diff --git a/Curved_kernel_via_analysis_2/doc_tex/Curved_kernel_via_analysis_2_ref/Curved_kernel_via_analysis_2.tex b/Curved_kernel_via_analysis_2/doc_tex/Curved_kernel_via_analysis_2_ref/Curved_kernel_via_analysis_2.tex
index a9e1c25bd31..fc0b80ffbed 100644
--- a/Curved_kernel_via_analysis_2/doc_tex/Curved_kernel_via_analysis_2_ref/Curved_kernel_via_analysis_2.tex
+++ b/Curved_kernel_via_analysis_2/doc_tex/Curved_kernel_via_analysis_2_ref/Curved_kernel_via_analysis_2.tex
@@ -100,19 +100,19 @@ type of \ccc{CKvA_2} used internally
 \ccNestedType{Curve_2}
 {
 type of curve that can be analyzed
- \ccc{boost::mpl::if_<boost::mpl::bool_< boost::is_void< CKvA_>::value} $>$, \ccc{Curved_kernel_via_analysis_2<CurveKernel_2>}, \ccc{CKvA_} $>$\ccc{::type}, \ccc{CurveKernel_2::Curve_analysis_2}, \ccc{boost::mpl::if_<boost::mpl::bool_< boost::is_void< Point_>::value} $>$, \ccc{CGALi::Point_2<boost::mpl::if_< boost::mpl::bool_< boost::is_void< CKvA_>::value} $>$, \ccc{Curved_kernel_via_analysis_2<CurveKernel_2>}, \ccc{CKvA_} $>$\ccc{::type} $>$, \ccc{Point_} $>$\ccc{::type}, \ccc{boost::mpl::if_<boost::mpl::bool_< boost::is_void< Arc_>::value} $>$, \ccc{CGALi::Arc_2<boost::mpl::if_< boost::mpl::bool_< boost::is_void< CKvA_>::value} $>$, \ccc{Curved_kernel_via_analysis_2<CurveKernel_2>}, \ccc{CKvA_} $>$\ccc{::type} $>$, \ccc{Arc_} $>$\ccc{::type} $>$ .
+%  \ccc{boost::mpl::if_<boost::mpl::bool_< boost::is_void< CKvA_>::value} $>$, \ccc{Curved_kernel_via_analysis_2<CurveKernel_2>}, \ccc{CKvA_} $>$\ccc{::type}, \ccc{CurveKernel_2::Curve_analysis_2}, \ccc{boost::mpl::if_<boost::mpl::bool_< boost::is_void< Point_>::value} $>$, \ccc{CGALi::Point_2<boost::mpl::if_< boost::mpl::bool_< boost::is_void< CKvA_>::value} $>$, \ccc{Curved_kernel_via_analysis_2<CurveKernel_2>}, \ccc{CKvA_} $>$\ccc{::type} $>$, \ccc{Point_} $>$\ccc{::type}, \ccc{boost::mpl::if_<boost::mpl::bool_< boost::is_void< Arc_>::value} $>$, \ccc{CGALi::Arc_2<boost::mpl::if_< boost::mpl::bool_< boost::is_void< CKvA_>::value} $>$, \ccc{Curved_kernel_via_analysis_2<CurveKernel_2>}, \ccc{CKvA_} $>$\ccc{::type} $>$, \ccc{Arc_} $>$\ccc{::type} $>$ .
 }
 \ccGlue
 \ccNestedType{Point_2}
 {
 type of a point on a curve that can be analyzed
- \ccc{boost::mpl::if_<boost::mpl::bool_< boost::is_void< CKvA_>::value} $>$, \ccc{Curved_kernel_via_analysis_2<CurveKernel_2>}, \ccc{CKvA_} $>$\ccc{::type}, \ccc{CurveKernel_2::Curve_analysis_2}, \ccc{boost::mpl::if_<boost::mpl::bool_< boost::is_void< Point_>::value} $>$, \ccc{CGALi::Point_2<boost::mpl::if_< boost::mpl::bool_< boost::is_void< CKvA_>::value} $>$, \ccc{Curved_kernel_via_analysis_2<CurveKernel_2>}, \ccc{CKvA_} $>$\ccc{::type} $>$, \ccc{Point_} $>$\ccc{::type}, \ccc{boost::mpl::if_<boost::mpl::bool_< boost::is_void< Arc_>::value} $>$, \ccc{CGALi::Arc_2<boost::mpl::if_< boost::mpl::bool_< boost::is_void< CKvA_>::value} $>$, \ccc{Curved_kernel_via_analysis_2<CurveKernel_2>}, \ccc{CKvA_} $>$\ccc{::type} $>$, \ccc{Arc_} $>$\ccc{::type} $>$ .
