From 161934a3929aa32c0ff2fad9ec7213504cbf772d Mon Sep 17 00:00:00 2001
From: Sven Oesau <sven.oesau@geometryfactory.com>
Date: Tue, 4 Mar 2025 20:57:35 +0100
Subject: [PATCH 01/21] adding Poisson_mesh_domain_3

---
 Mesh_3/include/CGAL/Poisson_mesh_domain_3.h | 398 ++++++++++++++++++++
 1 file changed, 398 insertions(+)
 create mode 100644 Mesh_3/include/CGAL/Poisson_mesh_domain_3.h

diff --git a/Mesh_3/include/CGAL/Poisson_mesh_domain_3.h b/Mesh_3/include/CGAL/Poisson_mesh_domain_3.h
new file mode 100644
index 00000000000..4631db75bbd
--- /dev/null
+++ b/Mesh_3/include/CGAL/Poisson_mesh_domain_3.h
@@ -0,0 +1,398 @@
+// Copyright (c) 2025 GeometryFactory (France).
+// All rights reserved.
+//
+// This file is part of CGAL (www.cgal.org).
+//
+// $URL$
+// $Id$
+// SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
+//
+//
+// Author(s)     : Sven Oesau
+//
+//******************************************************************************
+// File Description :
+// class Poisson_mesh_domain_3. See class description.
+//******************************************************************************
+
+#ifndef CGAL_POISSON_MESH_DOMAIN_3_H
+#define CGAL_POISSON_MESH_DOMAIN_3_H
+
+#include <CGAL/license/Mesh_3.h>
+
+#include <CGAL/Labeled_mesh_domain_3.h>
+#include <CGAL/Poisson_reconstruction_function.h>
+
+namespace CGAL {
+
+///!
+//\ingroup PkgMesh3Domains
+//
+//\brief The class `Poisson_mesh_domain_3` derives from `Labeled_mesh_domain_3` for the handling of `Poisson_reconstruction_function`.
+//
+// This class has a constructor taking a labeling function. It has also a static template member
+// function that acts as named constructor:
+// <ul><li>`create_poisson_mesh_domain()`, to create a domain from a `Poisson_reconstruction_function`</ ul>
+//
+//\tparam BGT is a geometric traits class that provides
+//    the basic operations to implement intersection tests and intersection computations through a bisection
+//    method.This parameter must be instantiated with a model of the concept `BisectionGeometricTraits_3`.
+//
+// This class is a model of concept `MeshDomain_3`.
+//\cgalModels{MeshDomain_3}
+//
+//\sa `CGAL::Labeled_mesh_domain_3`
+//\sa `CGAL::make_mesh_3()`
+//
+///
+template<class BGT,
+         class Subdomain_index_ = int,
+         class Surface_patch_index_ = std::pair<Subdomain_index_,
+                                                Subdomain_index_> >
+class Poisson_mesh_domain_3
+    : public Labeled_mesh_domain_3<BGT,
+                                                  Subdomain_index_,
+                                                  Surface_patch_index_>
+{
+public:
+  using Base = Labeled_mesh_domain_3<BGT, Subdomain_index_, Surface_patch_index_>;
+  typedef typename Base::Subdomain Subdomain;
+
+  // Type of indexes for cells of the input complex
+  typedef Surface_patch_index_ Surface_patch_index;
+  typedef std::optional<Surface_patch_index> Surface_patch;
+  typedef Subdomain_index_ Subdomain_index;
+  typedef typename Base::Index Index;
+  typedef typename Base::Intersection Intersection;
+
+  // Type of indexes to characterize the lowest dimensional face of the input
+  // complex on which a vertex lie
+  typedef typename CGAL::Mesh_3::internal::Index_generator<Subdomain_index, Surface_patch_index>::Index Index;
+
+  // Geometric object types
+  // /// \name Types imported from the geometric traits class
+  ///@{
+  /// The point type of the geometric traits class
+  typedef typename Geom_traits::Point_3 Point_3;
+  /// The sphere type of the geometric traits class
+  typedef typename Geom_traits::Sphere_3 Sphere_3;
+  /// The iso-cuboid type of the geometric traits class
+  typedef typename Geom_traits::Iso_cuboid_3 Iso_cuboid_3;
+  /// The bounding box type
+  typedef CGAL::Bbox_3 Bbox_3;
+  /// The number type (a field type) of the geometric traits class
+  typedef typename Geom_traits::FT FT;
+  /// The ray type of the geometric traits class
+  typedef typename BGT::Ray_3 Ray_3;
+  /// The line type of the geometric traits class
+  typedef typename BGT::Line_3 Line_3;
+  /// The segment type of the geometric traits class
+  typedef typename BGT::Segment_3 Segment_3;
+  ///@}
+
+
+  typedef CGAL::Poisson_reconstruction_function<BGT> Function;
+  Function poisson_function;
+  /// \name Creation
+/// @{
+  ///!  \brief Construction from a function, a bounding object and a relative error bound.
+   //
+   // \tparam Function a type compatible with `Labeling_function`
+   // \tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
+   // \tparam Bounding_object either a bounding sphere (of type `Sphere_3`), a bounding box (type `Bbox_3`),
+   //                         or a bounding `Iso_cuboid_3`
+   //
+   // \param function the labeling function
+   // \param bounding_object the bounding object bounding the meshable space.
+   // \param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below:
+   //
+   // \cgalNamedParamsBegin
+   //   \cgalParamNBegin{relative_error_bound}
+   //      \cgalParamDescription{the relative error bound used to compute intersection points between the implicit surface and query segments.
+   //                            The bisection is stopped when the length of the intersected segment is less than the product
+   //                            of `relative_error_bound` by the diameter of the bounding object.}
+   //      \cgalParamDefault{FT(1e-3)}
+   //   \cgalParamNEnd
+   // \cgalNamedParamsEnd
+   //
+   // \cgalHeading{Example}
+   // From the example (\ref Mesh_3/mesh_implicit_domains_2.cpp):
+   // \snippet Mesh_3/mesh_implicit_domains_2.cpp Domain creation
+   ///
+  template<typename Bounding_object, typename CGAL_NP_TEMPLATE_PARAMETERS>
+  Poisson_mesh_domain_3(const Function& function,
+                        const Bounding_object& bounding_object,
+                        const CGAL_NP_CLASS& np = parameters::default_values()
+#ifndef DOXYGEN_RUNNING
+                        , typename std::enable_if<!is_named_function_parameter<Function>>::type* = nullptr
+#endif // DOXYGEN_RUNNING
+                        )
+      : Base(make_implicit_to_labeling_function_wrapper<BGT>(function), bounding_object, np),
+        poisson_function(function)
+  {}
+///@}
+
+#ifndef DOXYGEN_RUNNING
+  template<typename CGAL_NP_TEMPLATE_PARAMETERS_NO_DEFAULT>
+  Poisson_mesh_domain_3(const CGAL_NP_CLASS& np)
+      : Base(np)
+  {}
+
+  // Overload handling parameters passed with operator=
+
+  template<typename CGAL_NP_TEMPLATE_PARAMETERS_NO_DEFAULT_1,
+           typename CGAL_NP_TEMPLATE_PARAMETERS_NO_DEFAULT_2,
+           typename ... NP>
+  Poisson_mesh_domain_3(const Function& function,
+                        const CGAL_NP_CLASS_1& np1,
+                        const CGAL_NP_CLASS_2&  np2,
+                        const NP& ... nps)
+      : Base(internal_np::combine_named_parameters(
+            CGAL::parameters::function(make_implicit_to_labeling_function_wrapper<BGT>(function)), np1, np2, nps...)),
+        poisson_function(function)
+  {}
+#endif
+
+/// \name Creation of domains from Poisson implicit functions
+/// @{
+
+  ///!
+   // \brief Construction from a Poisson implicit function
+   //
+   // This static method is a <em>named constructor</em>. It constructs a domain
+   // whose bounding surface is described implicitly as the zero level set of a
+   // function.  The domain to be discretized is assumed to be the domain where
+   // the function has negative values.
+   //
+   // The method takes as argument a bounding sphere which is required to
+   // circumscribe the surface and to have its center inside the domain.
+   //
+   // \tparam Function a type compatible with the signature `FT(Point_3)`: it takes a point as argument,
+   //                  and returns a scalar value. That object must be model of `CopyConstructible`
+   // \tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
+   // \tparam Bounding_object either a bounding sphere (of type `Sphere_3`), a bounding box (type `Bbox_3`),
+   //                         or a bounding `Iso_cuboid_3`
+   //
+   // \param function the implicit function
+   // \param bounding_object object boundint the meshable domain and its center is inside the domain.
+   // \param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below:
+   //
+   // \cgalNamedParamsBegin
+   //   \cgalParamNBegin{relative_error_bound}
+   //     \cgalParamDescription{ is the relative error
+   //                            bound, relative to the diameter of the box of the image.}
+   //     \cgalParamDefault{FT(1e-3)}
+   //   \cgalParamNEnd
+   // \cgalNamedParamsEnd
+   //
+   // \cgalHeading{Examples}
+   //
+   // From the example (\ref Mesh_3/mesh_implicit_sphere.cpp):
+   //
+   // \snippet Mesh_3/mesh_implicit_sphere.cpp Domain creation
+   //
+   // From the example (\ref Mesh_3/mesh_implicit_sphere_variable_size.cpp):
+   //
+   // \snippet Mesh_3/mesh_implicit_sphere_variable_size.cpp Domain creation
+   //
+   ///
+  template<typename Bounding_object, typename CGAL_NP_TEMPLATE_PARAMETERS>
+  static Poisson_mesh_domain_3 create_poisson_mesh_domain(const Function& function,
+                                                           const Bounding_object& bounding_object,
+                                                           const CGAL_NP_CLASS& np = parameters::default_values()
+#ifndef DOXYGEN_RUNNING
+                                                           ,typename std::enable_if<!is_named_function_parameter<Function>>::type* = nullptr
+#endif
+)
+  {
+    using parameters::get_parameter;
+    using parameters::choose_parameter;
+    FT relative_error_bound_ = choose_parameter(get_parameter(np, internal_np::error_bound), FT(1e-3));
+    CGAL::Random* p_rng_ = choose_parameter(get_parameter(np, internal_np::rng), nullptr);
+    auto null_subdomain_index_ = choose_parameter(get_parameter(np, internal_np::null_subdomain_index_param),
+Null_functor()); auto construct_surface_patch_index_ = choose_parameter(get_parameter(np,
+internal_np::surface_patch_index), Null_functor());
+    namespace p = CGAL::parameters;
+    return Poisson_mesh_domain_3
+            (function,
+             bounding_object,
+              CGAL::parameters::relative_error_bound(relative_error_bound_)
+              .function(make_implicit_to_labeling_function_wrapper<BGT>(function))
+              .p_rng(p_rng_)
+              .null_subdomain_index(Base::create_null_subdomain_index(null_subdomain_index_))
+              .construct_surface_patch_index(Base::create_construct_surface_patch_index(construct_surface_patch_index_)));
+  }
+/// @}
+#ifndef DOXYGEN_RUNNING
+  template<typename CGAL_NP_TEMPLATE_PARAMETERS>
+  static Poisson_mesh_domain_3 create_poisson_mesh_domain(const CGAL_NP_CLASS& np = parameters::default_values())
+  {
+    static_assert(!parameters::is_default_parameter<CGAL_NP_CLASS, internal_np::function_param_t>::value,
+      "Value for required parameter not found"); static_assert(!parameters::is_default_parameter<CGAL_NP_CLASS,
+internal_np::bounding_object_param_t>::value, "Value for required parameter not found");
+
+    using parameters::get_parameter;
+    return create_poisson_mesh_domain(parameters::get_parameter(np, internal_np::function_param),
+                                       parameters::get_parameter(np, internal_np::bounding_object_param),
+                                       np);
+  }
+
+  // Overload handling parameters passed with operator=
+  template<typename CGAL_NP_TEMPLATE_PARAMETERS_NO_DEFAULT_1,
+           typename CGAL_NP_TEMPLATE_PARAMETERS_NO_DEFAULT_2,
+           typename ... NP>
+  static Poisson_mesh_domain_3 create_poisson_mesh_domain(const CGAL_NP_CLASS_1& np1,
+                                                           const CGAL_NP_CLASS_2&  np2,
+                                                           const NP& ... nps)
+  {
+    return create_poisson_mesh_domain(internal_np::combine_named_parameters(np1, np2, nps...));
+  }
+#endif
+
+  /*
+   * Returns a point in the intersection of the primitive `type`
+   * with some boundary surface.
+   * `Type1` is either `Segment_3`, `Ray_3` or `Line_3`.
+   * The integer `dimension` is set to the dimension of the lowest
+   * dimensional face in the input complex containing the returned point, and
+   * `index` is set to the index to be stored at a mesh vertex lying
+   * on this face.
+   */
+  struct Construct_intersection
+  {
+    Construct_intersection(const Poisson_mesh_domain_3& domain)
+      : r_domain_(domain) {}
+
+    Intersection operator()(const Segment_3& s) const
+    {
+#ifndef CGAL_MESH_3_NO_LONGER_CALLS_DO_INTERSECT_3
+      CGAL_precondition(r_domain_.do_intersect_surface_object()(s) != std::nullopt);
+#endif // NOT CGAL_MESH_3_NO_LONGER_CALLS_DO_INTERSECT_3
+      return this->operator()(s.source(),s.target());
+    }
+
+    Intersection operator()(const Ray_3& r) const
+    {
+      return clip_to_segment(r);
+    }
+
+    Intersection operator()(const Line_3& l) const
+    {
+      return clip_to_segment(l);
+    }
+
+  private:
+    /*
+     * Returns a point in the intersection of [a,b] with the surface
+     *  `a` must be the source point, and `b` the out point. It's important
+     * because it drives bisection cuts.
+     * Indeed, the returned point is the first intersection from  `[a,b]`
+     * with a subdomain surface.
+     */
+    Intersection operator()(const Point_3& a, const Point_3& b) const
+    {
+      // Functors
+      typename BGT::Compute_squared_distance_3 squared_distance =
+                                      BGT().compute_squared_distance_3_object();
+      typename BGT::Construct_midpoint_3 midpoint =
+                                      BGT().construct_midpoint_3_object();
+
+      // Non const points
+      Point_3 p1 = a;
+      Point_3 p2 = b;
+      Point_3 mid = midpoint(p1, p2);
+
+      FT value_at_p1, value_at_p2;
+      typename Function::Cell_handle c1, c2;
+      bool c1_is_inf, c2_is_inf;
+
+      std::tie(value_at_p1, c1, c1_is_inf) = r_domain_.poisson_function.special_func(p1);
+      std::tie(value_at_p2, c2, c2_is_inf) = r_domain_.poisson_function.special_func(p2);
+
+      Subdomain_index label_at_p1 = (value_at_p1 < 0) ? 1 : 0;
+      Subdomain_index label_at_p2 = (value_at_p2 < 0) ? 1 : 0;
+
+      // If both extremities are in the same subdomain,
+      // there is no intersection.
+      // This should not happen...
+      if(label_at_p1 == label_at_p2)
+        return Intersection();
+
+      // Else lets find a point (by bisection)
+      // Bisection ends when the point is near than error bound from surface
+      while(true) {
+        if(c1 == c2) {
+          if(c1_is_inf) {
+            std::cout << "Intersection(): c1 == c2 and inf!" << std::endl;
+            return Intersection();
+          } else {
+            const Surface_patch_index sp_index = r_domain_.make_surface_index(label_at_p1, label_at_p2);
+            const Index index = r_domain_.index_from_surface_patch_index(sp_index);
+            return Intersection(Point(ORIGIN + ((value_at_p2 * (p1 - ORIGIN)) - (value_at_p1 * (p2 - ORIGIN))) /
+                                                  (value_at_p2 - value_at_p1)), index, 2);
+          }
+        }
+        mid = midpoint(p1, p2);
+        // If the two points are enough close, then we return midpoint
+        if ( squared_distance(p1, p2) < r_domain_.squared_error_bound_ )
+        {
+          CGAL_assertion(value_at_p1 * value_at_p2 <= 0);
+          const Surface_patch_index sp_index = r_domain_.make_surface_index(label_at_p1, label_at_p2);
+          const Index index = r_domain_.index_from_surface_patch_index(sp_index);
+          return Intersection(mid, index, 2);
+        }
+
+        // Cannot be const: those values are modified below.
+        FT value_at_mid;
+        typename Function::Cell_handle c_at_mid;
+        bool c_is_inf;
+        std::tie(value_at_mid, c_at_mid, c_is_inf) = r_domain_.poisson_function.special_func(mid);
+        Subdomain_index label_at_mid = (value_at_mid < 0) ? 1 : 0;
+
+        // Else we must go on
+        // Here we consider that p1(a) is the source point. Thus, we keep p1 and
+        // change p2 if f(p1)!=f(p2).
+        // That allows us to find the first intersection from a of [a,b] with
+        // a surface.
+        if(label_at_p1 != label_at_mid && !(r_domain_.null(label_at_p1) && r_domain_.null(label_at_mid)))
+        {
+          p2 = mid;
+          value_at_p2 = value_at_mid;
+          label_at_p2 = label_at_mid;
+        }
+        else
+        {
+          p1 = mid;
+          value_at_p1 = value_at_mid;
+          label_at_p1 = label_at_mid;
+        }
+      }
+    }
+
+    // Clips  `query` to a segment `s`, and call `operator()(s)`
+    template<typename Query>
+    Intersection clip_to_segment(const Query& query) const
+    {
+      const auto clipped = CGAL::intersection(query, r_domain_.bbox_);
+      if(clipped)
+        if(const Segment_3* s = std::get_if<Segment_3>(&*clipped))
+          return this->operator()(*s);
+
+      return Intersection();
+    }
+
+  private:
+    const Poisson_mesh_domain_3& r_domain_;
+  };
+
+  // Returns Construct_intersection object
+  Construct_intersection construct_intersection_object() const
+  {
+    return Construct_intersection(*this);
+  }
+
+};  // end class Poisson_mesh_domain_3
+
+} // end namespace CGAL
+
+#endif // CGAL_LABELED_MESH_DOMAIN_3_H

