diff --git a/Envelope_3/include/CGAL/Envelope_3/Envelope_pm_dcel.h b/Envelope_3/include/CGAL/Envelope_3/Envelope_pm_dcel.h
index c15c2dead3e2..33117b474f9f 100644
--- a/Envelope_3/include/CGAL/Envelope_3/Envelope_pm_dcel.h
+++ b/Envelope_3/include/CGAL/Envelope_3/Envelope_pm_dcel.h
@@ -7,10 +7,10 @@
 // $Id$
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
-// Author(s)     : Michal Meyerovitch     <gorgymic@post.tau.ac.il>
-//                 Baruch Zukerman        <baruchzu@post.tau.ac.il>
-//                 Ron Wein               <wein@post.tau.ac.il>
-//                 Efi Fogel              <efif@post.tau.ac.il>
+// Author(s) : Michal Meyerovitch     <gorgymic@post.tau.ac.il>
+//             Baruch Zukerman        <baruchzu@post.tau.ac.il>
+//             Ron Wein               <wein@post.tau.ac.il>
+//             Efi Fogel              <efif@post.tau.ac.il>
 
 #ifndef CGAL_ENVELOPE_PM_DCEL_H
 #define CGAL_ENVELOPE_PM_DCEL_H
@@ -21,19 +21,18 @@
 #include <CGAL/Arr_default_dcel.h>
 #include <CGAL/Envelope_3/Envelope_base.h>
 
-namespace CGAL
-{
-namespace Envelope_3
-{
+namespace CGAL {
 
-template <class Data>
-class Dcel_info
-{
+namespace Envelope_3 {
+
+template <typename Data_>
+class Dcel_info {
 public:
-  typedef Dcel_info<Data>                         Self;
-  typedef std::list<Data>                         Data_container;
-  typedef typename Data_container::iterator       Data_iterator;
-  typedef typename Data_container::const_iterator Data_const_iterator;
+  using Data = Data_;
+  using Self = Dcel_info<Data>;
+  using Data_container = std::list<Data>;
+  using Data_iterator =  typename Data_container::iterator;
+  using Data_const_iterator = typename Data_container::const_iterator;
 
 protected:
   /*! data container */
@@ -46,8 +45,7 @@ class Dcel_info
   Dac_decision m_decision;
 public:
   /*! Constructor */
-  Dcel_info() : m_is_set(false), m_decision(DAC_DECISION_NOT_SET)
-  {}
+  Dcel_info() : m_is_set(false), m_decision(DAC_DECISION_NOT_SET) {}
 
   /*! \brief returns true iff data has been set already */
   bool get_is_set() const { return m_is_set; }
@@ -55,194 +53,127 @@ class Dcel_info
   /*! \brief resets the flag  */
   void set_is_set(bool flag) { m_is_set = flag; }
 
-  bool is_decision_set()
-  {
-    return (m_decision != DAC_DECISION_NOT_SET);
-  }
+  bool is_decision_set() { return (m_decision != DAC_DECISION_NOT_SET); }
 
-  Dac_decision get_decision() const
-  {
-    return m_decision;
-  }
+  Dac_decision get_decision() const { return m_decision; }
 
   void set_decision(Comparison_result comp)
-  {
-    m_decision = enum_cast<Dac_decision>(comp);
-  }
+  { m_decision = enum_cast<Dac_decision>(comp); }
 
-  void set_decision(Dac_decision dec)
-  {
-    m_decision = dec;
-  }
+  void set_decision(Dac_decision dec) { m_decision = dec; }
 
   /*! User-friendly interface: */
-  size_t number_of_surfaces () const
-  {
-    return (m_data.size());
-  }
+  size_t number_of_surfaces() const { return m_data.size(); }
 
-  Data_const_iterator surfaces_begin () const
-  {
-    return (m_data.begin());
-  }
+  Data_const_iterator surfaces_begin() const { return m_data.begin(); }
 
-  Data_const_iterator surfaces_end () const
-  {
-    return (m_data.end());
-  }
+  Data_const_iterator surfaces_end() const { return m_data.end(); }
 