+%  \ccc{boost::mpl::if_<boost::mpl::bool_< boost::is_void< CKvA_>::value} $>$, \ccc{Curved_kernel_via_analysis_2<CurveKernel_2>}, \ccc{CKvA_} $>$\ccc{::type}, \ccc{CurveKernel_2::Curve_analysis_2}, \ccc{boost::mpl::if_<boost::mpl::bool_< boost::is_void< Point_>::value} $>$, \ccc{CGALi::Point_2<boost::mpl::if_< boost::mpl::bool_< boost::is_void< CKvA_>::value} $>$, \ccc{Curved_kernel_via_analysis_2<CurveKernel_2>}, \ccc{CKvA_} $>$\ccc{::type} $>$, \ccc{Point_} $>$\ccc{::type}, \ccc{boost::mpl::if_<boost::mpl::bool_< boost::is_void< Arc_>::value} $>$, \ccc{CGALi::Arc_2<boost::mpl::if_< boost::mpl::bool_< boost::is_void< CKvA_>::value} $>$, \ccc{Curved_kernel_via_analysis_2<CurveKernel_2>}, \ccc{CKvA_} $>$\ccc{::type} $>$, \ccc{Arc_} $>$\ccc{::type} $>$ .
 }
 \ccGlue
 \ccNestedType{Arc_2}
 {
 type of an arc on a curve that can be analyzed
- \ccc{boost::mpl::if_<boost::mpl::bool_< boost::is_void< CKvA_>::value} $>$, \ccc{Curved_kernel_via_analysis_2<CurveKernel_2>}, \ccc{CKvA_} $>$\ccc{::type}, \ccc{CurveKernel_2::Curve_analysis_2}, \ccc{boost::mpl::if_<boost::mpl::bool_< boost::is_void< Point_>::value} $>$, \ccc{CGALi::Point_2<boost::mpl::if_< boost::mpl::bool_< boost::is_void< CKvA_>::value} $>$, \ccc{Curved_kernel_via_analysis_2<CurveKernel_2>}, \ccc{CKvA_} $>$\ccc{::type} $>$, \ccc{Point_} $>$\ccc{::type}, \ccc{boost::mpl::if_<boost::mpl::bool_< boost::is_void< Arc_>::value} $>$, \ccc{CGALi::Arc_2<boost::mpl::if_< boost::mpl::bool_< boost::is_void< CKvA_>::value} $>$, \ccc{Curved_kernel_via_analysis_2<CurveKernel_2>}, \ccc{CKvA_} $>$\ccc{::type} $>$, \ccc{Arc_} $>$\ccc{::type} $>$ .
+%  \ccc{boost::mpl::if_<boost::mpl::bool_< boost::is_void< CKvA_>::value} $>$, \ccc{Curved_kernel_via_analysis_2<CurveKernel_2>}, \ccc{CKvA_} $>$\ccc{::type}, \ccc{CurveKernel_2::Curve_analysis_2}, \ccc{boost::mpl::if_<boost::mpl::bool_< boost::is_void< Point_>::value} $>$, \ccc{CGALi::Point_2<boost::mpl::if_< boost::mpl::bool_< boost::is_void< CKvA_>::value} $>$, \ccc{Curved_kernel_via_analysis_2<CurveKernel_2>}, \ccc{CKvA_} $>$\ccc{::type} $>$, \ccc{Point_} $>$\ccc{::type}, \ccc{boost::mpl::if_<boost::mpl::bool_< boost::is_void< Arc_>::value} $>$, \ccc{CGALi::Arc_2<boost::mpl::if_< boost::mpl::bool_< boost::is_void< CKvA_>::value} $>$, \ccc{Curved_kernel_via_analysis_2<CurveKernel_2>}, \ccc{CKvA_} $>$\ccc{::type} $>$, \ccc{Arc_} $>$\ccc{::type} $>$ .
 }
 \ccGlue
 \ccNestedType{X_monotone_curve_2}
diff --git a/Curved_kernel_via_analysis_2/doc_tex/Curved_kernel_via_analysis_2_ref/Non_x_monotone_arc_2.tex b/Curved_kernel_via_analysis_2/doc_tex/Curved_kernel_via_analysis_2_ref/Non_x_monotone_arc_2.tex
index f8aaa378ab0..056f384c0dc 100644
--- a/Curved_kernel_via_analysis_2/doc_tex/Curved_kernel_via_analysis_2_ref/Non_x_monotone_arc_2.tex
+++ b/Curved_kernel_via_analysis_2/doc_tex/Curved_kernel_via_analysis_2_ref/Non_x_monotone_arc_2.tex
@@ -28,7 +28,7 @@
 
 Class representing a (not necessary x-monotone) curve arc.
 
-This class represents either a full curve or a not necessarily x-monotone arc. In the latter case, one needs to specify a list of connected x-monotone pieces this arc is composed of.
+This class represents a not necessarily x-monotone curve arc. The arc is given as a list of connected x-monotone pieces.
 
 By constructing a new arc, its validity is checked to ensure that its x-monotone pieces form a single chain
 
@@ -167,7 +167,7 @@ returns a distinct ith x-monotone piece of the arc
 \ccGlue
 \ccMethod{Curve_2 curve() const;}
 {
-returns a supporting curve
+returns the supporting curve
 }
 \ccGlue
 \ccMethod{bool is_vertical() const;}