
}

-\begin{frame}[plain]
-\frametitle{Contents}
-  \tableofcontents
-  % You might wish to add the option [pausesections]
-\end{frame}

\begin{frame}
\frametitle{Summary}
\begin{itemize}
-               \item Vector graphics allow scaling but not arbitrary scaling
-               \item We implemented a vector graphics viewer that does allow arbitrary scaling
-               \item ... but it will take an arbitrary amount of time
+               \item Vector graphics allow detail to be scaled but not by an arbitrary amount
+               \item We've implemented a vector graphics viewer which does allow arbitrary scaling
\end{itemize}
\end{frame}

+%\begin{frame}[plain]
+%\frametitle{Contents}
+%  \tableofcontents
+  % You might wish to add the option [pausesections]
+%\end{frame}
+
+
% Start of presentation slides
-\section{Motivation \& Background}
+\section{Motivation}
\begin{frame}
\frametitle{Graphics Formats}
\begin{itemize}
\end{frame}

+
+
+
\begin{frame}
-\frametitle{Why is there a zoom limit?}
+\frametitle{Is there a zoom limit?}
\centering
\includegraphics{../figures/koch1.pdf}
\end{frame}

+\section{Floating Point}
+
\begin{frame}
-\frametitle{Why is there a zoom limit?}
+\frametitle{Is there a zoom limit?}
\begin{itemize}
\item SVG, PostScript, PDF specify IEEE-754 \emph{single} floating point number representations
\item Range of values: $\approx 3 \times 10^{-38} \to 3 \times 10^{+38}$
\includegraphics[width=0.8\textwidth]{../figures/floats.pdf}
\end{frame}

+\begin{frame}
+\frametitle{Visualisation of Floats II}
+\begin{itemize}
+       \item Difference between successive floats
+\end{itemize}
+\centering
+\includegraphics[width=0.8\textwidth]{../figures/floats_diff.pdf}
+\end{frame}
+
+\begin{frame}
+       \frametitle{Precision is limited}
+       \centering
+       \includegraphics[width=0.8\textwidth]{../figures/fox-vector_highzoom1.png}
+\end{frame}

\begin{frame}
\frametitle{Structure of Vector Graphics}

\end{frame}

+\section{Vector Graphics Viewer}
\begin{frame}
-\frametitle{Structure of Vector Graphics III}
+\frametitle{Structure of Vector Graphics II}
\begin{itemize}
+       \item \small{Upload \emph{bounding rectangles} of individual objects to renderer (OpenGL)}
\item Rectangles show individual B\'{e}ziers forming outline of the Fox
\end{itemize}
\centering
\end{frame}

+\begin{frame}
+\frametitle{Viewing Vector Graphics}
+\begin{itemize}
+       \item Tranform coordinates in document $\to$ display
+\end{itemize}
+\centering
+\includegraphics[width=0.8\textwidth]{../figures/view_transformation.pdf}
+\end{frame}
+
+
+\section{Precision Issues}
+
+
+
\begin{frame}
\frametitle{Floating point calculations \\ go wrong}
\begin{itemize}
-       \item Scaled to $~1\times 10^{-6}$, the fox is very sick
+       \item Example: Insert objects at very small scale
\end{itemize}
\centering
-       \includegraphics[width=0.5\textwidth]{../figures/fox-vector_highzoom1.png}
+       \includegraphics[width=0.8\textwidth]{../figures/view_transformation_fail.pdf}
+
+\end{frame}
+
+\begin{frame}
+\frametitle{Reducing error}
+               \begin{itemize}
+                       \item Don't apply view transformation directly
+                       \item Store object bounds relative to the display
+                       \item When modifying the view, modify object bounds
+                       \item Detail inserted into the view looks good, But...
+               \end{itemize}
+\centering
+       \includegraphics[width=0.9\textwidth]{../figures/view_transformation_cumulative.pdf}
+\end{frame}

+
+\begin{frame}
+\frametitle{Cumulated Errors \\ with intermediate coord system}
+       \begin{itemize}
+               \item Apply transformations to Paths not individual B\'{e}ziers
+               \item Paths render correctly, but drift appart
+       \end{itemize}
+\centering
+       \includegraphics[width=0.9\textwidth]{../figures/view_transformation_paths.pdf}
\end{frame}