-   /*!
-   * Get the first Xy-monotone surface associated with the face.
-   * \pre number_of_surfaces() is not 0.
-   */
-  const Data& surface() const
-  {
-    CGAL_precondition (m_data.size() > 0);
-    return (m_data.front());
+   /*! Obtain the first Xy-monotone surface associated with the face.
+    * \pre number_of_surfaces() is not 0.
+    */
+  const Data& surface() const {
+    CGAL_precondition(m_data.size() > 0);
+    return m_data.front();
   }
 
-  /*!
-   * Get the number of data objects associated with the face.
+  /*! Obtain the number of data objects associated with the face.
    */
-  int number_of_data_objects() const
-  {
-    return static_cast<int>(m_data.size());
-  }
+  int number_of_data_objects() const { return static_cast<int>(m_data.size()); }
 
-  /*!
-   * check if the data is set to be empty
+  /*! Check whether the data is set to be empty
    */
   bool has_no_data() const
-  {
-    return (m_is_set && number_of_data_objects() == 0);
-  }
+  { return (m_is_set && (number_of_data_objects() == 0)); }
 
-  /*!
-   * Get the first data object associated with the face.
+  /*! Obtain the first data object associated with the face.
    * \pre number_of_data_objects() is not 0.
    */
-  const Data& get_data() const
-  {
-    CGAL_precondition (m_data.size() > 0);
-
-    return (m_data.front());
+  const Data& get_env_data() const {
+    CGAL_precondition(m_data.size() > 0);
+    return m_data.front();
   }
 
-  /*!
-   * Get the data iterators (const version).
+  /*! Obtain the data iterators (const version).
    */
-  Data_const_iterator begin_data() const
-  {
-    return (m_data.begin());
-  }
+  Data_const_iterator begin_data() const { return m_data.begin(); }
 
-  Data_const_iterator end_data() const
-  {
-    return (m_data.end());
-  }
+  Data_const_iterator end_data() const { return m_data.end(); }
 
-  /*!
-   * Get the data iterators (non-const version).
+  /*! Obtain the data iterators (non-const version).
    */
-  Data_iterator begin_data()
-  {
-    return (m_data.begin());
-  }
+  Data_iterator begin_data() { return m_data.begin(); }
 
-  Data_iterator end_data()
-  {
-    return (m_data.end());
-  }
+  Data_iterator end_data() { return m_data.end(); }
 
-  /*!
-   * Set a data object to the face.
+  /*! Set a data object to the face.
    * \param data The data object to set.
    */
-  void set_data (const Data & data)
-  {
+  void set_env_data(const Data& data) {
     clear_data();
     add_data(data);
   }
 
-  /*!
-   * Set a range of data objects to the face.
+  /*! Set a range of data objects to the face.
    * \param begin A begin iterator for the data range.
    * \param end A past-the-end iterator for the data range.
    */
-  template <class InputIterator>
-  void set_data(const InputIterator & begin, const InputIterator & end)
-  {
+  template <typename InputIterator>
+  void set_env_data(InputIterator begin, InputIterator end) {
     clear_data();
     add_data(begin, end);
   }
 
-  /*!
-   * set the data to be empty.
+  /*! set the data to be empty.
    */
-  void set_no_data()
-  {
+  void set_no_data() {
     clear_data();
     m_is_set = true;
   }
 
-   /*!
-   * Add a data object to the face.
+   /*! Add a data object to the face.
    * \param data The additional data object.
    */
-  void add_data (const Data & data)
-  {
+  void add_data(const Data& data) {
     m_data.push_back(data);
     m_is_set = true;
   }
 
-  /*!
-   * Add a range of data objects to the face.
+  /*! Add a range of data objects to the face.
    * \param begin A begin iterator for the data range.
    * \param end A past-the-end iterator for the data range.
    */
-  template <class InputIterator>
-  void add_data (const InputIterator & begin, const InputIterator & end)
-  {
-    InputIterator    it;
-    for (it = begin; it != end; it++)
-      m_data.push_back(*it);
+  template <typename InputIterator>
+  void add_data(InputIterator begin, InputIterator end) {
+    for (auto it = begin; it != end; it++) m_data.push_back(*it);
     m_is_set = true;
   }
 
-  /*!
-   * Clear the data objects.
+  /*! Clear the data objects.
    */
-  void clear_data ()
-  {
+  void clear_data() {
     m_data.clear();
     m_is_set = false;
   }
 