From 80c951e88f01b053fcebae1049730bec3f2df858 Mon Sep 17 00:00:00 2001
From: Sven Oesau <sven.oesau@geometryfactory.com>
Date: Wed, 5 Mar 2025 08:05:07 +0100
Subject: [PATCH 02/21] update on tests and examples some documentation fixes

---
 Mesh_3/include/CGAL/Labeled_mesh_domain_3.h   |   2 +-
 Mesh_3/include/CGAL/Poisson_mesh_domain_3.h   |  51 ++++---
 .../poisson_and_parallel_mesh_3.cpp           |   6 +-
 .../poisson_reconstruction.cpp                |   6 +-
 .../poisson_reconstruction_example.cpp        |   6 +-
 ...e_mesh_3_vs_Poisson_implicit_surface_3.cpp |  91 +++++++++---
 .../poisson_reconstruction_test_mesh_3.cpp    | 133 ++++++++++++------
 7 files changed, 199 insertions(+), 96 deletions(-)

diff --git a/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h b/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h
index 019716cb1ba..5e51d26d0a7 100644
--- a/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h
+++ b/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h
@@ -1196,7 +1196,7 @@ class Labeled_mesh_domain_3
 
       // If both extremities are in the same subdomain,
       // there is no intersection.
-      // This should not happen...
+      // Should only happen during initial point generation.
       if( value_at_p1 == value_at_p2 )
       {
         return Intersection();
diff --git a/Mesh_3/include/CGAL/Poisson_mesh_domain_3.h b/Mesh_3/include/CGAL/Poisson_mesh_domain_3.h
index 4631db75bbd..3331ed649cd 100644
--- a/Mesh_3/include/CGAL/Poisson_mesh_domain_3.h
+++ b/Mesh_3/include/CGAL/Poisson_mesh_domain_3.h
@@ -70,7 +70,8 @@ class Poisson_mesh_domain_3
   typedef typename CGAL::Mesh_3::internal::Index_generator<Subdomain_index, Surface_patch_index>::Index Index;
 
   // Geometric object types
-  // /// \name Types imported from the geometric traits class
+#ifdef DOXYGEN_RUNNING
+/// \name Types imported from the geometric traits class
   ///@{
   /// The point type of the geometric traits class
   typedef typename Geom_traits::Point_3 Point_3;
@@ -83,26 +84,46 @@ class Poisson_mesh_domain_3
   /// The number type (a field type) of the geometric traits class
   typedef typename Geom_traits::FT FT;
   /// The ray type of the geometric traits class
+  typedef typename Geom_traits::Ray_3 Ray_3;
+  /// The line type of the geometric traits class
+  typedef typename Geom_traits::Line_3 Line_3;
+  /// The segment type of the geometric traits class
+  typedef typename Geom_traits::Segment_3 Segment_3;
+  /// The Poisson function type
+  typedef CGAL::Poisson_reconstruction_function<Geom_traits> Function;
+  ///@}
+#else
+  /// The point type of the geometric traits class
+  typedef typename BGT::Point_3 Point_3;
+  /// The sphere type of the geometric traits class
+  typedef typename BGT::Sphere_3 Sphere_3;
+  /// The iso-cuboid type of the geometric traits class
+  typedef typename BGT::Iso_cuboid_3 Iso_cuboid_3;
+  /// The bounding box type
+  typedef CGAL::Bbox_3 Bbox_3;
+  /// The number type (a field type) of the geometric traits class
+  typedef typename BGT::FT FT;
+  /// The ray type of the geometric traits class
   typedef typename BGT::Ray_3 Ray_3;
   /// The line type of the geometric traits class
   typedef typename BGT::Line_3 Line_3;
   /// The segment type of the geometric traits class
   typedef typename BGT::Segment_3 Segment_3;
-  ///@}
+  /// The Poisson function type
+  typedef CGAL::Poisson_reconstruction_function<BGT> Function;
+#endif
 
 
-  typedef CGAL::Poisson_reconstruction_function<BGT> Function;
   Function poisson_function;
   /// \name Creation
 /// @{
   ///!  \brief Construction from a function, a bounding object and a relative error bound.
    //
-   // \tparam Function a type compatible with `Labeling_function`
    // \tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
    // \tparam Bounding_object either a bounding sphere (of type `Sphere_3`), a bounding box (type `Bbox_3`),
    //                         or a bounding `Iso_cuboid_3`
    //
-   // \param function the labeling function
+   // \param function the Poisson reconstruction function
    // \param bounding_object the bounding object bounding the meshable space.
    // \param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below:
    //
@@ -114,10 +135,6 @@ class Poisson_mesh_domain_3
    //      \cgalParamDefault{FT(1e-3)}
    //   \cgalParamNEnd
    // \cgalNamedParamsEnd
-   //
-   // \cgalHeading{Example}
-   // From the example (\ref Mesh_3/mesh_implicit_domains_2.cpp):
-   // \snippet Mesh_3/mesh_implicit_domains_2.cpp Domain creation
    ///
   template<typename Bounding_object, typename CGAL_NP_TEMPLATE_PARAMETERS>
   Poisson_mesh_domain_3(const Function& function,
@@ -167,13 +184,11 @@ class Poisson_mesh_domain_3
    // The method takes as argument a bounding sphere which is required to
    // circumscribe the surface and to have its center inside the domain.
    //
-   // \tparam Function a type compatible with the signature `FT(Point_3)`: it takes a point as argument,
-   //                  and returns a scalar value. That object must be model of `CopyConstructible`
    // \tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
    // \tparam Bounding_object either a bounding sphere (of type `Sphere_3`), a bounding box (type `Bbox_3`),
    //                         or a bounding `Iso_cuboid_3`
    //
-   // \param function the implicit function
+   // \param function the Poisson reconstruction function
    // \param bounding_object object boundint the meshable domain and its center is inside the domain.
    // \param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below:
    //
@@ -185,16 +200,6 @@ class Poisson_mesh_domain_3
    //   \cgalParamNEnd
    // \cgalNamedParamsEnd
    //
-   // \cgalHeading{Examples}
-   //
-   // From the example (\ref Mesh_3/mesh_implicit_sphere.cpp):
-   //
-   // \snippet Mesh_3/mesh_implicit_sphere.cpp Domain creation
-   //
-   // From the example (\ref Mesh_3/mesh_implicit_sphere_variable_size.cpp):
-   //
-   // \snippet Mesh_3/mesh_implicit_sphere_variable_size.cpp Domain creation
-   //
    ///
   template<typename Bounding_object, typename CGAL_NP_TEMPLATE_PARAMETERS>
   static Poisson_mesh_domain_3 create_poisson_mesh_domain(const Function& function,
@@ -314,7 +319,7 @@ internal_np::bounding_object_param_t>::value, "Value for required parameter not
 
       // If both extremities are in the same subdomain,
       // there is no intersection.
-      // This should not happen...
+      // Should only happen during initial point generation.
       if(label_at_p1 == label_at_p2)
         return Intersection();
 
diff --git a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_and_parallel_mesh_3.cpp b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_and_parallel_mesh_3.cpp
index a415c23aab8..9f9f5a1f685 100644
--- a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_and_parallel_mesh_3.cpp
+++ b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_and_parallel_mesh_3.cpp
@@ -7,7 +7,7 @@
 #include <CGAL/Mesh_triangulation_3.h>
 #include <CGAL/Mesh_complex_3_in_triangulation_3.h>
 #include <CGAL/Mesh_criteria_3.h>
-#include <CGAL/Labeled_mesh_domain_3.h>
+#include <CGAL/Poisson_mesh_domain_3.h>
 #include <CGAL/make_mesh_3.h>
 #include <CGAL/facets_in_complex_3_to_triangle_mesh.h>
 
@@ -44,7 +44,7 @@ namespace params = CGAL::parameters;
 template<typename Concurrency_tag, typename PointSet>
 void poisson_reconstruction(const PointSet& points, const char* output)
 {
-  typedef CGAL::Labeled_mesh_domain_3<Kernel> Mesh_domain;
+  typedef CGAL::Poisson_mesh_domain_3<Kernel> Mesh_domain;
   typedef typename CGAL::Mesh_triangulation_3<Mesh_domain, CGAL::Default, Concurrency_tag>::type Tr;
   typedef CGAL::Mesh_complex_3_in_triangulation_3<Tr> C3t3;
   typedef CGAL::Mesh_criteria_3<Tr> Mesh_criteria;
@@ -111,7 +111,7 @@ void poisson_reconstruction(const PointSet& points, const char* output)
                          params::facet_size = sm_radius * average_spacing,
                          params::facet_distance = sm_distance * average_spacing);
 
-  Mesh_domain domain = Mesh_domain::create_implicit_mesh_domain(function, bsphere,
+  Mesh_domain domain = Mesh_domain::create_poisson_mesh_domain(function, bsphere,
     params::relative_error_bound(sm_dichotomy_error / sm_sphere_radius));
 
   // Generates surface mesh with manifold option
diff --git a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction.cpp b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction.cpp
index 72942c49c9f..dfeac4fa564 100644
--- a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction.cpp
+++ b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction.cpp
@@ -18,7 +18,7 @@
 #include <CGAL/Mesh_triangulation_3.h>
 #include <CGAL/Mesh_complex_3_in_triangulation_3.h>
 #include <CGAL/Mesh_criteria_3.h>
-#include <CGAL/Labeled_mesh_domain_3.h>
+#include <CGAL/Poisson_mesh_domain_3.h>
 #include <CGAL/make_mesh_3.h>
 #include <CGAL/facets_in_complex_3_to_triangle_mesh.h>
 
@@ -56,7 +56,7 @@ typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
 typedef CGAL::Poisson_reconstruction_function<Kernel> Poisson_reconstruction_function;
 
 // Mesh_3
-typedef CGAL::Labeled_mesh_domain_3<Kernel> Mesh_domain;
+typedef CGAL::Poisson_mesh_domain_3<Kernel> Mesh_domain;
 typedef typename CGAL::Mesh_triangulation_3<Mesh_domain>::type Tr;
 typedef CGAL::Mesh_complex_3_in_triangulation_3<Tr> C3t3;
 typedef CGAL::Mesh_criteria_3<Tr> Mesh_criteria;
@@ -327,7 +327,7 @@ int main(int argc, char * argv[])
                       << "                    manifold_with_boundary()\n";
 
     // Defines mesh domain
-    Mesh_domain domain = Mesh_domain::create_implicit_mesh_domain(function, bsphere,
+    Mesh_domain domain = Mesh_domain::create_poisson_mesh_domain(function, bsphere,
         CGAL::parameters::relative_error_bound(sm_dichotomy_error / sm_sphere_radius));
 
     // Generates mesh with manifold option
diff --git a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction_example.cpp b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction_example.cpp
index d44d13be084..52f48b01efc 100644
--- a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction_example.cpp
+++ b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction_example.cpp
@@ -5,7 +5,7 @@
 #include <CGAL/Mesh_triangulation_3.h>
 #include <CGAL/Mesh_complex_3_in_triangulation_3.h>
 #include <CGAL/Mesh_criteria_3.h>
-#include <CGAL/Labeled_mesh_domain_3.h>
+#include <CGAL/Poisson_mesh_domain_3.h>
 #include <CGAL/make_mesh_3.h>
 #include <CGAL/facets_in_complex_3_to_triangle_mesh.h>
 
@@ -32,7 +32,7 @@ typedef Kernel::Sphere_3 Sphere;
 typedef std::vector<Point_with_normal> PointList;
 typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
 typedef CGAL::Poisson_reconstruction_function<Kernel> Poisson_reconstruction_function;
-typedef CGAL::Labeled_mesh_domain_3<Kernel> Mesh_domain;
+typedef CGAL::Poisson_mesh_domain_3<Kernel> Mesh_domain;
 typedef CGAL::Mesh_triangulation_3<Mesh_domain>::type Tr;
 typedef CGAL::Mesh_complex_3_in_triangulation_3<Tr> C3t3;
 typedef CGAL::Mesh_criteria_3<Tr> Mesh_criteria;
@@ -85,7 +85,7 @@ int main(void)
                            CGAL::parameters::facet_distance = sm_distance*average_spacing);
 
     // Defines mesh domain
-    Mesh_domain domain = Mesh_domain::create_implicit_mesh_domain(function, bsphere,
+    Mesh_domain domain = Mesh_domain::create_poisson_mesh_domain(function, bsphere,
         CGAL::parameters::relative_error_bound(sm_dichotomy_error / sm_sphere_radius));
 
     // Generates mesh with manifold option
diff --git a/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/compare_mesh_3_vs_Poisson_implicit_surface_3.cpp b/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/compare_mesh_3_vs_Poisson_implicit_surface_3.cpp
index 1b8a2540acf..3d07a69c097 100644
--- a/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/compare_mesh_3_vs_Poisson_implicit_surface_3.cpp
+++ b/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/compare_mesh_3_vs_Poisson_implicit_surface_3.cpp
@@ -14,6 +14,7 @@
 #include <CGAL/Mesh_complex_3_in_triangulation_3.h>
 #include <CGAL/Mesh_criteria_3.h>
 #include <CGAL/Labeled_mesh_domain_3.h>
+#include <CGAL/Poisson_mesh_domain_3.h>
 #include <CGAL/make_mesh_3.h>
 #include <CGAL/facets_in_complex_3_to_triangle_mesh.h>
 
@@ -61,7 +62,12 @@ typedef CGAL::Surface_mesh_default_triangulation_3 STr;
 typedef CGAL::Surface_mesh_complex_2_in_triangulation_3<STr> C2t3;
 
 // Mesh_3
-typedef CGAL::Labeled_mesh_domain_3<Kernel> Mesh_domain;
+typedef CGAL::Labeled_mesh_domain_3<Kernel> LMesh_domain;
+typedef typename CGAL::Mesh_triangulation_3<LMesh_domain>::type LTr;
+typedef CGAL::Mesh_complex_3_in_triangulation_3<LTr> LC3t3;
+typedef CGAL::Mesh_criteria_3<LTr> LMesh_criteria;
+
+typedef CGAL::Poisson_mesh_domain_3<Kernel> Mesh_domain;
 typedef typename CGAL::Mesh_triangulation_3<Mesh_domain>::type Tr;
 typedef CGAL::Mesh_complex_3_in_triangulation_3<Tr> C3t3;
 typedef CGAL::Mesh_criteria_3<Tr> Mesh_criteria;
@@ -290,10 +296,10 @@ int main(int argc, char * argv[])
     }
     #endif
 
+    task_timer.stop();
 
     // Prints status
     std::cerr << "Total implicit function (triangulation+refinement+solver): " << task_timer.time() << " seconds\n";
-    task_timer.reset();
 
     //***************************************
     // Surface mesh generation
@@ -331,47 +337,88 @@ int main(int argc, char * argv[])
     const double implicit_function_time = reconstruction_timer.time();
     reconstruction_timer.reset();
 
-    // MESH_3
+    // MESH_3 labeled
     {
+      // Defines generation criteria
+      LMesh_criteria criteria(CGAL::parameters::facet_angle = fangle, CGAL::parameters::facet_size = fsize,
+                             CGAL::parameters::facet_distance = fdist);
+
+      std::cout << "* Use Mesh_3 implicit *" << std::endl;
+
       CGAL::Real_timer meshing_timer;
       meshing_timer.start();
 
-      std::cout << "* Use Mesh_3 *" << std::endl;
       // Defines generation criteria
-      Mesh_criteria criteria(CGAL::parameters::facet_angle = fangle,
-                             CGAL::parameters::facet_size = fsize,
+
+      // Defines mesh domain
+      LMesh_domain domain = LMesh_domain::create_implicit_mesh_domain(
+          function, bsphere, CGAL::parameters::relative_error_bound(sm_dichotomy_error / sm_sphere_radius));
+
+      // Generates mesh with manifold option
+      LC3t3 c3t3 =
+          CGAL::make_mesh_3<LC3t3>(domain, criteria, CGAL::parameters::no_exude().no_perturb().manifold_with_boundary());
+      meshing_timer.stop();
+
+      const LTr& tr = c3t3.triangulation();
+      // Prints status
+      std::cerr << "Mesh_3 meshing: " << meshing_timer.time() << " seconds, " << tr.number_of_vertices()
+                << " output vertices" << std::endl;
+
+      if(tr.number_of_vertices() == 0)
+        return EXIT_FAILURE;
+
+      // Prints total reconstruction duration
+      std::cerr << "Total reconstruction (implicit function + meshing): "
+                << (implicit_function_time + meshing_timer.time()) << " seconds\n";
+
+      // Converts to polyhedron
+      Polyhedron output_mesh;
+      CGAL::facets_in_complex_3_to_triangle_mesh(c3t3, output_mesh);
+
+      std::ofstream out(output_basename + "_implicit_mesh_3.off");
+      out << output_mesh;
+      out.close();
+    }
+
+    // MESH_3 poisson
+    {
+      // Defines generation criteria
+      Mesh_criteria criteria(CGAL::parameters::facet_angle = fangle, CGAL::parameters::facet_size = fsize,
                              CGAL::parameters::facet_distance = fdist);
+      std::cout << "* Use Mesh_3 poisson *" << std::endl;
+
+      CGAL::Real_timer meshing_timer;
+      meshing_timer.start();
+
+      // Defines generation criteria
 
       // Defines mesh domain
-      Mesh_domain domain = Mesh_domain::create_implicit_mesh_domain(function, bsphere,
-          CGAL::parameters::relative_error_bound(sm_dichotomy_error / sm_sphere_radius));
+      Mesh_domain domain = Mesh_domain::create_poisson_mesh_domain(
+          function, bsphere, CGAL::parameters::relative_error_bound(sm_dichotomy_error / sm_sphere_radius));
 
