diff --git a/Barycentric_coordinates_3/examples/Barycentric_coordinates_3/tetrahedron_coordinates.cpp b/Barycentric_coordinates_3/examples/Barycentric_coordinates_3/tetrahedron_coordinates.cpp
index c6223649e72..6f5172cc766 100644
--- a/Barycentric_coordinates_3/examples/Barycentric_coordinates_3/tetrahedron_coordinates.cpp
+++ b/Barycentric_coordinates_3/examples/Barycentric_coordinates_3/tetrahedron_coordinates.cpp
@@ -30,7 +30,7 @@ int main() {
   // Get an array of triangle coordinates for all query points
   for(std::size_t i = 0; i < queries.size(); i++){
     const auto coords_array =
-    CGAL::Barycentric_coordinates::tetrahedron_coordinates_in_array(p0, p1, p2, p3, queries[i]);
+    CGAL::Barycentric_coordinates::tetrahedron_coordinates(p0, p1, p2, p3, queries[i]);
 
     std::cout << "tetrahedra coordinates (query " << i << "): " <<
       coords_array[0] << " " << coords_array[1] << " " <<
diff --git a/Barycentric_coordinates_3/include/CGAL/Barycentric_coordinates_3/Discrete_harmonic_coordinates_3.h b/Barycentric_coordinates_3/include/CGAL/Barycentric_coordinates_3/Discrete_harmonic_coordinates_3.h
index 26fa52c9e15..64097c58cb6 100644
--- a/Barycentric_coordinates_3/include/CGAL/Barycentric_coordinates_3/Discrete_harmonic_coordinates_3.h
+++ b/Barycentric_coordinates_3/include/CGAL/Barycentric_coordinates_3/Discrete_harmonic_coordinates_3.h
@@ -103,10 +103,10 @@ public:
     an instance of `VertexPointMap` that maps a vertex from `tmesh` to `Point_3`;
     the default initialization is provided
 
-    \pre num_vertices(`tmesh`) >= 4.
-    \pre is_triangle_mesh(`tmesh`).
-    \pre is_closed(`tmesh`).
-    \pre is_strongly_convex_3(`tmesh`).
+    \pre boost::num_vertices(`tmesh`) >= 4.
+    \pre CGAL::is_triangle_mesh(`tmesh`).
+    \pre CGAL::is_closed(`tmesh`).
+    \pre CGAL::is_strongly_convex_3(`tmesh`).
   */
   Discrete_harmonic_coordinates_3(const TriangleMesh& tmesh,
                                   const Computation_policy_3 policy,
@@ -393,10 +393,10 @@ private:
   \return an output iterator to the element in the destination range,
   one past the last coordinate stored
 
-  \pre num_vertices(`tmesh`) >= 4.
-  \pre is_triangle_mesh(`tmesh`).
-  \pre is_closed(`tmesh`).
-  \pre is_strongly_convex_3(`tmesh`).
+  \pre boost::num_vertices(`tmesh`) >= 4.
+  \pre CGAL::is_triangle_mesh(`tmesh`).
+  \pre CGAL::is_closed(`tmesh`).
+  \pre CGAL::is_strongly_convex_3(`tmesh`).
 */
 template<typename Point_3,
          typename TriangleMesh,
diff --git a/Barycentric_coordinates_3/include/CGAL/Barycentric_coordinates_3/Mean_value_coordinates_3.h b/Barycentric_coordinates_3/include/CGAL/Barycentric_coordinates_3/Mean_value_coordinates_3.h
index fdd731bdd3b..975b6960fae 100644
--- a/Barycentric_coordinates_3/include/CGAL/Barycentric_coordinates_3/Mean_value_coordinates_3.h
+++ b/Barycentric_coordinates_3/include/CGAL/Barycentric_coordinates_3/Mean_value_coordinates_3.h
@@ -105,9 +105,9 @@ public:
     an instance of `VertexPointMap` that maps a vertex from `tmesh` to `Point_3`;
     the default initialization is provided
 