-  /*!
-   * Check if the set of data objects in the input range is equal to our
+  /*! Check whether the set of data objects in the input range is equal to our
    * set of data objects
    */
-  template <class InputIterator>
-  bool is_equal_data(const InputIterator & begin, const InputIterator & end)
-    const
-  {
-    if (!get_is_set())
-      return false;
+  template <typename InputIterator>
+  bool is_equal_data(InputIterator begin, InputIterator end) const {
+    if (! get_is_set()) return false;
 
     // insert the input data objects into a set
     std::set<Data> input_data(begin, end);
     std::set<Data> my_data(begin_data(), end_data());
-    if (input_data.size() != my_data.size())
-      return false;
+    if (input_data.size() != my_data.size()) return false;
     return (my_data == input_data);
   }
 
-  template <class InputIterator>
-  bool has_equal_data(const InputIterator & begin, const InputIterator & end)
-    const
-  {
-    if (!get_is_set())
-      return false;
+  template <typename InputIterator>
+  bool has_equal_data(InputIterator begin, InputIterator end) const {
+    if (! get_is_set()) return false;
+
     // insert the input data objects into a set
     std::set<Data> input_data(begin, end);
     std::set<Data> my_data(begin_data(), end_data());
@@ -260,49 +191,46 @@ class Dcel_info
 
 public:
   template<class HandleType>
-  void set_aux_source(unsigned int id, HandleType h)
-  {
+  void set_aux_source(unsigned int id, HandleType h) {
     CGAL_precondition(id < 2);
     m_aux_source[id] = make_object(h);
   }
-  void set_aux_source(unsigned int id, const Object& o)
-  {
+
+  void set_aux_source(unsigned int id, const Object& o) {
     CGAL_precondition(id < 2);
     CGAL_precondition(!o.is_empty());
     m_aux_source[id] = o;
   }
 
-  const Object& get_aux_source(unsigned int id)
-  {
+  const Object& get_aux_source(unsigned int id) {
     CGAL_precondition(id < 2);
     CGAL_precondition (!m_aux_source[id].is_empty());
     return m_aux_source[id];
   }
 
   /*! \brief returns true iff the point has been set already */
-  bool get_aux_is_set(unsigned int id) const
-  {
+  bool get_aux_is_set(unsigned int id) const {
     CGAL_precondition(id < 2);
-        return (!m_aux_source[id].is_empty());
+    return (! m_aux_source[id].is_empty());
   }
 };
 
 /*! Extend the planar-map vertex */
-template <class Point_2, class Data>
-class Envelope_pm_vertex : public CGAL::Arr_vertex_base<Point_2>,
-                           public Dcel_info<Data>
-{
-  typedef CGAL::Arr_vertex_base<Point_2>       Base_vertex;
-  typedef Dcel_info<Data>                      Base_info;
-  typedef Envelope_pm_vertex<Point_2, Data>    Self;
+template <typename BaseVertex, class VertexData>
+class Envelope_pm_vertex : public BaseVertex, public Dcel_info<VertexData> {
+public:
+  using Base_vertex = BaseVertex;
+  using Vertex_data = VertexData;
+
+private:
+  using Self = Envelope_pm_vertex<Base_vertex, Vertex_data>;
 
 protected:
   // all flags are bits in this variable:
   unsigned short flags;
 
   // the flags indications:
-  enum Bit_pos
-  {
+  enum Bit_pos {
     // for an isolated vertex only
     IS_EQUAL   = 0,
     IS_EQUAL_AUX = 1,
@@ -316,10 +244,12 @@ class Envelope_pm_vertex : public CGAL::Arr_vertex_base<Point_2>,
     // intersection points
     IS_INTERSECTION = 7
   };
+
 public:
+  using Base_info = Dcel_info<Vertex_data>;
+
   /*! Constructor */
-  Envelope_pm_vertex() : Dcel_info<Data>(), flags(0)
-  {}
+  Envelope_pm_vertex() : Dcel_info<Vertex_data>(), flags(0) {}
 
   /*void set_is_fake(bool b)
   {
@@ -339,42 +269,26 @@ class Envelope_pm_vertex : public CGAL::Arr_vertex_base<Point_2>,
     return get_bit(IS_FAKE);
   }*/
 