       // Generates mesh with manifold option
-      C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria,
-                                          CGAL::parameters::no_exude().no_perturb()
-                                          .manifold_with_boundary());
+      C3t3 c3t3 =
+          CGAL::make_mesh_3<C3t3>(domain, criteria, CGAL::parameters::no_exude().no_perturb().manifold_with_boundary());
+
       meshing_timer.stop();
 
       const Tr& tr = c3t3.triangulation();
       // Prints status
-      std::cerr << "Mesh_3 meshing: " << meshing_timer.time() << " seconds, "
-                                      << tr.number_of_vertices() << " output vertices"
-                                      << std::endl;
+      std::cerr << "Mesh_3 meshing: " << meshing_timer.time() << " seconds, " << tr.number_of_vertices()
+                << " output vertices" << std::endl;
 
-      if (tr.number_of_vertices() == 0)
+      if(tr.number_of_vertices() == 0)
         return EXIT_FAILURE;
 
       // Prints total reconstruction duration
-      reconstruction_timer.stop();
-      std::cerr << "Total reconstruction (implicit function + meshing): "
-        << (implicit_function_time + reconstruction_timer.time()) << " seconds\n";
-      reconstruction_timer.reset();
+      std::cerr << "Total reconstruction (poisson function + meshing): "
+                << (implicit_function_time + meshing_timer.time()) << " seconds\n";
 
       // Converts to polyhedron
       Polyhedron output_mesh;
       CGAL::facets_in_complex_3_to_triangle_mesh(c3t3, output_mesh);
 
-      std::ofstream out(output_basename + "_mesh_3.off");
+      std::ofstream out(output_basename + "_poisson_mesh_3.off");
       out << output_mesh;
       out.close();
     }
@@ -380,7 +427,6 @@ int main(int argc, char * argv[])
     {
       CGAL::Real_timer meshing_timer;
       meshing_timer.start();
-      reconstruction_timer.start();
 
       std::cout << "\n\n* Use Surface_mesher with Poisson_implicit_surface_3 *" << std::endl;
       Surface_3 surface(function,
@@ -408,9 +454,8 @@ int main(int argc, char * argv[])
         return EXIT_FAILURE;
 
       // Prints total reconstruction duration
-      reconstruction_timer.stop();
       std::cerr << "Total reconstruction (implicit function + meshing): "
-        << (implicit_function_time + reconstruction_timer.time()) << " seconds\n";
+                << (implicit_function_time + meshing_timer.time()) << " seconds\n";
 
       Polyhedron output_mesh;
       CGAL::facets_in_complex_2_to_triangle_mesh(c2t3, output_mesh);
diff --git a/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/poisson_reconstruction_test_mesh_3.cpp b/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/poisson_reconstruction_test_mesh_3.cpp
index 7007831e7e0..bda94293862 100644
--- a/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/poisson_reconstruction_test_mesh_3.cpp
+++ b/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/poisson_reconstruction_test_mesh_3.cpp
@@ -18,6 +18,7 @@
 #include <CGAL/Mesh_complex_3_in_triangulation_3.h>
 #include <CGAL/Mesh_criteria_3.h>
 #include <CGAL/Labeled_mesh_domain_3.h>
+#include <CGAL/Poisson_mesh_domain_3.h>
 #include <CGAL/make_mesh_3.h>
 #include <CGAL/facets_in_complex_3_to_triangle_mesh.h>
 
@@ -57,12 +58,18 @@ typedef CGAL::Polyhedron_3<Kernel> Polyhedron;
 // Poisson implicit function
 typedef CGAL::Poisson_reconstruction_function<Kernel> Poisson_reconstruction_function;
 
-// Mesh_3
+// Mesh_3 using Labeled_mesh_domain_3
 typedef CGAL::Labeled_mesh_domain_3<Kernel> Mesh_domain;
 typedef CGAL::Mesh_triangulation_3<Mesh_domain>::type Tr;
 typedef CGAL::Mesh_complex_3_in_triangulation_3<Tr> C3t3;
 typedef CGAL::Mesh_criteria_3<Tr> Mesh_criteria;
 
+// Mesh_3 using Poisson_mesh_domain_3
+typedef CGAL::Poisson_mesh_domain_3<Kernel> Poisson_mesh_domain;
+typedef CGAL::Mesh_triangulation_3<Poisson_mesh_domain>::type Poisson_Tr;
+typedef CGAL::Mesh_complex_3_in_triangulation_3<Poisson_Tr> Poisson_C3t3;
+typedef CGAL::Mesh_criteria_3<Poisson_Tr> Poisson_mesh_criteria;
+
 namespace params = CGAL::parameters;
 
 // ----------------------------------------------------------------------------
@@ -171,7 +178,6 @@ int main(int argc, char * argv[])
                                                         << task_timer.time() << " seconds, "
                                                         << (memory>>20) << " Mb allocated"
                                                         << std::endl;
-    task_timer.reset();
 
     //***************************************
     // Checks requirements
@@ -192,14 +198,14 @@ int main(int argc, char * argv[])
       continue;
     }
 
-    CGAL::Timer reconstruction_timer; reconstruction_timer.start();
-
     //***************************************
     // Computes implicit function
     //***************************************
 
     std::cerr << "Computes Poisson implicit function...\n";
 
+    task_timer.reset();
+
     // Creates implicit function from the read points.
     // Note: this method requires an iterator over points
     // + property maps to access each point's position and normal.
@@ -218,9 +224,9 @@ int main(int argc, char * argv[])
       continue;
     }
 
+    double poisson_time = task_timer.time();
     // Prints status
-    std::cerr << "Total implicit function (triangulation+refinement+solver): " << task_timer.time() << " seconds\n";
-    task_timer.reset();
+    std::cerr << "Total implicit function (triangulation+refinement+solver): " << poisson_time << " seconds\n";
 
     //***************************************
     // Surface mesh generation
@@ -250,45 +256,92 @@ int main(int argc, char * argv[])
     FT sm_sphere_radius = 5.0 * radius;
     FT sm_dichotomy_error = sm_distance*average_spacing/1000.0; // Dichotomy error must be << sm_distance
 
-    // Defines surface mesh generation criteria
-    Mesh_criteria criteria(params::facet_angle = sm_angle,
-                           params::facet_size = sm_radius*average_spacing,
-                           params::facet_distance = sm_distance*average_spacing);
-
-    std::cerr         << "  make_mesh_3 with  sphere center=("<<inner_point << "),\n"
-                      << "                    sphere radius="<<sm_sphere_radius<<",\n"
-                      << "                    angle="<<sm_angle << " degrees,\n"
-                      << "                    triangle size="<<sm_radius<<" * average spacing="<<sm_radius*average_spacing<<",\n"
-                      << "                    distance="<<sm_distance<<" * average spacing="<<sm_distance*average_spacing<<",\n"
-                      << "                    dichotomy = distance/"<<sm_distance*average_spacing/sm_dichotomy_error<<",\n"
-                      << "                    manifold_with_boundary()\n";
-
-    // Generates surface mesh with manifold option
-    Mesh_domain domain = Mesh_domain::create_implicit_mesh_domain(function, bsphere,
-        params::relative_error_bound(sm_dichotomy_error / sm_sphere_radius));
-    C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria,
-        params::no_exude().no_perturb().manifold_with_boundary());
+    {
+      task_timer.reset();
+      // Defines surface mesh generation criteria
+      Mesh_criteria criteria(params::facet_angle = sm_angle, params::facet_size = sm_radius * average_spacing,
+                             params::facet_distance = sm_distance * average_spacing);
+
+      std::cerr << "  make_mesh_3 with  sphere center=(" << inner_point << "),\n"
+                << "                    sphere radius=" << sm_sphere_radius << ",\n"
+                << "                    angle=" << sm_angle << " degrees,\n"
+                << "                    triangle size=" << sm_radius
+                << " * average spacing=" << sm_radius * average_spacing << ",\n"
+                << "                    distance=" << sm_distance
+                << " * average spacing=" << sm_distance * average_spacing << ",\n"
+                << "                    dichotomy = distance/" << sm_distance * average_spacing / sm_dichotomy_error
+                << ",\n"
+                << "                    manifold_with_boundary()\n";
+
+      // Generates surface mesh with manifold option
+      Mesh_domain domain = Mesh_domain::create_implicit_mesh_domain(
+          function, bsphere, params::relative_error_bound(sm_dichotomy_error / sm_sphere_radius));
+      C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria, params::no_exude().no_perturb().manifold_with_boundary());
+
+      // Prints status
+      /*long*/ memory = CGAL::Memory_sizer().virtual_size();
+      const Tr& tr = c3t3.triangulation();
+      std::cerr << "Surface meshing: " << task_timer.time() << " seconds, " << tr.number_of_vertices()
+                << " output vertices, " << (memory >> 20) << " Mb allocated" << std::endl;
+      task_timer.reset();
+
+      if(tr.number_of_vertices() == 0) {
+        accumulated_fatal_err = EXIT_FAILURE;
+        continue;
+      }
 
-    // Prints status
-    /*long*/ memory = CGAL::Memory_sizer().virtual_size();
-    const Tr& tr = c3t3.triangulation();
-    std::cerr << "Surface meshing: " << task_timer.time() << " seconds, "
-                                     << tr.number_of_vertices() << " output vertices, "
-                                     << (memory>>20) << " Mb allocated"
-                                     << std::endl;
-    task_timer.reset();
+      // Converts to polyhedron
+      Polyhedron output_mesh;
+      CGAL::facets_in_complex_3_to_triangle_mesh(c3t3, output_mesh);
 
-    if(tr.number_of_vertices() == 0) {
-      accumulated_fatal_err = EXIT_FAILURE;
-      continue;
+      // Prints total reconstruction duration
+      std::cerr << "Total reconstruction using Labeled_mesh_domain_3 (implicit function + meshing): "
+                << poisson_time + task_timer.time() << " seconds\n";
     }
 
-    // Converts to polyhedron
-    Polyhedron output_mesh;
-    CGAL::facets_in_complex_3_to_triangle_mesh(c3t3, output_mesh);
+    {
+      task_timer.reset();
+      // Defines surface mesh generation criteria
+      Poisson_mesh_criteria criteria(params::facet_angle = sm_angle, params::facet_size = sm_radius * average_spacing,
+                             params::facet_distance = sm_distance * average_spacing);
+
+      /*std::cerr << "  make_mesh_3 with  sphere center=(" << inner_point << "),\n"
+                << "                    sphere radius=" << sm_sphere_radius << ",\n"
+                << "                    angle=" << sm_angle << " degrees,\n"
+                << "                    triangle size=" << sm_radius
+                << " * average spacing=" << sm_radius * average_spacing << ",\n"
+                << "                    distance=" << sm_distance
+                << " * average spacing=" << sm_distance * average_spacing << ",\n"
+                << "                    dichotomy = distance/" << sm_distance * average_spacing / sm_dichotomy_error
+                << ",\n"
+                << "                    manifold_with_boundary()\n";
+
+      // Generates surface mesh with manifold option
+      Poisson_mesh_domain domain = Poisson_mesh_domain::create_poisson_mesh_domain(
+          function, bsphere, params::relative_error_bound(sm_dichotomy_error / sm_sphere_radius));
+      Poisson_C3t3 c3t3 =
+          CGAL::make_mesh_3<Poisson_C3t3>(domain, criteria, params::no_exude().no_perturb().manifold_with_boundary());
+
+      // Prints status
+      / *long* / memory = CGAL::Memory_sizer().virtual_size();
+      const Poisson_Tr& tr = c3t3.triangulation();
+      std::cerr << "Surface meshing: " << task_timer.time() << " seconds, " << tr.number_of_vertices()
+                << " output vertices, " << (memory >> 20) << " Mb allocated" << std::endl;
+      task_timer.reset();
+
+      if(tr.number_of_vertices() == 0) {
+        accumulated_fatal_err = EXIT_FAILURE;
+        continue;
+      }
+
+      // Converts to polyhedron
+      Polyhedron output_mesh;
+      CGAL::facets_in_complex_3_to_triangle_mesh(c3t3, output_mesh);*/
 
-    // Prints total reconstruction duration
-    std::cerr << "Total reconstruction (implicit function + meshing): " << reconstruction_timer.time() << " seconds\n";
+      // Prints total reconstruction duration
+      std::cerr << "Total reconstruction using Poisson_mesh_domain_3 (implicit function + meshing): "
+                << poisson_time + task_timer.time() << " seconds\n";
+    }
 
   } // for each input file
 

From 95c4204e37f79918af29aff32d67450f5a96f382 Mon Sep 17 00:00:00 2001
From: Sven Oesau <sven.oesau@geometryfactory.com>
Date: Wed, 5 Mar 2025 09:59:36 +0100
Subject: [PATCH 03/21] renaming create_poisson_mesh_domain ->
 create_Poisson_mesh_domain

---
 Mesh_3/include/CGAL/Poisson_mesh_domain_3.h          | 12 ++++++------
 .../poisson_and_parallel_mesh_3.cpp                  |  2 +-
 .../poisson_reconstruction.cpp                       |  2 +-
 .../poisson_reconstruction_example.cpp               |  2 +-
 .../compare_mesh_3_vs_Poisson_implicit_surface_3.cpp |  2 +-
 .../poisson_reconstruction_test_mesh_3.cpp           |  8 ++++----
 6 files changed, 14 insertions(+), 14 deletions(-)

diff --git a/Mesh_3/include/CGAL/Poisson_mesh_domain_3.h b/Mesh_3/include/CGAL/Poisson_mesh_domain_3.h
index 3331ed649cd..60dd7122ec9 100644
--- a/Mesh_3/include/CGAL/Poisson_mesh_domain_3.h
+++ b/Mesh_3/include/CGAL/Poisson_mesh_domain_3.h
@@ -32,7 +32,7 @@ namespace CGAL {
 //
 // This class has a constructor taking a labeling function. It has also a static template member
 // function that acts as named constructor:
-// <ul><li>`create_poisson_mesh_domain()`, to create a domain from a `Poisson_reconstruction_function`</ ul>
+// <ul><li>`create_Poisson_mesh_domain()`, to create a domain from a `Poisson_reconstruction_function`</ ul>
 //
 //\tparam BGT is a geometric traits class that provides
 //    the basic operations to implement intersection tests and intersection computations through a bisection
@@ -202,7 +202,7 @@ class Poisson_mesh_domain_3
    //
    ///
   template<typename Bounding_object, typename CGAL_NP_TEMPLATE_PARAMETERS>
-  static Poisson_mesh_domain_3 create_poisson_mesh_domain(const Function& function,
+  static Poisson_mesh_domain_3 create_Poisson_mesh_domain(const Function& function,
                                                            const Bounding_object& bounding_object,
                                                            const CGAL_NP_CLASS& np = parameters::default_values()
 #ifndef DOXYGEN_RUNNING
@@ -230,14 +230,14 @@ internal_np::surface_patch_index), Null_functor());
 /// @}
 #ifndef DOXYGEN_RUNNING
   template<typename CGAL_NP_TEMPLATE_PARAMETERS>
-  static Poisson_mesh_domain_3 create_poisson_mesh_domain(const CGAL_NP_CLASS& np = parameters::default_values())
+  static Poisson_mesh_domain_3 create_Poisson_mesh_domain(const CGAL_NP_CLASS& np = parameters::default_values())
   {
     static_assert(!parameters::is_default_parameter<CGAL_NP_CLASS, internal_np::function_param_t>::value,
       "Value for required parameter not found"); static_assert(!parameters::is_default_parameter<CGAL_NP_CLASS,
 internal_np::bounding_object_param_t>::value, "Value for required parameter not found");
 
     using parameters::get_parameter;
-    return create_poisson_mesh_domain(parameters::get_parameter(np, internal_np::function_param),
+    return create_Poisson_mesh_domain(parameters::get_parameter(np, internal_np::function_param),
                                        parameters::get_parameter(np, internal_np::bounding_object_param),
                                        np);
   }
@@ -246,11 +246,11 @@ internal_np::bounding_object_param_t>::value, "Value for required parameter not
   template<typename CGAL_NP_TEMPLATE_PARAMETERS_NO_DEFAULT_1,
            typename CGAL_NP_TEMPLATE_PARAMETERS_NO_DEFAULT_2,
            typename ... NP>
-  static Poisson_mesh_domain_3 create_poisson_mesh_domain(const CGAL_NP_CLASS_1& np1,
+  static Poisson_mesh_domain_3 create_Poisson_mesh_domain(const CGAL_NP_CLASS_1& np1,
                                                            const CGAL_NP_CLASS_2&  np2,
                                                            const NP& ... nps)
   {
-    return create_poisson_mesh_domain(internal_np::combine_named_parameters(np1, np2, nps...));
+    return create_Poisson_mesh_domain(internal_np::combine_named_parameters(np1, np2, nps...));
   }
 #endif
 
diff --git a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_and_parallel_mesh_3.cpp b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_and_parallel_mesh_3.cpp
index 9f9f5a1f685..d84974ce78f 100644
--- a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_and_parallel_mesh_3.cpp
+++ b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_and_parallel_mesh_3.cpp
@@ -111,7 +111,7 @@ void poisson_reconstruction(const PointSet& points, const char* output)
                          params::facet_size = sm_radius * average_spacing,
                          params::facet_distance = sm_distance * average_spacing);
 
-  Mesh_domain domain = Mesh_domain::create_poisson_mesh_domain(function, bsphere,
+  Mesh_domain domain = Mesh_domain::create_Poisson_mesh_domain(function, bsphere,
     params::relative_error_bound(sm_dichotomy_error / sm_sphere_radius));
 
   // Generates surface mesh with manifold option
diff --git a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction.cpp b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction.cpp
index dfeac4fa564..4e9bdf1360f 100644
--- a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction.cpp
+++ b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction.cpp
@@ -327,7 +327,7 @@ int main(int argc, char * argv[])
                       << "                    manifold_with_boundary()\n";
 
