typos

Boolean_set_operations_2/doc_tex/Boolean_set_operations_2/bso_def.tex

@@ -55,7 +55,7 @@ polygon vertices is referred to as the polygon \textbf{(outer) boundary}.
 
 \item A \textbf{Relatively simple} polygon allows vertices with a degree$>$2, but all of its edges are disjoint in their interior. Furthermore, it must be an orientable polygon.  Namely when it is inserted into an arrangement and its outer boundary is traversed, the same face is adjacent to all of the halfedges (no crossing over any curve during the traversal).  
 %\textbf{insert relativelySimplePolygon.tex}\\
-Note that while polygon C has the same curves as polygon B, traversal of the curves leads to crossing over a previouly traversed curve, and is therefore neither simple nor relatively simple.  
+Note that while polygon C has the same curves as polygon B, traversal of the curves leads to crossing over a previously traversed curve, and is therefore neither simple nor relatively simple.  
 %\textbf{insert NotRelativelySimplePolygon.tex}\\ \\
 
 \item A polygon in our context must be relatively simple and its outer boundary vertices must be ordered in a counterclockwise direction around the interior of the polygon.
@@ -98,7 +98,7 @@ In our context, a polygon must uphold the following conditions:\\
 \begin{enumerate}
  \item\textit{Closed Boundary} - the polygon's outer boundary must be a connected sequence of curves, that start and end at the same vertex.
 \item \textit{Simplicity} - the polygon must be simple.
-\item \textit{Orientaion} - the polygon's outer boundary must be \textit{counter-clockwise oriented}.
+\item \textit{Orientation} - the polygon's outer boundary must be \textit{counter-clockwise oriented}.
 \end{enumerate}
  
 

Boolean_set_operations_2/doc_tex/Boolean_set_operations_2/bso_general.tex

@@ -250,10 +250,10 @@ The class-template
 \ccc{Gps_traits_2<ArrDirectionalXMonotoneTraits,GeneralPolygon>}
 models the concept \ccc{GeneralPolygonSetTraits_2}, and can be used to
 instantiate the class template \ccc{General_polygon_set_2}.
-It serves as an adapter for a geoemtric traits class, which models the
+It serves as an adapter for a geometric traits class, which models the
 concept \ccc{ArrangementDirectionalXMonotoneTraits_2}.
 It can be used for performing set-operations on general polygons.
-The implementation of the adapetr is rather simple, as it is derived
+The implementation of the adapter is rather simple, as it is derived
 from the instantiated template-parameter \ccc{ArrXMonotoneTraits_2}
 inheriting its necessary types and methods. It further exploits 
 the methods provided by the instantiated parameter

Boolean_set_operations_2/doc_tex/Boolean_set_operations_2/bso_intro.tex

@@ -61,6 +61,6 @@ in more depth. In Section~\ref{bso_sec:bso_lin} we focus on Boolean
 set-operations on linear polygons, introducing the notion of polygons with 
 holes and of a general polygon set. Section~\ref{bso_sec:bso_gen}
 introduces general polygons.
-We first discuss polygons whose edges are either line segements or circular
+We first discuss polygons whose edges are either line segments or circular
 arcs and then explain how to construct and use general polygons whose edges
 can be arbitrary weakly $x$-monotone curves.

Boolean_set_operations_2/doc_tex/Boolean_set_operations_2/bso_linear.tex

@@ -5,7 +5,7 @@ The basic library of \cgal\ includes the \ccc{Polygon_2<Kernel,Container>}
 class-template that represents a linear polygon in the plane. The
 polygon is represented by its vertices stored in a container of
 objects of type \ccc{Kernel::Point_2}. The polygon edges are line
-segments (\ccc{Kenrel::Segment_2} objects) between adjacent points in
+segments (\ccc{Kernel::Segment_2} objects) between adjacent points in
 the container. By default, the \ccc{Container} is a vector of
 \ccc{Kernel::Point_2} objects.
 
