X-Git-Url: https://git.ucc.asn.au/?p=ipdf%2Fsam.git;a=blobdiff_plain;f=presentation%2Fpresentation.tex;h=8b4108cebdd398803dfe57ad4af5cb705bcfd2f4;hp=7d5494b8602e242c60b0813fdee46066bc929c4e;hb=253d241eb8279be539ad72a0283d3f1575b537ab;hpb=67c33e185edd820e2ea6fef334455645bacd432b

diff --git a/presentation/presentation.tex b/presentation/presentation.tex
index 7d5494b..8b4108c 100644
--- a/presentation/presentation.tex
+++ b/presentation/presentation.tex
@@ -64,23 +64,24 @@
 }
 
 
-\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}
@@ -95,14 +96,19 @@
 \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: $\approx 3 \times 10^{-38} \to 3 \times 10^{+38}$
@@ -127,6 +133,20 @@
 \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}
@@ -140,9 +160,11 @@
 
 \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
@@ -150,17 +172,56 @@
 \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}
@@ -174,29 +235,29 @@
 	\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
@@ -208,23 +269,23 @@
 
 \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
 		\item Allow for saving and loading SVGs with arbitrary precision
 	\end{itemize}
-\end{itemize}
 \end{frame}
-\section{References}
+%\section{References}
 \begin{frame}
 	\frametitle{References \& More information}
 	\begin{itemize}
@@ -240,25 +301,15 @@
 		\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/shady-the-fox.png}
-\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}
 
@@ -282,29 +333,16 @@
 \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/shady-the-fox.png}
+\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}