-  void set_is_equal_data_in_face(bool b)
-  {
-    set_bit(IS_EQUAL, b);
-  }
-  bool get_is_equal_data_in_face() const
-  {
-    return get_bit(IS_EQUAL);
-  }
+  void set_is_equal_data_in_face(bool b) { set_bit(IS_EQUAL, b); }
+  bool get_is_equal_data_in_face() const { return get_bit(IS_EQUAL); }
 
-  void set_has_equal_data_in_face(bool b)
-  {
-    set_bit(HAS_EQUAL, b);
-  }
-  bool get_has_equal_data_in_face() const
-  {
-    return get_bit(HAS_EQUAL);
-  }
+  void set_has_equal_data_in_face(bool b) { set_bit(HAS_EQUAL, b); }
+  bool get_has_equal_data_in_face() const { return get_bit(HAS_EQUAL); }
 
-  void set_is_equal_aux_data_in_face(unsigned int id, bool b)
-  {
+  void set_is_equal_aux_data_in_face(unsigned int id, bool b) {
     CGAL_assertion(id < 2);
     set_bit(IS_EQUAL_AUX+id, b);
   }
-  bool get_is_equal_aux_data_in_face(unsigned int id) const
-  {
+  bool get_is_equal_aux_data_in_face(unsigned int id) const {
     CGAL_assertion(id < 2);
     return get_bit(IS_EQUAL_AUX+id);
   }
 
-  void set_has_equal_aux_data_in_face(unsigned int id, bool b)
-  {
+  void set_has_equal_aux_data_in_face(unsigned int id, bool b) {
     CGAL_assertion(id < 2);
     set_bit(HAS_EQUAL_AUX+id, b);
   }
-  bool get_has_equal_aux_data_in_face(unsigned int id) const
-  {
+  bool get_has_equal_aux_data_in_face(unsigned int id) const {
     CGAL_assertion(id < 2);
     return get_bit(HAS_EQUAL_AUX+id);
   }
@@ -382,8 +296,7 @@ class Envelope_pm_vertex : public CGAL::Arr_vertex_base<Point_2>,
   /*! Assign from another vertex.
    * \param v the other vertex.
    */
-  virtual void assign(const Base_vertex & v)
-  {
+  virtual void assign(const Base_vertex& v) {
     Base_vertex::assign(v);
 
     const Self & ex_v = static_cast<const Self&>(v);
@@ -392,18 +305,13 @@ class Envelope_pm_vertex : public CGAL::Arr_vertex_base<Point_2>,
   }
 
 protected:
-  void set_bit(unsigned int ind, bool b)
-  {
-    if (b)
-      // set bit "ind" to 1:
-      flags |= (1 << ind);
-    else
-      // set bit "ind" to 0:
-      flags &= ~(1 << ind);
+  void set_bit(unsigned int ind, bool b) {
+    // set bit "ind" to 1 or 0:
+    if (b) flags |= (1 << ind);
+    else flags &= ~(1 << ind);
   }
 
-  bool get_bit(unsigned int ind) const
-  {
+  bool get_bit(unsigned int ind) const {
     // (1 << i) is bit i on, other bits off (start counting from 0)
     unsigned int mask = 1 << ind;
     return ((flags & mask) == mask);
@@ -411,23 +319,22 @@ class Envelope_pm_vertex : public CGAL::Arr_vertex_base<Point_2>,
 };
 
 /*! Extend the planar-map halfedge */
-template <class X_monotone_curve_2, class Data>
-class
-Envelope_pm_halfedge : public CGAL::Arr_halfedge_base<X_monotone_curve_2>,
-                       public Dcel_info<Data>
-{
-  typedef CGAL::Arr_halfedge_base<X_monotone_curve_2>     Base_halfedge;
-  typedef Dcel_info<Data>                                 Base_info;
-  typedef Envelope_pm_halfedge<X_monotone_curve_2, Data>  Self;
+template <typename BaseHalfedge, typename HalfedgeData>
+class Envelope_pm_halfedge : public BaseHalfedge,
+                             public Dcel_info<HalfedgeData> {
+public:
+  using Base_halfedge = BaseHalfedge;
+  using Halfedge_data = HalfedgeData;
 