-    \pre num_vertices(`tmesh`) >= 4.
-    \pre is_triangle_mesh(`tmesh`).
-    \pre is_closed(`tmesh`).
+    \pre boost::num_vertices(`tmesh`) >= 4.
+    \pre CGAL::is_triangle_mesh(`tmesh`).
+    \pre CGAL::is_closed(`tmesh`).
   */
   Mean_value_coordinates_3(const TriangleMesh& tmesh,
                            const Computation_policy_3 policy,
@@ -386,7 +386,7 @@ private:
   must be a model of the concept `FaceListGraph`
 
   \tparam OutputIterator
-  a model of `OutputIterator` that accepts values of type `GeomTraits::FT`
+  a model of `OutputIterator` that accepts values of type `Kernel_traits<Point_3>::Kernel::FT`
 
   \param tmesh
   an instance of `TriangleMesh`
@@ -404,9 +404,9 @@ private:
   \return an output iterator to the element in the destination range,
   one past the last coordinates stored
 
-  \pre num_vertices(`tmesh`) >= 4.
-  \pre is_triangle_mesh(`tmesh`).
-  \pre is_closed(`tmesh`).
+  \pre boost::num_vertices(`tmesh`) >= 4.
+  \pre CGAL::is_triangle_mesh(`tmesh`)
+  \pre CGAL::is_closed(`tmesh`).
 */
 template<typename Point_3,
          typename TriangleMesh,
diff --git a/Barycentric_coordinates_3/include/CGAL/Barycentric_coordinates_3/Wachspress_coordinates_3.h b/Barycentric_coordinates_3/include/CGAL/Barycentric_coordinates_3/Wachspress_coordinates_3.h
index 630c65c0f7f..c3d84c60e41 100644
--- a/Barycentric_coordinates_3/include/CGAL/Barycentric_coordinates_3/Wachspress_coordinates_3.h
+++ b/Barycentric_coordinates_3/include/CGAL/Barycentric_coordinates_3/Wachspress_coordinates_3.h
@@ -104,10 +104,10 @@ public:
     an instance of `VertexPointMap` that maps a vertex from `tmesh` to `Point_3`;
     the default initialization is provided
 
-    \pre num_vertices(`tmesh`) >= 4.
-    \pre is_triangle_mesh(`tmesh`).
-    \pre is_closed(`tmesh`).
-    \pre is_strongly_convex_3(`tmesh`).
+    \pre boost::num_vertices(`tmesh`) >= 4.
+    \pre CGAL::is_triangle_mesh(`tmesh`).
+    \pre CGAL::is_closed(`tmesh`).
+    \pre CGAL::is_strongly_convex_3(`tmesh`).
   */
   Wachspress_coordinates_3(const TriangleMesh& tmesh,
                            const Computation_policy_3 policy,
@@ -364,10 +364,10 @@ private:
   \return an output iterator to the element in the destination range,
   one past the last coordinate stored
 
-  \pre num_vertices(`tmesh`) >= 4.
-  \pre is_triangle_mesh(`tmesh`).
-  \pre is_closed(`tmesh`).
-  \pre is_strongly_convex_3(`tmesh`).
+  \pre boost::num_vertices(`tmesh`) >= 4.
+  \pre CGAL::is_triangle_mesh(`tmesh`).
+  \pre CGAL::is_closed(`tmesh`).
+  \pre CGAL::is_strongly_convex_3(`tmesh`).
 */
 template<typename Point_3,
          typename TriangleMesh,
diff --git a/Barycentric_coordinates_3/include/CGAL/Barycentric_coordinates_3/boundary_coordinates_3.h b/Barycentric_coordinates_3/include/CGAL/Barycentric_coordinates_3/boundary_coordinates_3.h
index d5be3fb4cad..229d741f070 100644
--- a/Barycentric_coordinates_3/include/CGAL/Barycentric_coordinates_3/boundary_coordinates_3.h
+++ b/Barycentric_coordinates_3/include/CGAL/Barycentric_coordinates_3/boundary_coordinates_3.h
@@ -20,8 +20,8 @@
 #include <CGAL/Barycentric_coordinates_3/barycentric_enum_3.h>
 #include <CGAL/boost/graph/property_maps.h>
 