     // Defines mesh domain
-    Mesh_domain domain = Mesh_domain::create_poisson_mesh_domain(function, bsphere,
+    Mesh_domain domain = Mesh_domain::create_Poisson_mesh_domain(function, bsphere,
         CGAL::parameters::relative_error_bound(sm_dichotomy_error / sm_sphere_radius));
 
     // Generates mesh with manifold option
diff --git a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction_example.cpp b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction_example.cpp
index 52f48b01efc..c73be4427e9 100644
--- a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction_example.cpp
+++ b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction_example.cpp
@@ -85,7 +85,7 @@ int main(void)
                            CGAL::parameters::facet_distance = sm_distance*average_spacing);
 
     // Defines mesh domain
-    Mesh_domain domain = Mesh_domain::create_poisson_mesh_domain(function, bsphere,
+    Mesh_domain domain = Mesh_domain::create_Poisson_mesh_domain(function, bsphere,
         CGAL::parameters::relative_error_bound(sm_dichotomy_error / sm_sphere_radius));
 
     // Generates mesh with manifold option
diff --git a/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/compare_mesh_3_vs_Poisson_implicit_surface_3.cpp b/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/compare_mesh_3_vs_Poisson_implicit_surface_3.cpp
index 3d07a69c097..5fb8c4a34e6 100644
--- a/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/compare_mesh_3_vs_Poisson_implicit_surface_3.cpp
+++ b/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/compare_mesh_3_vs_Poisson_implicit_surface_3.cpp
@@ -393,7 +393,7 @@ int main(int argc, char * argv[])
       // Defines generation criteria
 
       // Defines mesh domain
-      Mesh_domain domain = Mesh_domain::create_poisson_mesh_domain(
+      Mesh_domain domain = Mesh_domain::create_Poisson_mesh_domain(
           function, bsphere, CGAL::parameters::relative_error_bound(sm_dichotomy_error / sm_sphere_radius));
 
       // Generates mesh with manifold option
diff --git a/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/poisson_reconstruction_test_mesh_3.cpp b/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/poisson_reconstruction_test_mesh_3.cpp
index bda94293862..f171053e86d 100644
--- a/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/poisson_reconstruction_test_mesh_3.cpp
+++ b/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/poisson_reconstruction_test_mesh_3.cpp
@@ -305,7 +305,7 @@ int main(int argc, char * argv[])
       Poisson_mesh_criteria criteria(params::facet_angle = sm_angle, params::facet_size = sm_radius * average_spacing,
                              params::facet_distance = sm_distance * average_spacing);
 
-      /*std::cerr << "  make_mesh_3 with  sphere center=(" << inner_point << "),\n"
+      std::cerr << "  make_mesh_3 with  sphere center=(" << inner_point << "),\n"
                 << "                    sphere radius=" << sm_sphere_radius << ",\n"
                 << "                    angle=" << sm_angle << " degrees,\n"
                 << "                    triangle size=" << sm_radius
@@ -317,13 +317,13 @@ int main(int argc, char * argv[])
                 << "                    manifold_with_boundary()\n";
 
       // Generates surface mesh with manifold option
-      Poisson_mesh_domain domain = Poisson_mesh_domain::create_poisson_mesh_domain(
+      Poisson_mesh_domain domain = Poisson_mesh_domain::create_Poisson_mesh_domain(
           function, bsphere, params::relative_error_bound(sm_dichotomy_error / sm_sphere_radius));
       Poisson_C3t3 c3t3 =
           CGAL::make_mesh_3<Poisson_C3t3>(domain, criteria, params::no_exude().no_perturb().manifold_with_boundary());
 
       // Prints status
-      / *long* / memory = CGAL::Memory_sizer().virtual_size();
+      /* long */ memory = CGAL::Memory_sizer().virtual_size();
       const Poisson_Tr& tr = c3t3.triangulation();
       std::cerr << "Surface meshing: " << task_timer.time() << " seconds, " << tr.number_of_vertices()
                 << " output vertices, " << (memory >> 20) << " Mb allocated" << std::endl;
@@ -336,7 +336,7 @@ int main(int argc, char * argv[])
 
       // Converts to polyhedron
       Polyhedron output_mesh;
-      CGAL::facets_in_complex_3_to_triangle_mesh(c3t3, output_mesh);*/
+      CGAL::facets_in_complex_3_to_triangle_mesh(c3t3, output_mesh);
 
       // Prints total reconstruction duration
       std::cerr << "Total reconstruction using Poisson_mesh_domain_3 (implicit function + meshing): "

From 5a4e42c0abc1bc83b4551026cdf466b53ea2f392 Mon Sep 17 00:00:00 2001
From: Sven Oesau <sven.oesau@geometryfactory.com>
Date: Wed, 5 Mar 2025 10:07:50 +0100
Subject: [PATCH 04/21] fix for ci changes following review

---
 Mesh_3/include/CGAL/Labeled_mesh_domain_3.h | 6 +++---
 Mesh_3/include/CGAL/Poisson_mesh_domain_3.h | 7 +++----
 2 files changed, 6 insertions(+), 7 deletions(-)

diff --git a/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h b/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h
index 5e51d26d0a7..d40ec36318b 100644
--- a/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h
+++ b/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h
@@ -1170,10 +1170,10 @@ class Labeled_mesh_domain_3
 
   private:
     /*
-     * Returns a point in the intersection of [a,b] with the surface
-     *  `a` must be the source point, and `b` the out point. It's important
+     * Returns a point in the intersection of `[a,b]` with the surface
+     *  `a` must be the source point, and `b` the out point. It is important
      * because it drives bisection cuts.
-     * Indeed, the returned point is the first intersection from  `[a,b]`
+     * Indeed, the returned point is the first intersection of `[a,b]`
      * with a subdomain surface.
      */
     Intersection operator()(const Point_3& a, const Point_3& b) const
diff --git a/Mesh_3/include/CGAL/Poisson_mesh_domain_3.h b/Mesh_3/include/CGAL/Poisson_mesh_domain_3.h
index 60dd7122ec9..5f641739b3d 100644
--- a/Mesh_3/include/CGAL/Poisson_mesh_domain_3.h
+++ b/Mesh_3/include/CGAL/Poisson_mesh_domain_3.h
@@ -62,7 +62,6 @@ class Poisson_mesh_domain_3
   typedef Surface_patch_index_ Surface_patch_index;
   typedef std::optional<Surface_patch_index> Surface_patch;
   typedef Subdomain_index_ Subdomain_index;
-  typedef typename Base::Index Index;
   typedef typename Base::Intersection Intersection;
 
   // Type of indexes to characterize the lowest dimensional face of the input
@@ -288,10 +287,10 @@ internal_np::bounding_object_param_t>::value, "Value for required parameter not
 
   private:
     /*
-     * Returns a point in the intersection of [a,b] with the surface
-     *  `a` must be the source point, and `b` the out point. It's important
+     * Returns a point in the intersection of `[a,b]` with the surface
+     *  `a` must be the source point, and `b` the out point. It is important
      * because it drives bisection cuts.
-     * Indeed, the returned point is the first intersection from  `[a,b]`
+     * Indeed, the returned point is the first intersection of `[a,b]`
      * with a subdomain surface.
      */
     Intersection operator()(const Point_3& a, const Point_3& b) const

From 45d2053a7d6b8a6fc86e37aebfc4e69850dd434f Mon Sep 17 00:00:00 2001
From: Sven Oesau <sven.oesau@geometryfactory.com>
Date: Wed, 5 Mar 2025 11:22:11 +0100
Subject: [PATCH 05/21] moving Poisson_mesh_domain_3 to Poisson reconstruction
 package

---
 .../include/CGAL/Poisson_mesh_domain_3.h      | 135 +++++++++---------
 1 file changed, 66 insertions(+), 69 deletions(-)
 rename {Mesh_3 => Poisson_surface_reconstruction_3}/include/CGAL/Poisson_mesh_domain_3.h (79%)

diff --git a/Mesh_3/include/CGAL/Poisson_mesh_domain_3.h b/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h
similarity index 79%
rename from Mesh_3/include/CGAL/Poisson_mesh_domain_3.h
rename to Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h
index 5f641739b3d..c85fc3438f0 100644
--- a/Mesh_3/include/CGAL/Poisson_mesh_domain_3.h
+++ b/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h
@@ -25,26 +25,25 @@
 
 namespace CGAL {
 
-///!
-//\ingroup PkgMesh3Domains
-//
-//\brief The class `Poisson_mesh_domain_3` derives from `Labeled_mesh_domain_3` for the handling of `Poisson_reconstruction_function`.
-//
-// This class has a constructor taking a labeling function. It has also a static template member
-// function that acts as named constructor:
-// <ul><li>`create_Poisson_mesh_domain()`, to create a domain from a `Poisson_reconstruction_function`</ ul>
-//
-//\tparam BGT is a geometric traits class that provides
-//    the basic operations to implement intersection tests and intersection computations through a bisection
-//    method.This parameter must be instantiated with a model of the concept `BisectionGeometricTraits_3`.
-//
-// This class is a model of concept `MeshDomain_3`.
-//\cgalModels{MeshDomain_3}
-//
-//\sa `CGAL::Labeled_mesh_domain_3`
-//\sa `CGAL::make_mesh_3()`
-//
-///
+/*!
+\ingroup PkgMesh3Domains
+
+\brief The class `Poisson_mesh_domain_3` derives from `Labeled_mesh_domain_3` for the handling of `Poisson_reconstruction_function`.
+
+ This class has a constructor taking a labeling function. It has also a static template member
+ function that acts as named constructor:
+ <ul><li>`create_Poisson_mesh_domain()`, to create a domain from a `Poisson_reconstruction_function`</ ul>
+
+\tparam BGT is a geometric traits class that provides
+    the basic operations to implement intersection tests and intersection computations through a bisection
+    method.This parameter must be instantiated with a model of the concept `BisectionGeometricTraits_3`.
+
+ This class is a model of concept `MeshDomain_3`.
+\cgalModels{MeshDomain_3}
+
+\sa `CGAL::Labeled_mesh_domain_3`
+\sa `CGAL::make_mesh_3()`
+*/
 template<class BGT,
          class Subdomain_index_ = int,
          class Surface_patch_index_ = std::pair<Subdomain_index_,
@@ -114,27 +113,27 @@ class Poisson_mesh_domain_3
 
 
   Function poisson_function;
-  /// \name Creation
+/// \name Creation
 /// @{
-  ///!  \brief Construction from a function, a bounding object and a relative error bound.
-   //
-   // \tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
-   // \tparam Bounding_object either a bounding sphere (of type `Sphere_3`), a bounding box (type `Bbox_3`),
-   //                         or a bounding `Iso_cuboid_3`
-   //
-   // \param function the Poisson reconstruction function
-   // \param bounding_object the bounding object bounding the meshable space.
-   // \param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below:
-   //
-   // \cgalNamedParamsBegin
-   //   \cgalParamNBegin{relative_error_bound}
-   //      \cgalParamDescription{the relative error bound used to compute intersection points between the implicit surface and query segments.
-   //                            The bisection is stopped when the length of the intersected segment is less than the product
-   //                            of `relative_error_bound` by the diameter of the bounding object.}
-   //      \cgalParamDefault{FT(1e-3)}
-   //   \cgalParamNEnd
-   // \cgalNamedParamsEnd
-   ///
+  /*!  \brief Construction from a function, a bounding object and a relative error bound.
+   *
+   * \tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
+   * \tparam Bounding_object either a bounding sphere (of type `Sphere_3`), a bounding box (type `Bbox_3`),
+   *                         or a bounding `Iso_cuboid_3`
+   *
+   * \param function the Poisson reconstruction function
+   * \param bounding_object the bounding object bounding the meshable space.
+   * \param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below:
+   *
+   * \cgalNamedParamsBegin
+   *   \cgalParamNBegin{relative_error_bound}
+   *      \cgalParamDescription{the relative error bound used to compute intersection points between the implicit surface and query segments.
+   *                            The bisection is stopped when the length of the intersected segment is less than the product
+   *                            of `relative_error_bound` by the diameter of the bounding object.}
+   *      \cgalParamDefault{FT(1e-3)}
+   *   \cgalParamNEnd
+   * \cgalNamedParamsEnd
+   */
   template<typename Bounding_object, typename CGAL_NP_TEMPLATE_PARAMETERS>
   Poisson_mesh_domain_3(const Function& function,
                         const Bounding_object& bounding_object,
@@ -171,35 +170,33 @@ class Poisson_mesh_domain_3
 
 /// \name Creation of domains from Poisson implicit functions
 /// @{
-
-  ///!
-   // \brief Construction from a Poisson implicit function
-   //
-   // This static method is a <em>named constructor</em>. It constructs a domain
-   // whose bounding surface is described implicitly as the zero level set of a
-   // function.  The domain to be discretized is assumed to be the domain where
-   // the function has negative values.
-   //
-   // The method takes as argument a bounding sphere which is required to
-   // circumscribe the surface and to have its center inside the domain.
-   //
-   // \tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
-   // \tparam Bounding_object either a bounding sphere (of type `Sphere_3`), a bounding box (type `Bbox_3`),
-   //                         or a bounding `Iso_cuboid_3`
-   //
-   // \param function the Poisson reconstruction function
-   // \param bounding_object object boundint the meshable domain and its center is inside the domain.
-   // \param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below:
-   //
-   // \cgalNamedParamsBegin
-   //   \cgalParamNBegin{relative_error_bound}
-   //     \cgalParamDescription{ is the relative error
-   //                            bound, relative to the diameter of the box of the image.}
-   //     \cgalParamDefault{FT(1e-3)}
-   //   \cgalParamNEnd
-   // \cgalNamedParamsEnd
-   //
-   ///
+  /*! \brief Construction from a Poisson implicit function
+   *
+   * This static method is a <em>named constructor</em>. It constructs a domain
+   * whose bounding surface is described implicitly as the zero level set of a
+   * function.  The domain to be discretized is assumed to be the domain where
+   * the function has negative values.
+   *
+   * The method takes as argument a bounding sphere which is required to
+   * circumscribe the surface and to have its center inside the domain.
+   *
+   * \tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
+   * \tparam Bounding_object either a bounding sphere (of type `Sphere_3`), a bounding box (type `Bbox_3`),
+   *                         or a bounding `Iso_cuboid_3`
+   *
+   * \param function the Poisson reconstruction function
+   * \param bounding_object object boundint the meshable domain and its center is inside the domain.
+   * \param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below:
+   *
+   * \cgalNamedParamsBegin
+   *   \cgalParamNBegin{relative_error_bound}
+   *     \cgalParamDescription{ is the relative error
+   *                            bound, relative to the diameter of the box of the image.}
+   *     \cgalParamDefault{FT(1e-3)}
+   *   \cgalParamNEnd
+   * \cgalNamedParamsEnd
+   *
+   */
   template<typename Bounding_object, typename CGAL_NP_TEMPLATE_PARAMETERS>
   static Poisson_mesh_domain_3 create_Poisson_mesh_domain(const Function& function,
                                                            const Bounding_object& bounding_object,

From 5f196bf3d04f512013aba72bae455b2e0fa86e96 Mon Sep 17 00:00:00 2001
From: Sven Oesau <sven.oesau@geometryfactory.com>
Date: Thu, 13 Mar 2025 10:08:34 +0100
Subject: [PATCH 06/21] corrected type

---
 .../include/CGAL/Poisson_mesh_domain_3.h                        | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h b/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h
index c85fc3438f0..1db317cc854 100644
--- a/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h
+++ b/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h
@@ -329,7 +329,7 @@ internal_np::bounding_object_param_t>::value, "Value for required parameter not
           } else {
             const Surface_patch_index sp_index = r_domain_.make_surface_index(label_at_p1, label_at_p2);
             const Index index = r_domain_.index_from_surface_patch_index(sp_index);
-            return Intersection(Point(ORIGIN + ((value_at_p2 * (p1 - ORIGIN)) - (value_at_p1 * (p2 - ORIGIN))) /
+            return Intersection(Point_3(ORIGIN + ((value_at_p2 * (p1 - ORIGIN)) - (value_at_p1 * (p2 - ORIGIN))) /
                                                   (value_at_p2 - value_at_p1)), index, 2);
           }
         }

From 21f3456968c63337d933c7ffc54a754e35eb929c Mon Sep 17 00:00:00 2001
From: Sven Oesau <sven.oesau@geometryfactory.com>
Date: Tue, 18 Mar 2025 16:18:17 +0100
Subject: [PATCH 07/21] benchmark on new Poisson_mesh_domain_3 (also with
 parallel make_mesh_3) work on documentation

---
 .../Poisson_surface_reconstruction_3.txt      | 275 +++++++++++++-----
 .../dependencies                              |   3 +
 .../fig/contouring_bench.jpg                  | Bin 67065 -> 135966 bytes
 .../fig/simplification_bench.jpg              | Bin 66691 -> 54249 bytes
 .../include/CGAL/Poisson_mesh_domain_3.h      |  50 +++-
 .../CGAL/Poisson_reconstruction_function.h    |   2 +-
 .../CMakeLists.txt                            |   8 +-
 7 files changed, 252 insertions(+), 86 deletions(-)

diff --git a/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt b/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
index f76f4ad34e8..1ba028b1db2 100644
--- a/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
+++ b/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
@@ -13,7 +13,7 @@ This \cgal component implements a surface reconstruction method which
 takes as input point sets with oriented normals and computes an
 implicit function. We assume that the input points contain no outliers
 and little noise. The output surface mesh is generated by extracting
-an isosurface of this function with the \cgal Surface Mesh Generator
+an isosurface of this function with the \ref Chapter_3D_Mesh_Generation or \cgal Surface Mesh Generator
 \cgalCite{cgal:ry-gsddrm-06} or potentially with any other surface
 contouring algorithm.
 
