diff --git a/Curved_kernel/doc_tex/Curved_kernel_ref/FunctorEqual.tex b/Curved_kernel/doc_tex/Curved_kernel_ref/FunctorEqual.tex
index ac3dae2ea7b..fab72f85547 100644
--- a/Curved_kernel/doc_tex/Curved_kernel_ref/FunctorEqual.tex
+++ b/Curved_kernel/doc_tex/Curved_kernel_ref/FunctorEqual.tex
@@ -27,9 +27,9 @@ An object \ccVar\ of this type must provide in addition:
          const CircularKernel::Line_arc_2 &a1);}
 {For two segments.}
 
-For the sake of completeness, there must also be an
-\ccc{operator()} taking a \ccc{Line_arc_2} and a
-\ccc{Circular_arc_2} as arguments (in any order) that always 
+For the sake of completeness, the 
+\ccc{operator()} must also be defined for a \ccc{Line_arc_2} and a
+\ccc{Circular_arc_2} as arguments (in any order), and it always 
 returns \ccc{false}.
 
 \ccHasModels
diff --git a/Curved_kernel/doc_tex/Curved_kernel_ref/GeomFunctorsConstructions.tex b/Curved_kernel/doc_tex/Curved_kernel_ref/GeomFunctorsConstructions.tex
index deb0da613d6..9701d612023 100644
--- a/Curved_kernel/doc_tex/Curved_kernel_ref/GeomFunctorsConstructions.tex
+++ b/Curved_kernel/doc_tex/Curved_kernel_ref/GeomFunctorsConstructions.tex
@@ -14,6 +14,10 @@ A model \ccVar\ of this type must provide:
 {Splits the arc \ccc{ca} into monotone arcs that are returned through the 
 output iterator.}
 
+For the sake of completeness, the \ccc{operator()} must also be defined for a 
+\ccc{Line_arc_2}. In this case, the input line arc itself is the only
+arc returned through the \ccc{OutputIterator}. 
+
 \ccHasModels
 
 \ccc{Circular_kernel_2::Make_x_monotone_2;}