+\section{Arbitrary Precision Rationals}
+
\begin{frame}
\frametitle{Arbitrary Precision Rationals}
\begin{align}
\end{align}
\begin{itemize}
\item $d_i$ are fixed size integers, $\beta = 2^{64}$
-               \item Size $S$ grows as needed
+               \item {\bf Size $S$ grows as needed}
\item Operations are always exact
\item Implemented by GNU Multiple Precision Library
\end{itemize}
\end{frame}

\begin{frame}
-       \frametitle{Replace floats with rationals?}
+       \frametitle{Use Rationals to represent \\ Path Coordinates}
\begin{itemize}
-               \item Rationals are \emph{slow}
-               \item Screen coordinates always in range $0 \to 1$
-               \item Introduce intermediate coordinate system
-               \begin{itemize}
-                       \item Many B\'{e}ziers contained in a Path
-                       \item Use Rationals for bounds of the Path
-                       \item Use floats to transform B\'{e}zier coordinates
-               \end{itemize}
+               \item Can move view to arbitrary point
+               \item Insert detail (ie: Test SVG image) in Display coordinates
+               \item Move view to another arbitrary point
+               \item Move view back
+               \item Detail is unchanged
\end{itemize}
\end{frame}

-\section{Live Demo}
+
+
+
+\section{Demonstration}
\begin{frame}
-\frametitle{Live Demo}
+\frametitle{Demonstration}
\begin{itemize}
\item We can import standard SVGs wherever we want
\item If we are willing to wait long enough

\section{Conclusions}
\begin{frame}
-       \frametitle{Conclusions}
-\begin{itemize}
-       \item What we have done?
+       \frametitle{What was done}
\begin{itemize}
\item Implemented a basic SVG viewer
\item Demonstrated how precision affects rendering vector graphics
\item Using GMP rationals, demonstrated the ability to render SVGs scaled to an arbitrary position in a document
\end{itemize}
-       \item Possible future work
+\end{frame}
+
+\begin{frame}
+       \frametitle{Future work}
\begin{itemize}
\item Implement more of the SVG standard
\item Trial alternative number representations
\end{itemize}
-\end{itemize}
\end{frame}
-\section{References}
+%\section{References}
\begin{frame}
\frametitle{References \& More information}
\begin{itemize}
\item Kahan's website \url{http://http.cs.berkeley.edu/~wkahan}
\end{itemize}
\end{frame}
-\section{Questions}
+%\section{Questions}

-\begin{frame}
-\frametitle{Q: Why don't you have colour?}
-\begin{itemize}
-       \item We do!\footnote{If you are willing to wait long enough}
-       \item A complete implementation of SVG is future work''
-\end{itemize}
-\centering
-\includegraphics[width=0.5\textwidth]{../figures/who-the-hell-needs-antialiasing-anyway.png}

-\end{frame}

\begin{frame}
-\frametitle{Q: Why not just use doubles?}
+\frametitle{Q: Why not just increase \\ floating point precision?}
\begin{itemize}
\item Any fixed precision format will still give inexact results
-       \item But the inexact results will appear slower
+       \item Eg: Accuracy of rendering a grid
\end{itemize}
\end{frame}

\end{itemize}
\end{frame}

-
\begin{frame}
-       \frametitle{Floating Point calculations \\ go wrong}
-       \begin{itemize}
-               \item Plank Length: $1.61 \times 10^{-35}$ metres $> 3\times10^{-38}$
-               \item Size of Universe: $4.3 \times 10^{26}$ metres $<< 3 \times10^{38}$
-               \item Why isn't this good enough for $1\times 10^{-6}$
-       \end{itemize}
-\end{frame}
+\frametitle{Q: Why don't you have colour?}
+\begin{itemize}
+       \item We do!\footnote{If you are willing to wait long enough}
+       \item A complete implementation of SVG is future work''
+\end{itemize}
+\centering
+\includegraphics[width=0.5\textwidth]{../figures/who-the-hell-needs-antialiasing-anyway.png}

-\begin{frame}
-       \frametitle{Floating point calculations \\ go wrong}
-       \begin{itemize}
-               \item Transforming from document $(x,y)$ $\to$ screen $(X,Y)$
-               \item View is at $(v_x,v_y)$ in document, has dimensions $(v_w,v_h)$
-       \end{itemize}
-       \begin{align}
-               X = \frac{x - v_x}{v_w} &,\quad\quad Y = \frac{y - v_y}{v_h}
-       \end{align}
-       \begin{itemize}
-               \item Division by $v_w \approx 10^{-6}$ increases the error due to $x - v_x$
-               \item Using \emph{double} precision, render correctly down to $v_w \approx 10^{-37}$
-       \end{itemize}
\end{frame}

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