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eulerg/eulerg.tex

@@ -44,14 +44,53 @@ The interest here though, is to define relationships between the contours, that
 processing and parsing of the diagram without resorting to extra area operations in the concerete plane.
 
 \section{Defining `pure intersection' and `enclosure'}
-\begin{figure}[h]
- \centering
- \includegraphics[width=200pt,keepaspectratio=true]{./eulerg/eulerg1.jpg}
- % eulerg1.jpg: 513x215 pixel, 72dpi, 18.10x7.58 cm, bb=0 0 513 215
+
+%\begin{figure}[htp]
+%  \begin{center}
+%    \subfigure[Original image]{\label{fig:edge-a}\includegraphics[scale=0.75]{toucan.eps}}
+%    \subfigure[After Laplace edge detection]{\label{fig:edge-b}\includegraphics[scale=0.75]{laplace_toucan.eps}} \\
+%    \subfigure[After Sobel edge detection]{\label{fig:edge-c}\includegraphics[scale=0.75]{sobel_toucan.eps}}
+%  \end{center}
+%  \caption{Various edge detection algorithms}
+%  \label{fig:edge}
+%\end{figure}
+
+%
+%\begin{figure}[h]
+% \centering
+% \includegraphics[width=200pt,keepaspectratio=true]{./eulerg/eulerg1.jpg}
+% % eulerg1.jpg: 513x215 pixel, 72dpi, 18.10x7.58 cm, bb=0 0 513 215
+% \caption{An Euler Diagram showing enclosure and Pure Intersection}
+% \label{fig:eulerg1}
+%\end{figure}
+%
+%
+%
+
+\begin{figure}[ht]
+\centering
+   \subfigure[Euler Diagram]{
+   \includegraphics[width=200pt,keepaspectratio=true]{./eulerg/eulerg1.jpg}
+   \label{fig:subfig1}
+ }
+
+ \subfigure[Graph Representation]{
+   \includegraphics[width=50pt,keepaspectratio=true]{./eulerg/eulerg_g.jpg}
+   \label{fig:subfig2}
+ }
+
+% \subfigure[Subfigure 3 caption]{
+%   \includegraphics[width=100pt,keepaspectratio=true]{./eulerg/eulerg1.jpg}
+%   \label{fig:subfig3}
+% }
+
  \caption{An Euler Diagram showing enclosure and Pure Intersection}
  \label{fig:eulerg1}
+
 \end{figure}
 
+
+
 The set theory term `intersection' can apply to both the curves overlapping and to the sub-set case.
 Intersection in a concrete diagram can mean two curves bisecting.
 For instance in diagram \ref{fig:eulerg1} the set theoretic intersection between
@@ -95,8 +134,18 @@ then B encloses C, see figure \ref{fig:eulerg_enc}.
 
 \begin{figure}[h]
  \centering
+
+ \subfigure[Euler Diagram]{
  \includegraphics[width=200pt,keepaspectratio=true]{./eulerg/eulerg_enc.jpg}
  % eulerg_enc.jpg: 315x269 pixel, 72dpi, 11.11x9.49 cm, bb=0 0 315 269
+ \label{eulerenc}
+ }
+
+ \subfigure[Graph Representation]{
+ \includegraphics[width=100pt,bb=0 0 240 43,keepaspectratio=true]{./eulerg/eulerg_enc_g.jpg}
+ % eulerg_enc_g.jpg: 240x43 pixel, 72dpi, 8.47x1.52 cm, bb=0 0 240 43
+  \label{graphenc}
+ }
  \caption{Enclosure, a transitive relationship}
  \label{fig:eulerg_enc}
 \end{figure}
@@ -127,26 +176,6 @@ and {\em enclosure} is transitive and {\pic} is not, we can represent
 an {\em enclosure} relationship as a directed vertice and 
 {\pic} as non-directed.
 
-The diagram in figure \ref{fig:eulerg1} can now be represented as a graph thus:
-\begin{figure}[h]
- \centering
- \includegraphics[width=50pt,bb=0 0 128 108,keepaspectratio=true]{./eulerg/eulerg_g.jpg}
- % eulerg_g.jpg: 128x108 pixel, 72dpi, 4.52x3.81 cm, bb=0 0 128 108
- \caption{Graph Representaion of figure \ref{fig:eulerg1}}
- \label{fig:eulerg1_g}
-\end{figure}
-
-
-The diagram in figure \ref{fig:eulerg_enc} can now be represented as a graph thus:
-\begin{figure}[h]
- \centering
- \includegraphics[width=100pt,bb=0 0 240 43,keepaspectratio=true]{./eulerg/eulerg_enc_g.jpg}
- % eulerg_enc_g.jpg: 240x43 pixel, 72dpi, 8.47x1.52 cm, bb=0 0 240 43
- \caption{Graph representation of figure \ref{fig:eulerg_enc}}
- \label{fig:eulerg_enc_g}
-\end{figure}
-
-
 \pagebreak[0]
 \section{The {\pic}}
 In graph theory a node is said to be reachable from another node
@@ -218,6 +247,33 @@ Knowing this can save on unecessary area operations on the concrete diagram.
 %  \label{fig:eulerg_pic1}
 % \end{figure}
 
+\begin{figure}%
+\centering
+\parbox{1.2in}{%
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=100pt,bb=0 0 330 158,keepaspectratio=true]{./eulerg/eulerg_pic_g.jpg}
+ % eulerg_pic_g.jpg: 330x158 pixel, 72dpi, 11.64x5.57 cm, bb=0 0 330 158
+ \caption{The Pure Intersection Chain PIC1 as a graph}
+ \label{fig:eulerg_pic_g}
+\end{figure}
+
+\caption{First.}%
+\label{fig:2figsA}}%
+\qquad
+\begin{minipage}{1.2in}%
+\begin{figure}[h]
+ \centering
+ \includegraphics[width=100pt,bb=0 0 330 158,keepaspectratio=true]{./eulerg/eulerg_pic_g.jpg}
+ % eulerg_pic_g.jpg: 330x158 pixel, 72dpi, 11.64x5.57 cm, bb=0 0 330 158
+ \caption{The Pure Intersection Chain PIC1 as a graph}
+ \label{fig:eulerg_pic_g}
+\end{figure}
+
+\caption{Second.}%
+\label{fig:2figsB}%
+\end{minipage}%
+\end{figure}%
 
 \begin{figure}[h]
  \centering

eulerg/paper.tex

@@ -3,6 +3,7 @@
 \usepackage{graphicx}
 \usepackage{fancyhdr}
 \usepackage{tikz}
+\usepackage{subfigure}
 \usepackage{amsfonts,amsmath,amsthm}
 \usepackage{algorithm}
 \usepackage{algorithmic}

thesis.tex

@@ -3,6 +3,7 @@
 \usepackage{graphicx}
 \usepackage{fancyhdr}
 \usepackage{tikz} 
+\usepackage{subfigure}
 \usepackage{amsfonts,amsmath,amsthm}
 \usepackage{algorithm}
 \usepackage{algorithmic}