diff --git a/Triangulation_2/doc/Triangulation_2/CGAL/Constrained_triangulation_plus_2.h b/Triangulation_2/doc/Triangulation_2/CGAL/Constrained_triangulation_plus_2.h
index cef1af9c55f..da7bf476941 100644
--- a/Triangulation_2/doc/Triangulation_2/CGAL/Constrained_triangulation_plus_2.h
+++ b/Triangulation_2/doc/Triangulation_2/CGAL/Constrained_triangulation_plus_2.h
@@ -294,11 +294,19 @@ std::size_t insert_constraints(PointIterator points_first, PointIterator points_
 
 
 /*! 
-splits into constraints the subconstraint graph g at vertices of degree greater than 2.
+splits into polylines the graph `g` at vertices of degree greater than 2
+and at vertices for which `is_terminal(v)==true`.
 
 \warning all existing constraints will be discarded.
+
+\param is_terminal An optional function returning true if the vertex
+`v` of degree 2 is a polyline endpoint and false otherwise. If no
+function is provided, a default function is provided that returns true
+for vertices whose degree is different from 2.
+
+\sa `split_graph_into_polylines()`
 */ 
-void split_subconstraint_graph_into_constraints();
+void split_subconstraint_graph_into_constraints(const std::function<bool(Vertex_handle)>& is_terminal);
   
 /*! 
 removes the constraint `cid`, without removing the points from the triangulation.
diff --git a/Triangulation_2/doc/Triangulation_2/Triangulation_2.txt b/Triangulation_2/doc/Triangulation_2/Triangulation_2.txt
index 9451f88be77..fc94bccbf5e 100644
--- a/Triangulation_2/doc/Triangulation_2/Triangulation_2.txt
+++ b/Triangulation_2/doc/Triangulation_2/Triangulation_2.txt
@@ -1124,6 +1124,21 @@ through the edge.
 
 \cgalExample{Triangulation_2/polylines_triangulation.cpp}
 
+\subsection Triangulation_2ExampleBuildingFromSoup Example: Building a Triangulated Arrangement of Polylines from a Segment Soup
+
+The `Constrained_triangulation_plus_2` structure is initialized by a
+set of polylines. As users may only be able to provide a disconnected
+segment soup as input, a member function
+[split_subconstraint_graph_into_constraints()](@ref Constrained_triangulation_plus_2::split_subconstraint_graph_into_constraints())
+is provided: this function identifies the polylines by connecting
+segments until a vertex whose degree is different than 2 is reached.
+
+The following code shows how a "blind" insertion of disconnected
+polylines can be processed into a set of well-defined polyline
+constraints in a `Constrained_triangulation_plus_2`:
+
+\cgalExample{Triangulation_2/segment_soup_to_polylines.cpp}
+
 \section Section_2D_Triangulations_Hierarchy The Triangulation Hierarchy 
 
 The class `Triangulation_hierarchy_2<Tr>`
diff --git a/Triangulation_2/doc/Triangulation_2/dependencies b/Triangulation_2/doc/Triangulation_2/dependencies
index 84dba85f07d..22ae69dcfef 100644
--- a/Triangulation_2/doc/Triangulation_2/dependencies
+++ b/Triangulation_2/doc/Triangulation_2/dependencies
@@ -4,6 +4,7 @@ STL_Extension
 Algebraic_foundations
 Circulator
 Stream_support
+BGL
 TDS_2
 Triangulation_3
 Spatial_sorting