eulerg

eulerg/eulerg.tex

@@ -94,7 +94,7 @@ $A$ `enclosed' by $B$. We can express this as a directed relationship.
 
 $$ B {\enc} A $$
 
-
+%\clearpage
 \paragraph{Pair-wise Intersection}
 In the $D$, $E$ case we have 
 
@@ -117,7 +117,7 @@ then B encloses C, see figure \ref{fig:eulerg_enc}.
 No contour can be both pair-wisely intersected and enclosed with the same contour.
 \end{definition}
 
-
+\clearpage
 \begin{figure}[h]
  \centering
 
@@ -164,9 +164,9 @@ As the relationships {\em enclosure} and {\pic} are mutually exclusive
 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 on the same graph.
-Figures \ref{fig:eulerg1} and \ref{fig:eulergenc} show euler diagrams with corresponding 
+Figures \ref{fig:eulerg1} and \ref{fig:eulerg_enc} show euler diagrams with corresponding 
 graphs. The next section will introduce the concept of a {\pic}
-and will describe graphs where both enclosure and pair-wise
+and will  present graphs where both enclosure and pair-wise
 intersection are represented on the same graph.
 
 \pagebreak[1]
@@ -321,7 +321,7 @@ Searching for an available zone involves finding out if the intersection exists,
 by any other contours. 
 A brute force search for available zones using area operations
 is therefore of the order $N.2^N$ (where N is the number of contours in the diagram).
-Using $|P|$ to represent the number of conoutrs within a {\pic} 
+Using $|P|$ to represent the number of contours within a {\pic} 
 and $K$ to represent the number of {\pic}s in a diagram,
 using the result in definition \ref{picreduction}, we can break the diagram into small segments
 (the {\pic}s) which have an order $K.2^{|P|}$.