@@ -120,10 +120,12 @@ The following example reads a point set, creates a Poisson implicit function and
 
 
 The computed implicit functions can be iso-contoured to reconstruct a
-surface by using the \cgal surface mesh generator
+surface by using the \ref Chapter_3D_Mesh_Generation or the \cgal surface mesh generator
 \cgalCite{cgal:ry-gsddrm-06} \cgalCite{cgal:bo-pgsms-05} :
 
-`make_surface_mesh()`
+`make_mesh_3()` for using parallel Mesh_3
+
+`make_surface_mesh()` of using the deprecated 3D Surface Mesh Generation
 
 The parameter `Tag` affects the behavior of `make_surface_mesh()`:
 - `Manifold_tag`: the output mesh is guaranteed to be a manifold surface without boundary.
@@ -132,7 +134,10 @@ The parameter `Tag` affects the behavior of `make_surface_mesh()`:
 
 \subsection Poisson_surface_reconstruction_3Output Output
 
-The surface reconstructed by `make_surface_mesh()` is required to be a
+The surface reconstructed by `make_mesh_3()` is required to be a model of the concept 
+`MeshComplex_3InTriangulation_3`, a data structure devised to represent a three dimensional complex embedded into a three dimensional triangulation. The surface facets can then be extracted into a face graph by `facets_in_complex_3_to_triangle_mesh()`.
+
+The surface reconstructed by `make_surface_mesh()` instead is required to be a
 model of the concept `SurfaceMeshComplex_2InTriangulation_3`, a data
 structure devised to represent a two dimensional complex embedded into
 a three dimensional triangulation.
@@ -339,15 +344,15 @@ Left: 5K points sampled on a mechanical piece with sharp features (creases, dart
 
 We provide some performance numbers for scanning data. We measure the Poisson implicit function computation time,
 the contouring time for a range of approximation distances, the memory occupancy as well as the influence of
-the point set simplification. The machine used is a PC running Windows 7 64 bits with an Intel CPU Core 2 Duo
-processor clocked at 2.81 GHz and with 8 GB of RAM. The software is compiled with Visual \CC 2010 (VC9) compiler
+the point set simplification. The machine used is a PC running Windows 10 64 bits with an Intel CPU Core i7-11850H
+processor with 8 cores and 32 GB of RAM. The software is compiled with Visual \CC 2022 compiler
 with the 03 option which maximizes speed.  All measurements were done using the \ref thirdpartyEigen "Eigen" library.
 
-
 \subsection SurfReconstPerfPIF Poisson Implicit Function
 
-The point set chosen for benchmarking the Poisson implicit function is the Bimba con Nastrino point set
-(1.6 million points) depicted by \cgalFigureRef{Poisson_surface_reconstruction_3-fig-contouring_bench}.
+The point set chosen for benchmarking the Poisson implicit function is the Lucy statue point set from the 
+<a href="https://graphics.stanford.edu/data/3Dscanrep/">The Stanford 3D Scanning Repository</a> 
+(originally 14 million points, here downscaled to 2.9 million points) depicted by \cgalFigureRef{Poisson_surface_reconstruction_3-fig-contouring_bench}.
 We measure the Poisson implicit function computation (i.e., the call to
 `Poisson_reconstruction_function::compute_implicit_function()` denoted by Poisson solve hereafter)
 for this point set as well as for simplified versions obtained through random simplification.
@@ -357,115 +362,213 @@ The following table provides Poisson solve computation times in seconds for an i
 <TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
 <TR>
 <TD class="math" ALIGN=CENTER NOWRAP>
-
 Number of points (x1000)
 <TD class="math" ALIGN=CENTER NOWRAP>
 Poisson solve duration (in s)
 <TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
 <TR>
 <TD class="math" ALIGN=CENTER NOWRAP>
-60
+30
 <TD class="math" ALIGN=CENTER NOWRAP>
-15
+3.3
 <TR>
 <TD class="math" ALIGN=CENTER NOWRAP>
-100
+60
 <TD class="math" ALIGN=CENTER NOWRAP>
-25
+7.7
 <TR>
 
 <TD class="math" ALIGN=CENTER NOWRAP>
-250
+120
 <TD class="math" ALIGN=CENTER NOWRAP>
-96
+18.1
 <TR>
 <TD class="math" ALIGN=CENTER NOWRAP>
-500
+237.5
 <TD class="math" ALIGN=CENTER NOWRAP>
-150
+35.1
 <TR>
 <TD class="math" ALIGN=CENTER NOWRAP>
-1,000
+375
 <TD class="math" ALIGN=CENTER NOWRAP>
-249
+64
 <TR>
 
 <TD class="math" ALIGN=CENTER NOWRAP>
-1,800
+750
+<TD class="math" ALIGN=CENTER NOWRAP>
+129
+<TR>
+<TD class="math" ALIGN=CENTER NOWRAP>
+1,500
+<TD class="math" ALIGN=CENTER NOWRAP>
+303
+<TR>
 <TD class="math" ALIGN=CENTER NOWRAP>
-478
+2,900
+<TD class="math" ALIGN=CENTER NOWRAP>
+486
 <TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
 </TABLE>
 
 
 \subsection SurfReconstPerfCont Contouring
 
-The point set chosen for benchmarking the contouring stage is the Bimba con Nastrino point
-set simplified to 100k points. We measure the contouring (i.e.\ the call to `make_surface_mesh()`)
+The point set chosen for benchmarking the contouring stage is the Lucy point
+set simplified to 2.9M points. We measure the contouring (i.e.\ the calls to `make_mesh_3()` and `facets_in_complex_3_to_triangle_mesh()`)
 duration and the reconstruction error for a range of approximation distances.
-The reconstruction error is expressed as the average distance from input points to the reconstructed surface
-in mm (the Bimba con Nastrino statue is 324 mm tall).
+The reconstruction error is expressed as the average distance from input points to the reconstructed surface in mm (the Lucy statue is 1597 mm tall).
 
 <TABLE CELLSPACING=5 >
-<TR><TD ALIGN=LEFT NOWRAP COLSPAN=3><HR>
+<TR><TD ALIGN=LEFT NOWRAP COLSPAN=4><HR>
 <TR>
 <TD class="math" ALIGN=CENTER NOWRAP>
 Approx. distance (*average spacing)
 <TD class="math" ALIGN=CENTER NOWRAP>
-Contouring duration (in s)
+Contouring duration single-thread (in s)
+<TD class="math" ALIGN=CENTER NOWRAP>
+Contouring duration parallel (in s)
 <TD class="math" ALIGN=CENTER NOWRAP>
 Reconstruction error (mm)
-<TR><TD ALIGN=LEFT NOWRAP COLSPAN=3><HR>
+<TR><TD ALIGN=LEFT NOWRAP COLSPAN=4><HR>
+<TR>
+
+<TD class="math" ALIGN=CENTER NOWRAP>
+0.05
+<TD class="math" ALIGN=CENTER NOWRAP>
+582
+<TD class="math" ALIGN=CENTER NOWRAP>
+112
+<TD class="math" ALIGN=CENTER NOWRAP>
+0.114
 <TR>
 
 <TD class="math" ALIGN=CENTER NOWRAP>
 0.1
 <TD class="math" ALIGN=CENTER NOWRAP>
-19.2
+221
+<TD class="math" ALIGN=CENTER NOWRAP>
+26
 <TD class="math" ALIGN=CENTER NOWRAP>
-0.055
+0.119
 <TR>
+
+<TD class="math" ALIGN=CENTER NOWRAP>
+0.15
+<TD class="math" ALIGN=CENTER NOWRAP>
+104
+<TD class="math" ALIGN=CENTER NOWRAP>
+25
+<TD class="math" ALIGN=CENTER NOWRAP>
+0.129
+<TR>
+
+<TD class="math" ALIGN=CENTER NOWRAP>
+0.2
+<TD class="math" ALIGN=CENTER NOWRAP>
+69.4
+<TD class="math" ALIGN=CENTER NOWRAP>
+9.2
+<TD class="math" ALIGN=CENTER NOWRAP>
+0.14
+<TR>
+
 <TD class="math" ALIGN=CENTER NOWRAP>
 0.25
 <TD class="math" ALIGN=CENTER NOWRAP>
-6.9
+53.6
 <TD class="math" ALIGN=CENTER NOWRAP>
-0.106
+7.0
+<TD class="math" ALIGN=CENTER NOWRAP>
+0.151
 <TR>
+
 <TD class="math" ALIGN=CENTER NOWRAP>
 0.5
 <TD class="math" ALIGN=CENTER NOWRAP>
-3.2
+25.2
+<TD class="math" ALIGN=CENTER NOWRAP>
+3.6
 <TD class="math" ALIGN=CENTER NOWRAP>
-0.18
+0.209
 <TR>
+
+<TD class="math" ALIGN=CENTER NOWRAP>
+0.75
+<TD class="math" ALIGN=CENTER NOWRAP>
+16.4
+<TD class="math" ALIGN=CENTER NOWRAP>
+4.9
+<TD class="math" ALIGN=CENTER NOWRAP>
+0.209
+<TR>
+
 <TD class="math" ALIGN=CENTER NOWRAP>
 1
 <TD class="math" ALIGN=CENTER NOWRAP>
-1.65
+12.4
+<TD class="math" ALIGN=CENTER NOWRAP>
+2.3
+<TD class="math" ALIGN=CENTER NOWRAP>
+0.33
+<TR>
+
+<TD class="math" ALIGN=CENTER NOWRAP>
+1.5
 <TD class="math" ALIGN=CENTER NOWRAP>
-0.36
+8.2
+<TD class="math" ALIGN=CENTER NOWRAP>
+1.4
+<TD class="math" ALIGN=CENTER NOWRAP>
+0.455
 <TR>
+
 <TD class="math" ALIGN=CENTER NOWRAP>
 2
 <TD class="math" ALIGN=CENTER NOWRAP>
+6.1
+<TD class="math" ALIGN=CENTER NOWRAP>
+1.1
+<TD class="math" ALIGN=CENTER NOWRAP>
+0.59
+<TR>
+
+<TD class="math" ALIGN=CENTER NOWRAP>
+3
+<TD class="math" ALIGN=CENTER NOWRAP>
+4.0
+<TD class="math" ALIGN=CENTER NOWRAP>
 0.8
 <TD class="math" ALIGN=CENTER NOWRAP>
-0.76
-<TR><TD ALIGN=LEFT NOWRAP COLSPAN=3><HR>
-</TABLE>
+0.87
+<TR>
 
+<TD class="math" ALIGN=CENTER NOWRAP>
+5
+<TD class="math" ALIGN=CENTER NOWRAP>
+2.3
+<TD class="math" ALIGN=CENTER NOWRAP>
+0.7
+<TD class="math" ALIGN=CENTER NOWRAP>
+1.50
+<TR>
+<TD ALIGN=LEFT NOWRAP COLSPAN=3><HR>
+</TABLE>
 
-\cgalFigureBegin{Poisson_surface_reconstruction_3-fig-contouring_bench,contouring_bench.jpg}
+\cgalFigureAnchor{Poisson_surface_reconstruction_3-fig-contouring_bench}
+<center>
+<img src="contouring_bench_4.jpg" style="max-width:80%;"/>
+</center>
+\cgalFigureCaptionBegin{Poisson_surface_reconstruction_3-fig-contouring_bench}
 Contouring duration (in s) and reconstruction error (mm)
 against several approximation distance parameters
-for the Bimba con Nastrino point set simplified to 100k points.
-\cgalFigureEnd
+for the Lucy point set simplified to 100k points.
+\cgalFigureCaptionEnd
 
 \subsection SurfReconstPerfMem Memory
 
-We measure the memory occupancy for the reconstruction of the full Bimba con Nastrino point
-set (1.8 millions points) as well as for simplified versions.\n
+We measure the memory occupancy for the reconstruction of the Lucy point
+set (2.9 millions points) as well as for further simplified versions.\n
 The Poisson implicit function computation has a memory peak when solving the Poisson linear
 system using the sparse linear solver.
 
@@ -479,34 +582,44 @@ Memory occupancy (MBytes)
 <TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
 <TR>
 <TD class="math" ALIGN=CENTER NOWRAP>
+30
+<TD class="math" ALIGN=CENTER NOWRAP>
+128
+<TR>
+<TD class="math" ALIGN=CENTER NOWRAP>
 60
 <TD class="math" ALIGN=CENTER NOWRAP>
-180
+226
+<TR>
+<TD class="math" ALIGN=CENTER NOWRAP>
+120
+<TD class="math" ALIGN=CENTER NOWRAP>
+431
 <TR>
 <TD class="math" ALIGN=CENTER NOWRAP>
-100
+237.5
 <TD class="math" ALIGN=CENTER NOWRAP>
-270
+813
 <TR>
 <TD class="math" ALIGN=CENTER NOWRAP>
-250
+375
 <TD class="math" ALIGN=CENTER NOWRAP>
-790
+1,232
 <TR>
 <TD class="math" ALIGN=CENTER NOWRAP>
-500
+750
 <TD class="math" ALIGN=CENTER NOWRAP>
-1300
+2,283
 <TR>
 <TD class="math" ALIGN=CENTER NOWRAP>
-1,000
+1,500
 <TD class="math" ALIGN=CENTER NOWRAP>
-2200
+4,042
 <TR>
 <TD class="math" ALIGN=CENTER NOWRAP>
-1,800
+2,900
 <TD class="math" ALIGN=CENTER NOWRAP>
-3800
+6,868
 <TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
 </TABLE>
 
@@ -514,11 +627,11 @@ Memory occupancy (MBytes)
 \subsection SurfReconstPerfPSS Point Set Simplification
 
 Due to the memory limitations described above, we recommend to simplify the point sets captured by laser scanners.\n
-We measure the reconstruction error for the Bimba con Nastrino point set (1.6M points) as well as for
+We measure the reconstruction error for the Lucy point set (2.9M points) as well as for
 simplified versions. All reconstructions use the recommended contouring parameter
 `approximation distance = 0.25 * the input point` set's average spacing.
 The reconstruction error is expressed as the average distance from input points to the reconstructed surface in mm
-(the Bimba con Nastrino statue is 324 mm tall).
+(the Lucy statue is 1597 mm tall).
 
 <TABLE CELLSPACING=5 >
 <TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
@@ -530,46 +643,66 @@ Reconstruction error (mm)
 <TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
 <TR>
 <TD class="math" ALIGN=CENTER NOWRAP>
+3.75
+<TD class="math" ALIGN=CENTER NOWRAP>
+9.88395
+<TR>
+<TD class="math" ALIGN=CENTER NOWRAP>
+7.5
+<TD class="math" ALIGN=CENTER NOWRAP>
+5.81843
+<TR>
+<TD class="math" ALIGN=CENTER NOWRAP>
+15
+<TD class="math" ALIGN=CENTER NOWRAP>
+3.13479
+<TR>
+<TD class="math" ALIGN=CENTER NOWRAP>
+30
+<TD class="math" ALIGN=CENTER NOWRAP>
+2.25391
+<TR>
+<TD class="math" ALIGN=CENTER NOWRAP>
 60
 <TD class="math" ALIGN=CENTER NOWRAP>
-0.27
+1.42965
 <TR>
 <TD class="math" ALIGN=CENTER NOWRAP>
 120
 <TD class="math" ALIGN=CENTER NOWRAP>
-0.15
+1.17589
 <TR>
 <TD class="math" ALIGN=CENTER NOWRAP>
-250
+237.5
 <TD class="math" ALIGN=CENTER NOWRAP>
-0.11
+0.99509
 <TR>
 <TD class="math" ALIGN=CENTER NOWRAP>
-500
+375
 <TD class="math" ALIGN=CENTER NOWRAP>
-0.079
+0.75215
 <TR>
 <TD class="math" ALIGN=CENTER NOWRAP>
-1,000
+750
 <TD class="math" ALIGN=CENTER NOWRAP>
-0.066
+0.344654
 <TR>
 <TD class="math" ALIGN=CENTER NOWRAP>
 1,500
 <TD class="math" ALIGN=CENTER NOWRAP>
-0.061
+0.225341
 <TR>
 <TD class="math" ALIGN=CENTER NOWRAP>
-1,600
+2,900
 <TD class="math" ALIGN=CENTER NOWRAP>
-0.06
+0.150947
 <TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
 </TABLE>
 
 
-\cgalFigureBegin{Poisson_surface_reconstruction_3-fig-simplification_bench,simplification_bench.jpg}
+\cgalFigureBegin{Poisson_surface_reconstruction_3-fig-simplification_bench,simplification_bench_2.jpg}
 Reconstruction error (mm) against number of points
-for the Bimba con Nastrino point set with 1.6M points
+for the Lucy point set with 2.9M points
 as well as for simplified versions.
 \cgalFigureEnd
 
diff --git a/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/dependencies b/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/dependencies
index cc72c124cd4..f2994343101 100644
--- a/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/dependencies
+++ b/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/dependencies
@@ -1,8 +1,11 @@
 Manual
 Kernel_23
+BGL
 STL_Extension
+Mesh_3
 Algebraic_foundations
 Circulator
 Stream_support
 Point_set_processing_3
 Solver_interface
+SMDS_3
diff --git a/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/fig/contouring_bench.jpg b/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/fig/contouring_bench.jpg
index 70fbd8b61c59e8e7b81d3d531369500b7de9cc42..34f241f13a61f9819a1f81dd2e8940c9c11671ae 100644
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diff --git a/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h b/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h
index 1db317cc854..44e89efd100 100644
--- a/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h
+++ b/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h
@@ -18,7 +18,7 @@
 #ifndef CGAL_POISSON_MESH_DOMAIN_3_H
 #define CGAL_POISSON_MESH_DOMAIN_3_H
 
-#include <CGAL/license/Mesh_3.h>
+#include <CGAL/license/Poisson_surface_reconstruction_3.h>
 
 #include <CGAL/Labeled_mesh_domain_3.h>
 #include <CGAL/Poisson_reconstruction_function.h>
@@ -26,13 +26,13 @@
 namespace CGAL {
 
 /*!
-\ingroup PkgMesh3Domains
+\ingroup PkgPoissonSurfaceReconstruction3Ref
 
 \brief The class `Poisson_mesh_domain_3` derives from `Labeled_mesh_domain_3` for the handling of `Poisson_reconstruction_function`.
 