@@ -37,7 +37,7 @@ computes the union of two polygons is called \ccc{join()}, since
 the word \ccc{union} is reserved in \CC.} \ccc{difference()},
 \ccc{symmetric_difference()} and the predicate \ccc{do_intersect()}
 that accept two \ccc{Polygon_2} objects as their input. We explain how
-these functions should be used throught several examples in the
+these functions should be used through several examples in the
 following sections.
 
 % ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
@@ -151,7 +151,7 @@ upside-down triangle. In general, there are many ways to arrive at
 a particular point set. However, the set of polygons with holes
 obtained through the application of any sequence of operations is
 unique. The set depicted on the right is represented as a single
-polygon having a triangular outer boundary with a single triangluar
+polygon having a triangular outer boundary with a single triangular
 hole in its interior --- and not as three triangles that have no holes
 at all. As a general rule, if two point sets are connected, then they
 belong to the same polygon with holes.
@@ -233,7 +233,7 @@ output polygons to its associated container.
 \subsubsection{Example --- Joining and Intersecting Simple Polygons\label{bso_sssec:ex_simple_bops}}
 % ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 
-The following example demonstartes the usage of the free functions
+The following example demonstrates the usage of the free functions
 \ccc{join()} and \ccc{intersect()} for computing the union and the
 intersection of the two simple polygons depicted in
 Figure~\ref{fig:simple}~(b). The example uses the auxiliary function
@@ -245,7 +245,7 @@ the header file \ccc{print_utils.h} under the examples folder.
 % ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
 \subsubsection{Operations on Polygons with Holes\label{bso_sssec:pwh_bops}}
 % ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-We have demonstrated that free functions that perform boolean set operations on simple polygons may output polygons with holes. In addition to these functions, the Boolean set-operations package provides the following overriden free functions that accept
+We have demonstrated that free functions that perform boolean set operations on simple polygons may output polygons with holes. In addition to these functions, the Boolean set-operations package provides the following overridden free functions that accept
 \ccc{General_polygon_with_holes_2} objects as their input - 
 %Having introduced polygons with holes and explained how the free functions
 %output such objects, it is only natural to perform operations on sets that
@@ -284,7 +284,7 @@ contains of five holes:
 
 \ccIncludeExampleCode{Boolean_set_operations_2/symmetric_difference.cpp}
 
-In some cases it is convinient to connect the outer boundary of a
+In some cases it is convenient to connect the outer boundary of a
 polygon with holes with the holes inside it. The
 function \ccc{connect_holes()} accepts a polygon with
 holes, and connects the topmost vertex in each hole with the polygon
@@ -331,7 +331,7 @@ into the set using the \ccc{insert()} method, as long as the inserted
 polygons and the existing polygons in the set are disjoint. 
 The \ccc{Polygon_set_2} class also provides access functions for
 accessing the polygons with holes it contains, and a few queries. The
-most improtant query is \ccc{S.oriented_side(q)}, which determined
+most important query is \ccc{S.oriented_side(q)}, which determined
 whether the query point $q$ is contained in the interior of the set
 $S$, lies on the boundary of the set, or neither.
 
@@ -347,8 +347,8 @@ functions.
 
 Member functions of the \ccc{General_polygon_set_2} that perform
 Boolean set-operations come in two flavors: for example, \ccc{S.join(P, Q)}
-computes the union of $P$ and $Q$ and assigned the reuslt to $S$, while
-\ccc{S.join(P)} preformes the operation $S \longleftarrow S \cup P$.
+computes the union of $P$ and $Q$ and assigned the result to $S$, while
+\ccc{S.join(P)} performs the operation $S \longleftarrow S \cup P$.
 Similarly, \ccc{S.complement(P)} sets $S$ to be the complement of $P$,
 while $S.complement()$ simply negates the set $S$.
 
@@ -358,7 +358,7 @@ while $S.complement()$ simply negates the set $S$.
 
 The free functions reviewed in Section~\ref{bso_ssec:polygons_with_holes}
 serve as a wrapper for the polygon-set class, and are only provided for
-convinience. A typical such function constructs a pair of
+convenience. A typical such function constructs a pair of
 \ccc{General_polygon_set_2} objects, invokes the appropriate method to
 apply the desired Boolean operation, and transforms the resulting
 polygon set to the required output format. Thus, when several