diff --git a/Triangulation_2/doc_tex/Triangulation_2/triangulation_user.tex b/Triangulation_2/doc_tex/Triangulation_2/triangulation_user.tex
index d086d358ddd..8e06062204a 100644
--- a/Triangulation_2/doc_tex/Triangulation_2/triangulation_user.tex
+++ b/Triangulation_2/doc_tex/Triangulation_2/triangulation_user.tex
@@ -1199,16 +1199,17 @@ for a subconstraint.
 It is more powerful, as constraints are not only segments, but
 arbitrary polylines. These polyline constraints can be concatenated,
 and split, and vertices can be removed and inserted in a polyline
-constraint.  Finally, polylines can be simplified while respecting
-the topology.
+constraint.  
 
-\subsection{Example: Getting Started with Polylines}
+\subsection{Example: Polylines as Constraints}
+
+The following example shows how to insert polylines
+and what to do with them.
 
 \ccIncludeExampleCode{Triangulation_2/polylines.cpp}
 
-\subsection{Example: Polyline Simplification}
 
-\ccIncludeExampleCode{Triangulation_2/simplify.cpp} 
+
 
 
 \section{The Triangulation Hierarchy\label{Section_2D_Triangulations_Hierarchy}}
diff --git a/Triangulation_2/doc_tex/Triangulation_2_ref/Polyline_constrained_triangulation_2.tex b/Triangulation_2/doc_tex/Triangulation_2_ref/Polyline_constrained_triangulation_2.tex
index b06c0ec6872..92cd9837d99 100755
--- a/Triangulation_2/doc_tex/Triangulation_2_ref/Polyline_constrained_triangulation_2.tex
+++ b/Triangulation_2/doc_tex/Triangulation_2_ref/Polyline_constrained_triangulation_2.tex
@@ -1,20 +1,6 @@
-% +------------------------------------------------------------------------+
-% | Reference manual page: Polyline_constrained_triangulation_2.tex
-% +------------------------------------------------------------------------+
-% | 05.02.2002   Mariette Yvinec
-% | Package: Triangulation_2
-% | 
-\RCSdef{\RCSConstrainedtriangulationplusRev}{$Id$}
-\RCSdefDate{\RCSConstrainedtriangulationplusDate}{$Date$}
-% |
-%%RefPage: end of header, begin of main body
-% +------------------------------------------------------------------------+
 
+\begin{ccRefClass}{Polyline_constrained_triangulation_2<Tr>}
 
-\begin{ccRefClass}{Polyline_constrained_triangulation_2<Tr>}  %% add template arg's if necessary
-
-%% \ccHtmlCrossLink{}     %% add further rules for cross referencing links
-%% \ccHtmlIndexC[class]{} %% add further index entries
 
 The class \ccRefName\ 
 implements a constrained triangulation 
@@ -274,32 +260,18 @@ have changed into \ccc{out}.}.
 
 \ccHeading{Polyline Simplification}
 
+The polyline simplification algorithm described in Chapter~ref{{chapter-polylinesimplification}
+operates on \ccRefName{}.  Application code can fix vertices in
+polyline constraints with the following functions.
+
 \ccMethod{bool is_fixed(Vertices_in_constraint_iterator it) const;}
 {Returns \ccc{true} iff the vertex shall never be simplified.}
 
 \ccMethod{bool set_fixed(Vertices_in_constraint_iterator it, bool b);}
 {Sets the marker of a vertex to \ccc{b}, and returns the previous value.}
 
-\ccMethod{fix();}
-{Fixes on each polyline the vertices with minimal and maximal \ccc{x}
- and \ccc{y} coordinate.}
 
-\ccMethod{template <typename StopFunction, typename CostFunction>
-          std::size_t simplify(StopFunction sf, CostFunction cf);}
-{Simplifies all polyline constraints according to the stop and cost function.
-Points marked as \ccc{fixed} will not get removed. 
-After a call of \ccc{simplify} the the {Vertices_in_constraint_iterator}
-allows to traverse the vertices of the simplified polyline,
-and the \ccc{{Points_in_constraint_iterator} allows to traverse
-the points of the original polyline. 
-\ccc{StopFunction} must be a model of \ccc{PolylineSimplificationStopFunction}.
-\ccc{CostFunction} must be a model of \ccc{PolylineSimplificationCostFunction}.
-\ccPrecond All vertices are on constraints.}
 
-\ccMethod{remove_points();}
-{Removes the points of the vertices which were removed by the \ccc{simplify}.
-When this method gets applied the next call to \ccc{simplify}
-measures the error for the points on the current polylines.}
 
 \ccSeeAlso
 \ccc{CGAL::Constrained_triangulation_plus_2<Tr>} \\
@@ -310,8 +282,3 @@ measures the error for the points on the current polylines.}
 
 \end{ccRefClass}
 
-% +------------------------------------------------------------------------+
-%%RefPage: end of main body, begin of footer
-% EOF
-% +------------------------------------------------------------------------+
-