  This class has a constructor taking a labeling function. It has also a static template member
  function that acts as named constructor:
- <ul><li>`create_Poisson_mesh_domain()`, to create a domain from a `Poisson_reconstruction_function`</ ul>
+ <ul><li>`create_Poisson_mesh_domain()`</li>, to create a domain from a `Poisson_reconstruction_function`</ul>
 
 \tparam BGT is a geometric traits class that provides
     the basic operations to implement intersection tests and intersection computations through a bisection
@@ -117,9 +117,10 @@ class Poisson_mesh_domain_3
 /// @{
   /*!  \brief Construction from a function, a bounding object and a relative error bound.
    *
-   * \tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
    * \tparam Bounding_object either a bounding sphere (of type `Sphere_3`), a bounding box (type `Bbox_3`),
    *                         or a bounding `Iso_cuboid_3`
+   * \tparam NamedParameters
+   *  a sequence of \ref bgl_namedparameters "Named Parameters"
    *
    * \param function the Poisson reconstruction function
    * \param bounding_object the bounding object bounding the meshable space.
@@ -136,14 +137,41 @@ class Poisson_mesh_domain_3
    */
   template<typename Bounding_object, typename CGAL_NP_TEMPLATE_PARAMETERS>
   Poisson_mesh_domain_3(const Function& function,
-                        const Bounding_object& bounding_object,
-                        const CGAL_NP_CLASS& np = parameters::default_values()
+    const Bounding_object& bounding_object,
+    const CGAL_NP_CLASS& np = parameters::default_values()
 #ifndef DOXYGEN_RUNNING
-                        , typename std::enable_if<!is_named_function_parameter<Function>>::type* = nullptr
+    , typename std::enable_if<!is_named_function_parameter<Function>>::type* = nullptr
 #endif // DOXYGEN_RUNNING
-                        )
-      : Base(make_implicit_to_labeling_function_wrapper<BGT>(function), bounding_object, np),
-        poisson_function(function)
+  )
+    : Base(make_implicit_to_labeling_function_wrapper<BGT>(function), bounding_object, np),
+    poisson_function(function)
+  {}
+
+  /*!  \brief Construction from a function, a bounding object and a relative error bound.
+   *
+   * \tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
+   *
+   * \param function the Poisson reconstruction function
+   * \param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below:
+   *
+   * \cgalNamedParamsBegin
+   *   \cgalParamNBegin{relative_error_bound}
+   *      \cgalParamDescription{the relative error bound used to compute intersection points between the implicit surface and query segments.
+   *                            The bisection is stopped when the length of the intersected segment is less than the product
+   *                            of `relative_error_bound` by the diameter of the bounding object.}
+   *      \cgalParamDefault{FT(1e-3)}
+   *   \cgalParamNEnd
+   * \cgalNamedParamsEnd
+   */
+  template<typename CGAL_NP_TEMPLATE_PARAMETERS>
+  Poisson_mesh_domain_3(const Function & function,
+    const CGAL_NP_CLASS& np = parameters::default_values()
+#ifndef DOXYGEN_RUNNING
+    , typename std::enable_if<!is_named_function_parameter<Function>>::type * = nullptr
+#endif // DOXYGEN_RUNNING
+  )
+    : Base(make_implicit_to_labeling_function_wrapper<BGT>(function), function.bounding_sphere(), np),
+    poisson_function(function)
   {}
 ///@}
 
@@ -185,7 +213,7 @@ class Poisson_mesh_domain_3
    *                         or a bounding `Iso_cuboid_3`
    *
    * \param function the Poisson reconstruction function
-   * \param bounding_object object boundint the meshable domain and its center is inside the domain.
+   * \param bounding_object object bounding the meshable domain and its center is inside the domain.
    * \param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below:
    *
    * \cgalNamedParamsBegin
diff --git a/Poisson_surface_reconstruction_3/include/CGAL/Poisson_reconstruction_function.h b/Poisson_surface_reconstruction_3/include/CGAL/Poisson_reconstruction_function.h
index 488e15b0b3a..01215b09963 100644
--- a/Poisson_surface_reconstruction_3/include/CGAL/Poisson_reconstruction_function.h
+++ b/Poisson_surface_reconstruction_3/include/CGAL/Poisson_reconstruction_function.h
@@ -460,7 +460,7 @@ class Poisson_reconstruction_function
       // Add a pass of Delaunay refinement.
       //
       // In that pass, the sizing field, of the refinement process of the
-      // triangulation, is based on the result of a poisson function with a
+      // triangulation, is based on the result of a Poisson function with a
       // sample of the input points. The ratio is 'approximation_ratio'.
       //
       // For optimization reasons, the cell criteria of the refinement
diff --git a/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/CMakeLists.txt b/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/CMakeLists.txt
index 3592fc3e950..204812566e8 100644
--- a/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/CMakeLists.txt
+++ b/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/CMakeLists.txt
@@ -5,6 +5,8 @@ project(Poisson_surface_reconstruction_3_Tests)
 
 # Find CGAL
 find_package(CGAL REQUIRED)
+find_package(TBB REQUIRED)
+include(CGAL_TBB_support)
 
 # VisualC++ optimization for applications dealing with large data
 if(MSVC)
@@ -23,13 +25,13 @@ include(CGAL_Eigen3_support)
 if(TARGET CGAL::Eigen3_support)
   # Executables that require Eigen 3.1
   create_single_source_cgal_program("poisson_reconstruction_test_surface_mesher.cpp")
-  target_link_libraries(poisson_reconstruction_test_surface_mesher PRIVATE CGAL::Eigen3_support)
+  target_link_libraries(poisson_reconstruction_test_surface_mesher PRIVATE CGAL::Eigen3_support CGAL::TBB_support)
 
   create_single_source_cgal_program("poisson_reconstruction_test_mesh_3.cpp")
-  target_link_libraries(poisson_reconstruction_test_mesh_3 PRIVATE CGAL::Eigen3_support)
+  target_link_libraries(poisson_reconstruction_test_mesh_3 PRIVATE CGAL::Eigen3_support CGAL::TBB_support)
 
   create_single_source_cgal_program("compare_mesh_3_vs_Poisson_implicit_surface_3.cpp")
-  target_link_libraries(compare_mesh_3_vs_Poisson_implicit_surface_3  PRIVATE CGAL::Eigen3_support)
+  target_link_libraries(compare_mesh_3_vs_Poisson_implicit_surface_3  PRIVATE CGAL::Eigen3_support CGAL::TBB_support)
 
 else()
   message("NOTICE: Tests in this directory require Eigen 3.1 (or greater), and will not be compiled.")

From c79f408718bb53e862a922e8c95825e17585e001 Mon Sep 17 00:00:00 2001
From: Sven Oesau <sven.oesau@geometryfactory.com>
Date: Wed, 19 Mar 2025 08:53:46 +0100
Subject: [PATCH 08/21] removing whitespaces

---
 .../Poisson_surface_reconstruction_3.txt                    | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt b/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
index 1ba028b1db2..f878e04d7f1 100644
--- a/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
+++ b/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
@@ -134,7 +134,7 @@ The parameter `Tag` affects the behavior of `make_surface_mesh()`:
 
 \subsection Poisson_surface_reconstruction_3Output Output
 
-The surface reconstructed by `make_mesh_3()` is required to be a model of the concept 
+The surface reconstructed by `make_mesh_3()` is required to be a model of the concept
 `MeshComplex_3InTriangulation_3`, a data structure devised to represent a three dimensional complex embedded into a three dimensional triangulation. The surface facets can then be extracted into a face graph by `facets_in_complex_3_to_triangle_mesh()`.
 
 The surface reconstructed by `make_surface_mesh()` instead is required to be a
@@ -350,8 +350,8 @@ with the 03 option which maximizes speed.  All measurements were done using the
 
 \subsection SurfReconstPerfPIF Poisson Implicit Function
 
-The point set chosen for benchmarking the Poisson implicit function is the Lucy statue point set from the 
-<a href="https://graphics.stanford.edu/data/3Dscanrep/">The Stanford 3D Scanning Repository</a> 
+The point set chosen for benchmarking the Poisson implicit function is the Lucy statue point set from the
+<a href="https://graphics.stanford.edu/data/3Dscanrep/">The Stanford 3D Scanning Repository</a>
 (originally 14 million points, here downscaled to 2.9 million points) depicted by \cgalFigureRef{Poisson_surface_reconstruction_3-fig-contouring_bench}.
 We measure the Poisson implicit function computation (i.e., the call to
 `Poisson_reconstruction_function::compute_implicit_function()` denoted by Poisson solve hereafter)

From 56ecacda1eb56b7b6414320d541dcff8a2d98f86 Mon Sep 17 00:00:00 2001
From: Sven Oesau <sven.oesau@geometryfactory.com>
Date: Wed, 19 Mar 2025 09:01:35 +0100
Subject: [PATCH 09/21] tbb is optional

---
 .../CMakeLists.txt                            | 23 +++++++++++++------
 1 file changed, 16 insertions(+), 7 deletions(-)

diff --git a/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/CMakeLists.txt b/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/CMakeLists.txt
index 204812566e8..18469f6ee22 100644
--- a/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/CMakeLists.txt
+++ b/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/CMakeLists.txt
@@ -5,7 +5,7 @@ project(Poisson_surface_reconstruction_3_Tests)
 
 # Find CGAL
 find_package(CGAL REQUIRED)
-find_package(TBB REQUIRED)
+find_package(TBB QUIET)
 include(CGAL_TBB_support)
 
 # VisualC++ optimization for applications dealing with large data
@@ -24,15 +24,24 @@ find_package(Eigen3 3.1.0 QUIET) #(requires 3.1.0 or greater)
 include(CGAL_Eigen3_support)
 if(TARGET CGAL::Eigen3_support)
   # Executables that require Eigen 3.1
-  create_single_source_cgal_program("poisson_reconstruction_test_surface_mesher.cpp")
-  target_link_libraries(poisson_reconstruction_test_surface_mesher PRIVATE CGAL::Eigen3_support CGAL::TBB_support)
+  if(TARGET CGAL::TBB_support)
+    create_single_source_cgal_program("poisson_reconstruction_test_surface_mesher.cpp")
+    target_link_libraries(poisson_reconstruction_test_surface_mesher PRIVATE CGAL::Eigen3_support CGAL::TBB_support)
 
-  create_single_source_cgal_program("poisson_reconstruction_test_mesh_3.cpp")
-  target_link_libraries(poisson_reconstruction_test_mesh_3 PRIVATE CGAL::Eigen3_support CGAL::TBB_support)
+    create_single_source_cgal_program("poisson_reconstruction_test_mesh_3.cpp")
+    target_link_libraries(poisson_reconstruction_test_mesh_3 PRIVATE CGAL::Eigen3_support CGAL::TBB_support)
 
-  create_single_source_cgal_program("compare_mesh_3_vs_Poisson_implicit_surface_3.cpp")
-  target_link_libraries(compare_mesh_3_vs_Poisson_implicit_surface_3  PRIVATE CGAL::Eigen3_support CGAL::TBB_support)
+    create_single_source_cgal_program("compare_mesh_3_vs_Poisson_implicit_surface_3.cpp")
+    target_link_libraries(compare_mesh_3_vs_Poisson_implicit_surface_3  PRIVATE CGAL::Eigen3_support CGAL::TBB_support)
+  else()
+    create_single_source_cgal_program("poisson_reconstruction_test_surface_mesher.cpp")
+    target_link_libraries(poisson_reconstruction_test_surface_mesher PRIVATE CGAL::Eigen3_support)
 
+    create_single_source_cgal_program("poisson_reconstruction_test_mesh_3.cpp")
+    target_link_libraries(poisson_reconstruction_test_mesh_3 PRIVATE CGAL::Eigen3_support)
+
+    create_single_source_cgal_program("compare_mesh_3_vs_Poisson_implicit_surface_3.cpp")
+    target_link_libraries(compare_mesh_3_vs_Poisson_implicit_surface_3  PRIVATE CGAL::Eigen3_support)
 else()
   message("NOTICE: Tests in this directory require Eigen 3.1 (or greater), and will not be compiled.")
 endif()

From 6f4aa07e317b6b86ee079af68002d22adc88855e Mon Sep 17 00:00:00 2001
From: Sven Oesau <sven.oesau@geometryfactory.com>
Date: Wed, 19 Mar 2025 09:06:53 +0100
Subject: [PATCH 10/21] CMakeLists.txt fix

---
 .../test/Poisson_surface_reconstruction_3/CMakeLists.txt         | 1 +
 1 file changed, 1 insertion(+)

diff --git a/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/CMakeLists.txt b/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/CMakeLists.txt
index 18469f6ee22..e7adcfdc21a 100644
--- a/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/CMakeLists.txt
+++ b/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/CMakeLists.txt
@@ -42,6 +42,7 @@ if(TARGET CGAL::Eigen3_support)
 
     create_single_source_cgal_program("compare_mesh_3_vs_Poisson_implicit_surface_3.cpp")
     target_link_libraries(compare_mesh_3_vs_Poisson_implicit_surface_3  PRIVATE CGAL::Eigen3_support)
+  endif()
 else()
   message("NOTICE: Tests in this directory require Eigen 3.1 (or greater), and will not be compiled.")
 endif()

From 2df3538244ce306994d8b2aa53a2ee14327cc1b9 Mon Sep 17 00:00:00 2001
From: Sven Oesau <sven.oesau@geometryfactory.com>
Date: Wed, 19 Mar 2025 10:00:51 +0100
Subject: [PATCH 11/21] fixed image paths

---
 .../Poisson_surface_reconstruction_3.txt                      | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt b/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
index f878e04d7f1..2a225b0953b 100644
--- a/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
+++ b/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
@@ -557,7 +557,7 @@ Reconstruction error (mm)
 
 \cgalFigureAnchor{Poisson_surface_reconstruction_3-fig-contouring_bench}
 <center>
-<img src="contouring_bench_4.jpg" style="max-width:80%;"/>
+<img src="contouring_bench.jpg" style="max-width:80%;"/>
 </center>
 \cgalFigureCaptionBegin{Poisson_surface_reconstruction_3-fig-contouring_bench}
 Contouring duration (in s) and reconstruction error (mm)
@@ -700,7 +700,7 @@ Reconstruction error (mm)
 </TABLE>
 
 
-\cgalFigureBegin{Poisson_surface_reconstruction_3-fig-simplification_bench,simplification_bench_2.jpg}
+\cgalFigureBegin{Poisson_surface_reconstruction_3-fig-simplification_bench,simplification_bench.jpg}
 Reconstruction error (mm) against number of points
 for the Lucy point set with 2.9M points
 as well as for simplified versions.

From f4ae852e858b790dd3362a78bf3fc92db2461063 Mon Sep 17 00:00:00 2001
From: Sven Oesau <sven.oesau@geometryfactory.com>
Date: Wed, 19 Mar 2025 11:53:46 +0100
Subject: [PATCH 12/21] updated Changed.md [skip ci]

---
 Installation/CHANGES.md | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/Installation/CHANGES.md b/Installation/CHANGES.md
index bdae9dd56fb..e089d5ccb63 100644
--- a/Installation/CHANGES.md
+++ b/Installation/CHANGES.md
@@ -28,7 +28,9 @@
 -   Added two new meshing parameters that enable mesh initialization customization :
   - `initial_points_generator` : enables the user to specify a functor that generates initial points,
   - `initial_points` : enables the user to specify a `Range` of initial points.
-
+  
+### [Poisson Surface Reconstruction](https://doc.cgal.org/6.1/Manual/packages.html#PkgPoissonSurfaceReconstruction3)
+-   Added a new mesh domain `Poisson_mesh_domain_3` that integrates some optimizations from the deprecated 3D Surface Mesh Generation package.
 