-namespace CGAL{
-namespace Barycentric_coordinates{
+namespace CGAL {
+namespace Barycentric_coordinates {
 
 /*!
   \ingroup PkgBarycentricCoordinates3RefFunctions
@@ -72,10 +72,10 @@ namespace Barycentric_coordinates{
   one past the last coordinate stored + the flag indicating whether the
   query point belongs to the polyhedron boundary
 
-  \pre num_vertices(`tmesh`) >= 4.
-  \pre is_triangle_mesh(`tmesh`).
-  \pre is_closed(`tmesh`).
-  \pre is_strongly_convex_3(`tmesh`).
+  \pre boost::num_vertices(`tmesh`) >= 4.
+  \pre CGAL::is_triangle_mesh(`tmesh`).
+  \pre CGAL::is_closed(`tmesh`).
+  \pre CGAL::is_strongly_convex_3(`tmesh`).
 */
 template<typename TriangleMesh,
          typename OutputIterator,
@@ -145,9 +145,10 @@ boundary_coordinates_3(const TriangleMesh& tmesh,
   one past the last coordinate stored + the flag indicating whether the
   query point belongs to the polyhedron boundary
 
-  \pre is_triangle_mesh(`tmesh`)
-  \pre num_vertices(`tmesh`) >= 4.
-  \pre `tmesh` is simplicial.
+  \pre boost::num_vertices(`tmesh`) >= 4.
+  \pre CGAL::is_triangle_mesh(`tmesh`)
+  \pre CGAL::is_closed(`tmesh`).
+  \pre CGAL::is_strongly_convex_3(`tmesh`).
 */
 template<typename TriangleMesh,
          typename Point_3,
diff --git a/Barycentric_coordinates_3/include/CGAL/Barycentric_coordinates_3/tetrahedron_coordinates.h b/Barycentric_coordinates_3/include/CGAL/Barycentric_coordinates_3/tetrahedron_coordinates.h
index d5d679daf70..73fc42baf68 100644
--- a/Barycentric_coordinates_3/include/CGAL/Barycentric_coordinates_3/tetrahedron_coordinates.h
+++ b/Barycentric_coordinates_3/include/CGAL/Barycentric_coordinates_3/tetrahedron_coordinates.h
@@ -18,8 +18,8 @@
 
 #include <CGAL/Barycentric_coordinates_3/internal/utils_3.h>
 
-namespace CGAL{
-namespace Barycentric_coordinates{
+namespace CGAL {
+namespace Barycentric_coordinates {
 
 /*!
   \ingroup PkgBarycentricCoordinates3RefFunctions
@@ -142,7 +142,7 @@ OutputIterator tetrahedron_coordinates(
 */
 template<typename GeomTraits>
 std::array<typename GeomTraits::FT, 4>
-tetrahedron_coordinates_in_array(
+tetrahedron_coordinates(
   const typename GeomTraits::Point_3& p0,
   const typename GeomTraits::Point_3& p1,
   const typename GeomTraits::Point_3& p2,
@@ -162,7 +162,7 @@ tetrahedron_coordinates_in_array(
 //return array (infer from point_3)
 template<typename Point_3>
 std::array<typename Kernel_traits<Point_3>::Kernel::FT, 4>
-tetrahedron_coordinates_in_array(
+tetrahedron_coordinates(
   const Point_3& p0,
   const Point_3& p1,
   const Point_3& p2,
@@ -171,7 +171,7 @@ tetrahedron_coordinates_in_array(
 
   using GeomTraits = typename Kernel_traits<Point_3>::Kernel;
   const GeomTraits traits;
-  return tetrahedron_coordinates_in_array(
+  return tetrahedron_coordinates(
     p0, p1, p2, p3, query, traits);
 }