-protected:
+private:
+  using Self = Envelope_pm_halfedge<Base_halfedge, Halfedge_data>;
 
+protected:
   // all flags are bits in this variable:
   unsigned int flags;
 
   // flags indications
-  enum Bit_pos
-  {
+  enum Bit_pos {
     // indications for the Envelope algorithm
     // relation between halfedge and incident face
     IS_EQUAL_FACE   = 0,
@@ -448,8 +355,9 @@ Envelope_pm_halfedge : public CGAL::Arr_halfedge_base<X_monotone_curve_2>,
   };
 
 public:
-  Envelope_pm_halfedge() : Dcel_info<Data>(), flags(0)
-  {}
+  using Base_info = Dcel_info<Halfedge_data>;
+
+  Envelope_pm_halfedge() : Dcel_info<Halfedge_data>(), flags(0) {}
 
  /* void set_is_fake(bool b)
   {
@@ -460,102 +368,64 @@ Envelope_pm_halfedge : public CGAL::Arr_halfedge_base<X_monotone_curve_2>,
     return get_bit(IS_FAKE);
   }*/
 
-  void set_is_equal_data_in_face(bool b)
-  {
-    set_bit(IS_EQUAL_FACE, b);
-  }
-  bool get_is_equal_data_in_face() const
-  {
-    return get_bit(IS_EQUAL_FACE);
-  }
+  void set_is_equal_data_in_face(bool b) { set_bit(IS_EQUAL_FACE, b); }
+  bool get_is_equal_data_in_face() const { return get_bit(IS_EQUAL_FACE); }
 
-  void set_has_equal_data_in_face(bool b)
-  {
-    set_bit(HAS_EQUAL_FACE, b);
-  }
-  bool get_has_equal_data_in_face() const
-  {
-    return get_bit(HAS_EQUAL_FACE);
-  }
+  void set_has_equal_data_in_face(bool b) { set_bit(HAS_EQUAL_FACE, b); }
+  bool get_has_equal_data_in_face() const { return get_bit(HAS_EQUAL_FACE); }
 
-  void set_is_equal_aux_data_in_face(unsigned int id, bool b)
-  {
+  void set_is_equal_aux_data_in_face(unsigned int id, bool b) {
     CGAL_assertion(id < 2);
     set_bit(IS_EQUAL_AUX_FACE+id, b);
   }
-  bool get_is_equal_aux_data_in_face(unsigned int id) const
-  {
+  bool get_is_equal_aux_data_in_face(unsigned int id) const {
     CGAL_assertion(id < 2);
     return get_bit(IS_EQUAL_AUX_FACE+id);
   }
 
-  void set_has_equal_aux_data_in_face(unsigned int id, bool b)
-  {
+  void set_has_equal_aux_data_in_face(unsigned int id, bool b) {
     CGAL_assertion(id < 2);
     set_bit(HAS_EQUAL_AUX_FACE+id, b);
   }
-  bool get_has_equal_aux_data_in_face(unsigned int id) const
-  {
+  bool get_has_equal_aux_data_in_face(unsigned int id) const {
     CGAL_assertion(id < 2);
     return get_bit(HAS_EQUAL_AUX_FACE+id);
   }
 
-  void set_is_equal_data_in_target(bool b)
-  {
-    set_bit(IS_EQUAL_TARGET, b);
-  }
-  bool get_is_equal_data_in_target() const
-  {
-    return get_bit(IS_EQUAL_TARGET);
-  }
+  void set_is_equal_data_in_target(bool b) { set_bit(IS_EQUAL_TARGET, b); }
+  bool get_is_equal_data_in_target() const { return get_bit(IS_EQUAL_TARGET); }
 
-  void set_has_equal_data_in_target(bool b)
-  {
-    set_bit(HAS_EQUAL_TARGET, b);
-  }
-  bool get_has_equal_data_in_target() const
-  {
-    return get_bit(HAS_EQUAL_TARGET);
-  }
+  void set_has_equal_data_in_target(bool b) { set_bit(HAS_EQUAL_TARGET, b); }
+  bool get_has_equal_data_in_target() const { return get_bit(HAS_EQUAL_TARGET); }
 