 ### [2D Triangulations](https://doc.cgal.org/6.1/Manual/packages.html#PkgTriangulation2)
 

From 62833a6baef15bfd7bc2e85a028671e5e873fe98 Mon Sep 17 00:00:00 2001
From: Sven Oesau <sven.oesau@geometryfactory.com>
Date: Mon, 31 Mar 2025 14:36:30 +0200
Subject: [PATCH 13/21] adapting Poisson_surface_reconstruction_3 to
 surface_only()

---
 .../poisson_and_parallel_mesh_3.cpp                       | 3 +--
 .../poisson_reconstruction.cpp                            | 2 +-
 .../poisson_reconstruction_example.cpp                    | 2 +-
 .../include/CGAL/poisson_surface_reconstruction.h         | 8 ++++----
 .../compare_mesh_3_vs_Poisson_implicit_surface_3.cpp      | 4 ++--
 .../poisson_reconstruction_test_mesh_3.cpp                | 4 ++--
 6 files changed, 11 insertions(+), 12 deletions(-)

diff --git a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_and_parallel_mesh_3.cpp b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_and_parallel_mesh_3.cpp
index d84974ce78f..3706b1ec196 100644
--- a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_and_parallel_mesh_3.cpp
+++ b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_and_parallel_mesh_3.cpp
@@ -118,8 +118,7 @@ void poisson_reconstruction(const PointSet& points, const char* output)
   std::cout << "Start meshing...";
   std::cout.flush();
   C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria,
-                                      params::no_exude()
-                                             .no_perturb()
+                                      params::surface_only()
                                              .manifold_with_boundary());
 
   time.stop();
diff --git a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction.cpp b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction.cpp
index 4e9bdf1360f..82c3a623d2c 100644
--- a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction.cpp
+++ b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction.cpp
@@ -332,7 +332,7 @@ int main(int argc, char * argv[])
 
     // Generates mesh with manifold option
     C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria,
-                                        CGAL::parameters::no_exude().no_perturb()
+                                        CGAL::parameters::surface_only()
                                         .manifold_with_boundary());
 
     // Prints status
diff --git a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction_example.cpp b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction_example.cpp
index c73be4427e9..4d4806a7d25 100644
--- a/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction_example.cpp
+++ b/Poisson_surface_reconstruction_3/examples/Poisson_surface_reconstruction_3/poisson_reconstruction_example.cpp
@@ -90,7 +90,7 @@ int main(void)
 
     // Generates mesh with manifold option
     C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria,
-                                        CGAL::parameters::no_exude().no_perturb()
+                                        CGAL::parameters::surface_only()
                                         .manifold_with_boundary());
 
     const Tr& tr = c3t3.triangulation();
diff --git a/Poisson_surface_reconstruction_3/include/CGAL/poisson_surface_reconstruction.h b/Poisson_surface_reconstruction_3/include/CGAL/poisson_surface_reconstruction.h
index 9584e34f59f..fa39d55b131 100644
--- a/Poisson_surface_reconstruction_3/include/CGAL/poisson_surface_reconstruction.h
+++ b/Poisson_surface_reconstruction_3/include/CGAL/poisson_surface_reconstruction.h
@@ -17,7 +17,7 @@
 #include <CGAL/Mesh_triangulation_3.h>
 #include <CGAL/Mesh_complex_3_in_triangulation_3.h>
 #include <CGAL/Mesh_criteria_3.h>
-#include <CGAL/Labeled_mesh_domain_3.h>
+#include <CGAL/Poisson_mesh_domain_3.h>
 #include <CGAL/make_mesh_3.h>
 #include <CGAL/facets_in_complex_3_to_triangle_mesh.h>
 #include <CGAL/Poisson_reconstruction_function.h>
@@ -99,7 +99,7 @@ namespace CGAL {
     typedef typename Kernel::FT FT;
 
     typedef CGAL::Poisson_reconstruction_function<Kernel> Poisson_reconstruction_function;
-    typedef CGAL::Labeled_mesh_domain_3<Kernel> Mesh_domain;
+    typedef CGAL::Poisson_mesh_domain_3<Kernel> Mesh_domain;
     typedef typename CGAL::Mesh_triangulation_3<Mesh_domain, CGAL::Default, Sequential_tag>::type Tr;
     typedef CGAL::Mesh_complex_3_in_triangulation_3<Tr> C3t3;
     typedef CGAL::Mesh_criteria_3<Tr> Mesh_criteria;
@@ -115,7 +115,7 @@ namespace CGAL {
     FT sm_sphere_radius = 5.0 * radius;
     FT sm_dichotomy_error = sm_distance * spacing / 1000.0;
 
-    Mesh_domain domain = Mesh_domain::create_implicit_mesh_domain(function, Sphere(inner_point, sm_sphere_radius),
+    Mesh_domain domain = Mesh_domain::create_Poisson_mesh_domain(function, Sphere(inner_point, sm_sphere_radius),
       CGAL::parameters::relative_error_bound(sm_dichotomy_error / sm_sphere_radius));
 
     Mesh_criteria criteria(CGAL::parameters::facet_angle = sm_angle,
@@ -134,7 +134,7 @@ namespace CGAL {
 
     C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria,
                                         turn_tag_into_mesh_3_manifold_option(tag)
-                                        .no_exude().no_perturb()
+                                        .surface_only()
                                         .manifold_with_boundary());
 
     const auto& tr = c3t3.triangulation();
diff --git a/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/compare_mesh_3_vs_Poisson_implicit_surface_3.cpp b/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/compare_mesh_3_vs_Poisson_implicit_surface_3.cpp
index 5fb8c4a34e6..117ccf97729 100644
--- a/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/compare_mesh_3_vs_Poisson_implicit_surface_3.cpp
+++ b/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/compare_mesh_3_vs_Poisson_implicit_surface_3.cpp
@@ -356,7 +356,7 @@ int main(int argc, char * argv[])
 
       // Generates mesh with manifold option
       LC3t3 c3t3 =
-          CGAL::make_mesh_3<LC3t3>(domain, criteria, CGAL::parameters::no_exude().no_perturb().manifold_with_boundary());
+          CGAL::make_mesh_3<LC3t3>(domain, criteria, CGAL::parameters::surface_only().manifold_with_boundary());
       meshing_timer.stop();
 
       const LTr& tr = c3t3.triangulation();
@@ -398,7 +398,7 @@ int main(int argc, char * argv[])
 
       // Generates mesh with manifold option
       C3t3 c3t3 =
-          CGAL::make_mesh_3<C3t3>(domain, criteria, CGAL::parameters::no_exude().no_perturb().manifold_with_boundary());
+          CGAL::make_mesh_3<C3t3>(domain, criteria, CGAL::parameters::surface_only().manifold_with_boundary());
 
       meshing_timer.stop();
 
diff --git a/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/poisson_reconstruction_test_mesh_3.cpp b/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/poisson_reconstruction_test_mesh_3.cpp
index f171053e86d..720e3f4b18b 100644
--- a/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/poisson_reconstruction_test_mesh_3.cpp
+++ b/Poisson_surface_reconstruction_3/test/Poisson_surface_reconstruction_3/poisson_reconstruction_test_mesh_3.cpp
@@ -276,7 +276,7 @@ int main(int argc, char * argv[])
       // Generates surface mesh with manifold option
       Mesh_domain domain = Mesh_domain::create_implicit_mesh_domain(
           function, bsphere, params::relative_error_bound(sm_dichotomy_error / sm_sphere_radius));
-      C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria, params::no_exude().no_perturb().manifold_with_boundary());
+      C3t3 c3t3 = CGAL::make_mesh_3<C3t3>(domain, criteria, params::surface_only().manifold_with_boundary());
 
       // Prints status
       /*long*/ memory = CGAL::Memory_sizer().virtual_size();
@@ -320,7 +320,7 @@ int main(int argc, char * argv[])
       Poisson_mesh_domain domain = Poisson_mesh_domain::create_Poisson_mesh_domain(
           function, bsphere, params::relative_error_bound(sm_dichotomy_error / sm_sphere_radius));
       Poisson_C3t3 c3t3 =
-          CGAL::make_mesh_3<Poisson_C3t3>(domain, criteria, params::no_exude().no_perturb().manifold_with_boundary());
+          CGAL::make_mesh_3<Poisson_C3t3>(domain, criteria, params::surface_only().manifold_with_boundary());
 
       // Prints status
       /* long */ memory = CGAL::Memory_sizer().virtual_size();

From 675c10766dacd176036e11f471af4aac46b97102 Mon Sep 17 00:00:00 2001
From: Sven Oesau <sven.oesau@geometryfactory.com>
Date: Mon, 31 Mar 2025 16:15:24 +0200
Subject: [PATCH 14/21] changed link to better picture [skip ci]

---
 .../Poisson_surface_reconstruction_3.txt                        | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt b/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
index 2a225b0953b..22d533a0e67 100644
--- a/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
+++ b/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
@@ -352,7 +352,7 @@ with the 03 option which maximizes speed.  All measurements were done using the
 
 The point set chosen for benchmarking the Poisson implicit function is the Lucy statue point set from the
 <a href="https://graphics.stanford.edu/data/3Dscanrep/">The Stanford 3D Scanning Repository</a>
-(originally 14 million points, here downscaled to 2.9 million points) depicted by \cgalFigureRef{Poisson_surface_reconstruction_3-fig-contouring_bench}.
+(originally 14 million points, here downscaled to 2.9 million points) depicted by \cgalFigureRef{Poisson_surface_reconstruction_3-fig-simplification_bench}.
 We measure the Poisson implicit function computation (i.e., the call to
 `Poisson_reconstruction_function::compute_implicit_function()` denoted by Poisson solve hereafter)
 for this point set as well as for simplified versions obtained through random simplification.

From 25443ddc54994b8f23eb5f9b8d97d0129b24ba45 Mon Sep 17 00:00:00 2001
From: Sven Oesau <sven.oesau@geometryfactory.com>
Date: Wed, 2 Apr 2025 11:47:12 +0200
Subject: [PATCH 15/21] pass on code and doc following reviews

---
 Mesh_3/include/CGAL/Labeled_mesh_domain_3.h   | 17 ++---
 .../Poisson_surface_reconstruction_3.txt      | 48 ++++++------
 .../include/CGAL/Poisson_mesh_domain_3.h      | 73 ++++++++-----------
 3 files changed, 57 insertions(+), 81 deletions(-)

diff --git a/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h b/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h
index d40ec36318b..4bdf2fbb1c3 100644
--- a/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h
+++ b/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h
@@ -7,13 +7,8 @@
 // $Id$
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
-//
 // Author(s)     : Stéphane Tayeb, Aymeric PELLE
-//
-//******************************************************************************
-// File Description :
-// class Labeled_mesh_domain_3. See class description.
-//******************************************************************************
+
 
 #ifndef CGAL_LABELED_MESH_DOMAIN_3_H
 #define CGAL_LABELED_MESH_DOMAIN_3_H
@@ -875,17 +870,15 @@ class Labeled_mesh_domain_3
    * function.  The domain to be discretized is assumed to be the domain where
    * the function has negative values.
    *
-   * The method takes as argument a bounding sphere which is required to
-   * circumscribe the surface and to have its center inside the domain.
-   *
    * \tparam Function a type compatible with the signature `FT(Point_3)`: it takes a point as argument,
    *                  and returns a scalar value. That object must be model of `CopyConstructible`
    * \tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
    * \tparam Bounding_object either a bounding sphere (of type `Sphere_3`), a bounding box (type `Bbox_3`),
-   *                         or a bounding `Iso_cuboid_3`
+   *                         or a bounding `Iso_cuboid_3` which is required to circumscribe
+   *                         the surface and to have its center inside the domain.
    *
    * \param function the implicit function
-   * \param bounding_object object boundint the meshable domain and its center is inside the domain.
+   * \param bounding_object object bounding the meshable domain and its center is inside the domain.
    * \param np an optional sequence of \ref bgl_namedparameters "Named Parameters" among the ones listed below:
    *
    * \cgalNamedParamsBegin
@@ -1196,7 +1189,7 @@ class Labeled_mesh_domain_3
 
       // If both extremities are in the same subdomain,
       // there is no intersection.
-      // Should only happen during initial point generation.
+      // Should only be able to happen during initial point generation.
       if( value_at_p1 == value_at_p2 )
       {
         return Intersection();
diff --git a/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt b/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
index 22d533a0e67..9ff2ad918a7 100644
--- a/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
+++ b/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
@@ -13,8 +13,7 @@ This \cgal component implements a surface reconstruction method which
 takes as input point sets with oriented normals and computes an
 implicit function. We assume that the input points contain no outliers
 and little noise. The output surface mesh is generated by extracting
-an isosurface of this function with the \ref Chapter_3D_Mesh_Generation or \cgal Surface Mesh Generator
-\cgalCite{cgal:ry-gsddrm-06} or potentially with any other surface
+an isosurface of this function with the \ref 3D Mesh Generator or potentially with any other surface
 contouring algorithm.
 
 \cgalFigureBegin{Poisson_surface_reconstruction_3figintroduction,introduction.jpg}
@@ -76,7 +75,7 @@ indicator function \f$ f\f$ represented as a piecewise linear function
 over the refined triangulation. More specifically, it solves for the
 Poisson equation \f$ \Delta f = div(\mathbf{n})\f$ at each vertex of
 the triangulation using a sparse linear solver. Eventually, the \cgal
-surface mesh generator extracts an isosurface with function value set
+3D mesh generator extracts an isosurface with function value set
 by default to be the median value of \f$ f\f$ at all input points.
 
 \section Poisson_surface_reconstruction_3Function Reconstruction Function
@@ -86,9 +85,7 @@ provided. It takes points with normals as input and handles the whole
 reconstruction pipeline :
 
 - it computes the implicit function
-- it reconstructs the surface with a given precision using the \cgal
-surface mesh generator based on Delaunay refinement
-\cgalCite{cgal:ry-gsddrm-06} \cgalCite{cgal:bo-pgsms-05}
+- it reconstructs the surface with a given precision using the \cgal 3D mesh generator
 - it outputs the result in a polygon mesh.
 
 This function aims at providing a quick and user-friendly API for
@@ -120,14 +117,11 @@ The following example reads a point set, creates a Poisson implicit function and
 
 
 The computed implicit functions can be iso-contoured to reconstruct a
-surface by using the \ref Chapter_3D_Mesh_Generation or the \cgal surface mesh generator
-\cgalCite{cgal:ry-gsddrm-06} \cgalCite{cgal:bo-pgsms-05} :
+surface by using the \cgal 3D mesh generator :
 
-`make_mesh_3()` for using parallel Mesh_3
+`make_mesh_3()` with the `surface_only()` parameter for using parallel Mesh_3 
 
-`make_surface_mesh()` of using the deprecated 3D Surface Mesh Generation
-
-The parameter `Tag` affects the behavior of `make_surface_mesh()`:
+The parameter `Tag` affects the behavior of `make_mesh_3()`:
 - `Manifold_tag`: the output mesh is guaranteed to be a manifold surface without boundary.
 - `Manifold_with_boundary_tag`: the output mesh is guaranteed to be manifold and may have boundaries.
 - `Non_manifold_tag`: the output mesh has no guarantee and hence is outputted as a polygon soup.
@@ -137,13 +131,6 @@ The parameter `Tag` affects the behavior of `make_surface_mesh()`:
 The surface reconstructed by `make_mesh_3()` is required to be a model of the concept
 `MeshComplex_3InTriangulation_3`, a data structure devised to represent a three dimensional complex embedded into a three dimensional triangulation. The surface facets can then be extracted into a face graph by `facets_in_complex_3_to_triangle_mesh()`.
 
-The surface reconstructed by `make_surface_mesh()` instead is required to be a
-model of the concept `SurfaceMeshComplex_2InTriangulation_3`, a data
-structure devised to represent a two dimensional complex embedded into
-a three dimensional triangulation.
-
-`SurfaceMeshComplex_2InTriangulation_3` defines the methods to traverse the reconstructed surface, and e.g. convert it to a triangle soup.
-
 Other \cgal components provide functions to write the reconstructed
 surface mesh to the %Object File Format (OFF) \cgalCite{cgal:p-gmgv16-96}
 and to convert it to a polyhedron (when it is manifold):
@@ -223,7 +210,7 @@ function over the tetrahedra of a 3D Delaunay triangulation
 constructed from the input points then refined through Delaunay
 refinement. For this reason, any iso-surface is also piecewise linear
 and hence may contain sharp creases. As the contouring algorithm
-`make_surface_mesh()` expects a smooth implicit function these
+`make_mesh_3()` expects a smooth implicit function these
 sharp creases may create spurious clusters of vertices in the final
 reconstructed surface mesh when setting a small mesh sizing or surface
 approximation error parameter (see
@@ -352,12 +339,13 @@ with the 03 option which maximizes speed.  All measurements were done using the
 
 The point set chosen for benchmarking the Poisson implicit function is the Lucy statue point set from the
 <a href="https://graphics.stanford.edu/data/3Dscanrep/">The Stanford 3D Scanning Repository</a>
-(originally 14 million points, here downscaled to 2.9 million points) depicted by \cgalFigureRef{Poisson_surface_reconstruction_3-fig-simplification_bench}.
+(originally 14 million points, here downsampled to 2.9 million points) depicted by \cgalFigureRef{Poisson_surface_reconstruction_3-fig-contouring_bench}.
 We measure the Poisson implicit function computation (i.e., the call to
 `Poisson_reconstruction_function::compute_implicit_function()` denoted by Poisson solve hereafter)
 for this point set as well as for simplified versions obtained through random simplification.
 The following table provides Poisson solve computation times in seconds for an increasing number of points.
 
+<CENTER>
 <TABLE CELLSPACING=5 >
 <TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
 <TR>
@@ -408,19 +396,20 @@ Poisson solve duration (in s)
 2,900
 <TD class="math" ALIGN=CENTER NOWRAP>
 486
-<TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
+<TR><TD ALIGN=CENTER NOWRAP COLSPAN=2><HR>
 </TABLE>
-
+</CENTER>
 
 \subsection SurfReconstPerfCont Contouring
 
 The point set chosen for benchmarking the contouring stage is the Lucy point
-set simplified to 2.9M points. We measure the contouring (i.e.\ the calls to `make_mesh_3()` and `facets_in_complex_3_to_triangle_mesh()`)
+set simplified to 2.9M points. We measure the contouring (i.e., the calls to `make_mesh_3()` and `facets_in_complex_3_to_triangle_mesh()`)
 duration and the reconstruction error for a range of approximation distances.
 The reconstruction error is expressed as the average distance from input points to the reconstructed surface in mm (the Lucy statue is 1597 mm tall).
 
+<CENTER>
 <TABLE CELLSPACING=5 >
-<TR><TD ALIGN=LEFT NOWRAP COLSPAN=4><HR>
+<TR><TD ALIGN=CENTER NOWRAP COLSPAN=4><HR>
 <TR>
 <TD class="math" ALIGN=CENTER NOWRAP>
 Approx. distance (*average spacing)
@@ -430,7 +419,7 @@ Contouring duration single-thread (in s)
 Contouring duration parallel (in s)
 <TD class="math" ALIGN=CENTER NOWRAP>
 Reconstruction error (mm)
-<TR><TD ALIGN=LEFT NOWRAP COLSPAN=4><HR>
+<TR><TD ALIGN=CENTER NOWRAP COLSPAN=4><HR>
 <TR>
 
 <TD class="math" ALIGN=CENTER NOWRAP>
@@ -552,8 +541,9 @@ Reconstruction error (mm)
 <TD class="math" ALIGN=CENTER NOWRAP>
 1.50
 <TR>
-<TD ALIGN=LEFT NOWRAP COLSPAN=3><HR>
+<TD ALIGN=CENTER NOWRAP COLSPAN=4><HR>
 </TABLE>
+</CENTER>
 
 \cgalFigureAnchor{Poisson_surface_reconstruction_3-fig-contouring_bench}
 <center>
@@ -572,6 +562,7 @@ set (2.9 millions points) as well as for further simplified versions.\n
 The Poisson implicit function computation has a memory peak when solving the Poisson linear
 system using the sparse linear solver.
 