-  void set_is_equal_aux_data_in_target(unsigned int id, bool b)
-  {
+  void set_is_equal_aux_data_in_target(unsigned int id, bool b) {
     CGAL_assertion(id < 2);
     set_bit(IS_EQUAL_AUX_TARGET+id, b);
   }
-  bool get_is_equal_aux_data_in_target(unsigned int id) const
-  {
+  bool get_is_equal_aux_data_in_target(unsigned int id) const {
     CGAL_assertion(id < 2);
     return get_bit(IS_EQUAL_AUX_TARGET+id);
   }
 
-  void set_has_equal_aux_data_in_target(unsigned int id, bool b)
-  {
+  void set_has_equal_aux_data_in_target(unsigned int id, bool b) {
     CGAL_assertion(id < 2);
     set_bit(HAS_EQUAL_AUX_TARGET+id, b);
   }
-  bool get_has_equal_aux_data_in_target(unsigned int id) const
-  {
+  bool get_has_equal_aux_data_in_target(unsigned int id) const {
     CGAL_assertion(id < 2);
     return get_bit(HAS_EQUAL_AUX_TARGET+id);
   }
   // access to flags that contain relation between target and face
   void set_has_equal_data_in_target_and_face(bool b)
-  {
-    set_bit(HAS_EQUAL_F_T, b);
-  }
+  { set_bit(HAS_EQUAL_F_T, b); }
   bool get_has_equal_data_in_target_and_face() const
-  {
-    return get_bit(HAS_EQUAL_F_T);
-  }
+  { return get_bit(HAS_EQUAL_F_T); }
 
-  void set_has_equal_aux_data_in_target_and_face(unsigned int id, bool b)
-  {
+  void set_has_equal_aux_data_in_target_and_face(unsigned int id, bool b) {
     CGAL_assertion(id < 2);
     set_bit(HAS_EQUAL_AUX_F_T+id, b);
   }
-  bool get_has_equal_aux_data_in_target_and_face(unsigned int id) const
-  {
+  bool get_has_equal_aux_data_in_target_and_face(unsigned int id) const {
     CGAL_assertion(id < 2);
     return get_bit(HAS_EQUAL_AUX_F_T+id);
   }
@@ -563,8 +433,7 @@ Envelope_pm_halfedge : public CGAL::Arr_halfedge_base<X_monotone_curve_2>,
   /*! Assign from another halfedge.
    * \param h the other halfedge.
    */
-  virtual void assign(const Base_halfedge & h)
-  {
+  virtual void assign(const Base_halfedge& h) {
     Base_halfedge::assign(h);
 
     const Self & ex_h = static_cast<const Self&>(h);
@@ -573,99 +442,93 @@ Envelope_pm_halfedge : public CGAL::Arr_halfedge_base<X_monotone_curve_2>,
   }
 
 protected:
-  void set_bit(unsigned int ind, bool b)
-  {
-    if (b)
-      // set bit "ind" to 1:
-      flags |= (1 << ind);
-    else
-      // set bit "ind" to 0:
-      flags &= ~(1 << ind);
+  void set_bit(unsigned int ind, bool b) {
+    if (b) flags |= (1 << ind);
+    else flags &= ~(1 << ind);
     CGAL_assertion(get_bit(ind) == b);
   }
 
-  bool get_bit(unsigned int ind) const
-  {
+  bool get_bit(unsigned int ind) const {
     // (1 << i) is bit i on, other bits off (start counting from 0)
     unsigned int mask = 1 << ind;
     return ((flags & mask) == mask);
   }
 };
 
-/*! Extend the planar-map face */
-template <class Data>
-class Envelope_pm_face : public CGAL::Arr_face_base,
-                         public Dcel_info<Data>
-{
-  typedef CGAL::Arr_face_base       Base_face;
-  typedef Dcel_info<Data>           Base_info;
-  typedef Envelope_pm_face<Data>    Self;
+  //! Extend the planar-map face.
+template <typename BaseFace, typename FaceData>
+class Envelope_pm_face : public BaseFace, public Dcel_info<FaceData> {
+public:
+  using Base_face = BaseFace;
+  using Face_data = FaceData;
+
+private:
+  using Self = Envelope_pm_face<Base_face, Face_data>;
 
 public:
-  typedef std::list<Data>                         Data_container;
-  typedef typename Data_container::iterator       Data_iterator;
-  typedef typename Data_container::const_iterator Data_const_iterator;
+  using Base_info = Dcel_info<Face_data>;
+  using Data_container = std::list<Face_data>;
+  using Data_iterator = typename Data_container::iterator;
+  using Data_const_iterator = typename Data_container::const_iterator;
 
-  /*! Constructor */
-  Envelope_pm_face() : Dcel_info<Data>()
-  {}
+  /*! Construct.
+   */
+  Envelope_pm_face() : Dcel_info<Face_data>() {}
 
   /*! Assign from another face.
    * \param f the other face.
    */
-  virtual void assign (const Base_face & f)
-  {
+  virtual void assign(const Base_face& f) {
     Base_face::assign(f);
 
-    const Self & ex_f = static_cast<const Self&>(f);
+    const Self& ex_f = static_cast<const Self&>(f);
     this->Base_info::operator=(ex_f);
   }
 };
 
 /*! A new dcel builder with full Envelope features */
-template <class Traits, class Data>
-class Envelope_pm_dcel : public
-CGAL::Arr_dcel_base<Envelope_pm_vertex<typename Traits::Point_2, Data>,
-                    Envelope_pm_halfedge<typename Traits::X_monotone_curve_2,
-                                         Data>,
-                    Envelope_pm_face<Data> >
-{
+template <typename Traits_, typename DcelData,
+          typename VertexBase = Arr_vertex_base<typename Traits_::Point_2>,
+          typename HalfedgeBase =
+            Arr_halfedge_base<typename Traits_::X_monotone_curve_2>,
+          typename FaceBase = Arr_face_base>
+class Envelope_pm_dcel :
+  public CGAL::Arr_dcel_base<Envelope_pm_vertex<VertexBase, DcelData>,
+                             Envelope_pm_halfedge<HalfedgeBase, DcelData>,
+                             Envelope_pm_face<FaceBase, DcelData>> {
 public:
+  using Dcel_data = DcelData;
+  using Face_base = FaceBase;
 
-  typedef Data                                    Face_data;
-  typedef typename Envelope_pm_face<Data>::Data_iterator
-                                                  Face_data_iterator;
-  typedef typename Envelope_pm_face<Data>::Data_const_iterator
-                                                  Face_data_const_iterator;
-
-  typedef Data                                    Edge_data;
-  typedef Face_data_iterator                      Edge_data_iterator;
-  typedef Face_data_const_iterator                Edge_data_const_iterator;
+  using Face_data = Dcel_data;
+  using Env_pm_face = Envelope_pm_face<Face_base, Dcel_data>;
+  using Face_data_iterator = typename Env_pm_face::Data_iterator;
+  using Face_data_const_iterator = typename Env_pm_face::Data_const_iterator;
 
-  typedef Data                                    Vertex_data;
-  typedef Face_data_iterator                      Vertex_data_iterator;
-  typedef Face_data_const_iterator                Vertex_data_const_iterator;
+  using Edge_data = Dcel_data;
+  using Edge_data_iterator = Face_data_iterator;
+  using Edge_data_const_iterator = Face_data_const_iterator;
 
-  typedef Dcel_info<Data>                         Dcel_elem_with_data;
+  using Vertex_data = Dcel_data;
+  using Vertex_data_iterator = Face_data_iterator;
+  using Vertex_data_const_iterator = Face_data_const_iterator;
 
-  typedef Data                                    Dcel_data;
-  typedef Face_data_iterator                      Dcel_data_iterator;
-  typedef Face_data_const_iterator                Dcel_data_const_iterator;
+  using Dcel_elem_with_data = Dcel_info<Dcel_data>;
+  using Dcel_data_iterator = Face_data_iterator;
+  using Dcel_data_const_iterator = Face_data_const_iterator;
 
   /*! \struct
    * An auxiliary structure for rebinding the DCEL with a new traits class.
    */
   template<typename T>
-  struct rebind
-  {
-    typedef Envelope_pm_dcel<T, Face_data> other;
-  };
+  struct rebind { typedef Envelope_pm_dcel<T, Face_data> other; };
 
   /*! Constructor */
   Envelope_pm_dcel() {}
 };
 
 } // namespace Envelope_3
+
 } // namespace CGAL
 
 #endif