+<CENTER>
 <TABLE CELLSPACING=5 >
 <TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
 <TR>
@@ -622,6 +613,7 @@ Memory occupancy (MBytes)
 6,868
 <TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
 </TABLE>
+</CENTER>
 
 
 \subsection SurfReconstPerfPSS Point Set Simplification
@@ -633,6 +625,7 @@ simplified versions. All reconstructions use the recommended contouring paramete
 The reconstruction error is expressed as the average distance from input points to the reconstructed surface in mm
 (the Lucy statue is 1597 mm tall).
 
+<CENTER>
 <TABLE CELLSPACING=5 >
 <TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
 <TR>
@@ -698,6 +691,7 @@ Reconstruction error (mm)
 0.150947
 <TR><TD ALIGN=LEFT NOWRAP COLSPAN=2><HR>
 </TABLE>
+</CENTER>
 
 
 \cgalFigureBegin{Poisson_surface_reconstruction_3-fig-simplification_bench,simplification_bench.jpg}
diff --git a/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h b/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h
index 44e89efd100..3eabdf979c7 100644
--- a/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h
+++ b/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h
@@ -7,13 +7,7 @@
 // $Id$
 // SPDX-License-Identifier: GPL-3.0-or-later OR LicenseRef-Commercial
 //
-//
 // Author(s)     : Sven Oesau
-//
-//******************************************************************************
-// File Description :
-// class Poisson_mesh_domain_3. See class description.
-//******************************************************************************
 
 #ifndef CGAL_POISSON_MESH_DOMAIN_3_H
 #define CGAL_POISSON_MESH_DOMAIN_3_H
@@ -38,7 +32,6 @@ namespace CGAL {
     the basic operations to implement intersection tests and intersection computations through a bisection
     method.This parameter must be instantiated with a model of the concept `BisectionGeometricTraits_3`.
 
- This class is a model of concept `MeshDomain_3`.
 \cgalModels{MeshDomain_3}
 
 \sa `CGAL::Labeled_mesh_domain_3`
@@ -111,16 +104,15 @@ class Poisson_mesh_domain_3
   typedef CGAL::Poisson_reconstruction_function<BGT> Function;
 #endif
 
-
   Function poisson_function;
+
 /// \name Creation
 /// @{
   /*!  \brief Construction from a function, a bounding object and a relative error bound.
    *
    * \tparam Bounding_object either a bounding sphere (of type `Sphere_3`), a bounding box (type `Bbox_3`),
    *                         or a bounding `Iso_cuboid_3`
-   * \tparam NamedParameters
-   *  a sequence of \ref bgl_namedparameters "Named Parameters"
+   * \tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
    *
    * \param function the Poisson reconstruction function
    * \param bounding_object the bounding object bounding the meshable space.
@@ -144,7 +136,7 @@ class Poisson_mesh_domain_3
 #endif // DOXYGEN_RUNNING
   )
     : Base(make_implicit_to_labeling_function_wrapper<BGT>(function), bounding_object, np),
-    poisson_function(function)
+      poisson_function(function)
   {}
 
   /*!  \brief Construction from a function, a bounding object and a relative error bound.
@@ -171,14 +163,14 @@ class Poisson_mesh_domain_3
 #endif // DOXYGEN_RUNNING
   )
     : Base(make_implicit_to_labeling_function_wrapper<BGT>(function), function.bounding_sphere(), np),
-    poisson_function(function)
+      poisson_function(function)
   {}
 ///@}
 
 #ifndef DOXYGEN_RUNNING
   template<typename CGAL_NP_TEMPLATE_PARAMETERS_NO_DEFAULT>
   Poisson_mesh_domain_3(const CGAL_NP_CLASS& np)
-      : Base(np)
+    : Base(np)
   {}
 
   // Overload handling parameters passed with operator=
@@ -188,11 +180,11 @@ class Poisson_mesh_domain_3
            typename ... NP>
   Poisson_mesh_domain_3(const Function& function,
                         const CGAL_NP_CLASS_1& np1,
-                        const CGAL_NP_CLASS_2&  np2,
+                        const CGAL_NP_CLASS_2& np2,
                         const NP& ... nps)
-      : Base(internal_np::combine_named_parameters(
-            CGAL::parameters::function(make_implicit_to_labeling_function_wrapper<BGT>(function)), np1, np2, nps...)),
-        poisson_function(function)
+    : Base(internal_np::combine_named_parameters(
+          CGAL::parameters::function(make_implicit_to_labeling_function_wrapper<BGT>(function)), np1, np2, nps...)),
+      poisson_function(function)
   {}
 #endif
 
@@ -205,12 +197,10 @@ class Poisson_mesh_domain_3
    * function.  The domain to be discretized is assumed to be the domain where
    * the function has negative values.
    *
-   * The method takes as argument a bounding sphere which is required to
-   * circumscribe the surface and to have its center inside the domain.
-   *
    * \tparam NamedParameters a sequence of \ref bgl_namedparameters "Named Parameters"
    * \tparam Bounding_object either a bounding sphere (of type `Sphere_3`), a bounding box (type `Bbox_3`),
-   *                         or a bounding `Iso_cuboid_3`
+   *                         or a bounding `Iso_cuboid_3` which is required to circumscribe
+   *                         the surface and to have its center inside the domain.
    *
    * \param function the Poisson reconstruction function
    * \param bounding_object object bounding the meshable domain and its center is inside the domain.
@@ -236,33 +226,32 @@ class Poisson_mesh_domain_3
   {
     using parameters::get_parameter;
     using parameters::choose_parameter;
+
     FT relative_error_bound_ = choose_parameter(get_parameter(np, internal_np::error_bound), FT(1e-3));
     CGAL::Random* p_rng_ = choose_parameter(get_parameter(np, internal_np::rng), nullptr);
-    auto null_subdomain_index_ = choose_parameter(get_parameter(np, internal_np::null_subdomain_index_param),
-Null_functor()); auto construct_surface_patch_index_ = choose_parameter(get_parameter(np,
-internal_np::surface_patch_index), Null_functor());
-    namespace p = CGAL::parameters;
-    return Poisson_mesh_domain_3
-            (function,
+    auto null_subdomain_index_ = choose_parameter(get_parameter(np, internal_np::null_subdomain_index_param), Null_functor());
+    auto construct_surface_patch_index_ = choose_parameter(get_parameter(np, internal_np::surface_patch_index), Null_functor());
+
+    return Poisson_mesh_domain_3(function,
              bounding_object,
-              CGAL::parameters::relative_error_bound(relative_error_bound_)
-              .function(make_implicit_to_labeling_function_wrapper<BGT>(function))
-              .p_rng(p_rng_)
-              .null_subdomain_index(Base::create_null_subdomain_index(null_subdomain_index_))
-              .construct_surface_patch_index(Base::create_construct_surface_patch_index(construct_surface_patch_index_)));
+             CGAL::parameters::relative_error_bound(relative_error_bound_)
+             .function(make_implicit_to_labeling_function_wrapper<BGT>(function))
+             .p_rng(p_rng_)
+             .null_subdomain_index(Base::create_null_subdomain_index(null_subdomain_index_))
+             .construct_surface_patch_index(Base::create_construct_surface_patch_index(construct_surface_patch_index_)));
   }
 /// @}
 #ifndef DOXYGEN_RUNNING
   template<typename CGAL_NP_TEMPLATE_PARAMETERS>
   static Poisson_mesh_domain_3 create_Poisson_mesh_domain(const CGAL_NP_CLASS& np = parameters::default_values())
   {
-    static_assert(!parameters::is_default_parameter<CGAL_NP_CLASS, internal_np::function_param_t>::value,
-      "Value for required parameter not found"); static_assert(!parameters::is_default_parameter<CGAL_NP_CLASS,
-internal_np::bounding_object_param_t>::value, "Value for required parameter not found");
-
     using parameters::get_parameter;
-    return create_Poisson_mesh_domain(parameters::get_parameter(np, internal_np::function_param),
-                                       parameters::get_parameter(np, internal_np::bounding_object_param),
+
+    static_assert(!parameters::is_default_parameter<CGAL_NP_CLASS, internal_np::function_param_t>::value, "Value for required parameter not found");
+    static_assert(!parameters::is_default_parameter<CGAL_NP_CLASS, internal_np::bounding_object_param_t>::value, "Value for required parameter not found");
+
+    return create_Poisson_mesh_domain(get_parameter(np, internal_np::function_param),
+                                       get_parameter(np, internal_np::bounding_object_param),
                                        np);
   }
 
@@ -271,8 +260,8 @@ internal_np::bounding_object_param_t>::value, "Value for required parameter not
            typename CGAL_NP_TEMPLATE_PARAMETERS_NO_DEFAULT_2,
            typename ... NP>
   static Poisson_mesh_domain_3 create_Poisson_mesh_domain(const CGAL_NP_CLASS_1& np1,
-                                                           const CGAL_NP_CLASS_2&  np2,
-                                                           const NP& ... nps)
+                                                          const CGAL_NP_CLASS_2& np2,
+                                                          const NP& ... nps)
   {
     return create_Poisson_mesh_domain(internal_np::combine_named_parameters(np1, np2, nps...));
   }
@@ -343,12 +332,12 @@ internal_np::bounding_object_param_t>::value, "Value for required parameter not
 
       // If both extremities are in the same subdomain,
       // there is no intersection.
-      // Should only happen during initial point generation.
+      // Should only be able to happen during initial point generation.
       if(label_at_p1 == label_at_p2)
         return Intersection();
 
       // Else lets find a point (by bisection)
-      // Bisection ends when the point is near than error bound from surface
+      // Bisection ends when the point is nearer from surface than the error bound
       while(true) {
         if(c1 == c2) {
           if(c1_is_inf) {

From daea460016927de5a4fe303c2c8908ca6575c6a8 Mon Sep 17 00:00:00 2001
From: Sven Oesau <sven.oesau@geometryfactory.com>
Date: Wed, 2 Apr 2025 12:04:14 +0200
Subject: [PATCH 16/21] removing trailing whitespace

---
 .../Poisson_surface_reconstruction_3.txt                        | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt b/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
index 9ff2ad918a7..a19c5ae2094 100644
--- a/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
+++ b/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
@@ -119,7 +119,7 @@ The following example reads a point set, creates a Poisson implicit function and
 The computed implicit functions can be iso-contoured to reconstruct a
 surface by using the \cgal 3D mesh generator :
 
-`make_mesh_3()` with the `surface_only()` parameter for using parallel Mesh_3 
+`make_mesh_3()` with the `surface_only()` parameter for using parallel Mesh_3
 
 The parameter `Tag` affects the behavior of `make_mesh_3()`:
 - `Manifold_tag`: the output mesh is guaranteed to be a manifold surface without boundary.

From 96664743f55a6231c0eebd39ae5737a2806068dc Mon Sep 17 00:00:00 2001
From: Sven Oesau <sven.oesau@geometryfactory.com>
Date: Wed, 2 Apr 2025 16:58:47 +0200
Subject: [PATCH 17/21] remove default value for named parameter object

---
 Mesh_3/include/CGAL/Labeled_mesh_domain_3.h                    | 3 +--
 .../include/CGAL/Poisson_mesh_domain_3.h                       | 3 +--
 2 files changed, 2 insertions(+), 4 deletions(-)

diff --git a/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h b/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h
index 4bdf2fbb1c3..5ad1060e6c5 100644
--- a/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h
+++ b/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h
@@ -929,12 +929,11 @@ class Labeled_mesh_domain_3
 /// @}
 #ifndef DOXYGEN_RUNNING
   template<typename CGAL_NP_TEMPLATE_PARAMETERS>
-  static Labeled_mesh_domain_3 create_implicit_mesh_domain(const CGAL_NP_CLASS& np = parameters::default_values())
+  static Labeled_mesh_domain_3 create_implicit_mesh_domain(const CGAL_NP_CLASS &np)
   {
     static_assert(!parameters::is_default_parameter<CGAL_NP_CLASS, internal_np::function_param_t>::value, "Value for required parameter not found");
     static_assert(!parameters::is_default_parameter<CGAL_NP_CLASS, internal_np::bounding_object_param_t>::value, "Value for required parameter not found");
 
-    using parameters::get_parameter;
     return create_implicit_mesh_domain(parameters::get_parameter(np, internal_np::function_param),
                                        parameters::get_parameter(np, internal_np::bounding_object_param),
                                        np);
diff --git a/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h b/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h
index 3eabdf979c7..19bc672f4f4 100644
--- a/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h
+++ b/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h
@@ -243,8 +243,7 @@ class Poisson_mesh_domain_3
 /// @}
 #ifndef DOXYGEN_RUNNING
   template<typename CGAL_NP_TEMPLATE_PARAMETERS>
-  static Poisson_mesh_domain_3 create_Poisson_mesh_domain(const CGAL_NP_CLASS& np = parameters::default_values())
-  {
+  static Poisson_mesh_domain_3 create_Poisson_mesh_domain(const CGAL_NP_CLASS& np) {
     using parameters::get_parameter;
 
     static_assert(!parameters::is_default_parameter<CGAL_NP_CLASS, internal_np::function_param_t>::value, "Value for required parameter not found");

From adba9aeb6b7fff036c71cabe7dc2882c338a106a Mon Sep 17 00:00:00 2001
From: Sven Oesau <sven.oesau@geometryfactory.com>
Date: Wed, 2 Apr 2025 17:19:52 +0200
Subject: [PATCH 18/21] doc fix [skip ci]

---
 .../Poisson_surface_reconstruction_3.txt               | 10 +++++-----
 1 file changed, 5 insertions(+), 5 deletions(-)

diff --git a/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt b/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
index a19c5ae2094..184e087e3a7 100644
--- a/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
+++ b/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
@@ -13,7 +13,7 @@ This \cgal component implements a surface reconstruction method which
 takes as input point sets with oriented normals and computes an
 implicit function. We assume that the input points contain no outliers
 and little noise. The output surface mesh is generated by extracting
-an isosurface of this function with the \ref 3D Mesh Generator or potentially with any other surface
+an isosurface of this function with the \ref PkgMesh3 or potentially with any other surface
 contouring algorithm.
 
 \cgalFigureBegin{Poisson_surface_reconstruction_3figintroduction,introduction.jpg}
@@ -74,8 +74,8 @@ during refinement is set to zero. It then solves for a scalar
 indicator function \f$ f\f$ represented as a piecewise linear function
 over the refined triangulation. More specifically, it solves for the
 Poisson equation \f$ \Delta f = div(\mathbf{n})\f$ at each vertex of
-the triangulation using a sparse linear solver. Eventually, the \cgal
-3D mesh generator extracts an isosurface with function value set
+the triangulation using a sparse linear solver. Eventually, the \ref PkgMesh3
+ extracts an isosurface with function value set
 by default to be the median value of \f$ f\f$ at all input points.
 
 \section Poisson_surface_reconstruction_3Function Reconstruction Function
@@ -85,7 +85,7 @@ provided. It takes points with normals as input and handles the whole
 reconstruction pipeline :
 
 - it computes the implicit function
-- it reconstructs the surface with a given precision using the \cgal 3D mesh generator
+- it reconstructs the surface with a given precision using the \ref PkgMesh3
 - it outputs the result in a polygon mesh.
 
 This function aims at providing a quick and user-friendly API for
@@ -117,7 +117,7 @@ The following example reads a point set, creates a Poisson implicit function and
 
 
 The computed implicit functions can be iso-contoured to reconstruct a
-surface by using the \cgal 3D mesh generator :
+surface by using the \ref PkgMesh3 :
 
 `make_mesh_3()` with the `surface_only()` parameter for using parallel Mesh_3
 

From 5e2ba724eb28fca801932b89527aff993a135410 Mon Sep 17 00:00:00 2001
From: Sven Oesau <sven.oesau@geometryfactory.com>
Date: Thu, 10 Apr 2025 13:01:13 +0200
Subject: [PATCH 19/21] update following reviews

---
 .../include/CGAL/Poisson_mesh_domain_3.h      | 58 +++++++++----------
 1 file changed, 27 insertions(+), 31 deletions(-)

diff --git a/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h b/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h
index 19bc672f4f4..a88fa7d5412 100644
--- a/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h
+++ b/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h
@@ -37,24 +37,19 @@ namespace CGAL {
 \sa `CGAL::Labeled_mesh_domain_3`
 \sa `CGAL::make_mesh_3()`
 */
-template<class BGT,
-         class Subdomain_index_ = int,
-         class Surface_patch_index_ = std::pair<Subdomain_index_,
-                                                Subdomain_index_> >
+template<class BGT>
 class Poisson_mesh_domain_3
-    : public Labeled_mesh_domain_3<BGT,
-                                                  Subdomain_index_,
-                                                  Surface_patch_index_>
+    : public Labeled_mesh_domain_3<BGT>
 {
 public:
-  using Base = Labeled_mesh_domain_3<BGT, Subdomain_index_, Surface_patch_index_>;
+  using Base = Labeled_mesh_domain_3<BGT>;
   typedef typename Base::Subdomain Subdomain;
+  typedef typename Base::Subdomain_index Subdomain_index;
+  typedef typename Base::Surface_patch_index Surface_patch_index;
+  typedef typename Base::Intersection Intersection;
 
   // Type of indexes for cells of the input complex
-  typedef Surface_patch_index_ Surface_patch_index;
   typedef std::optional<Surface_patch_index> Surface_patch;
-  typedef Subdomain_index_ Subdomain_index;
-  typedef typename Base::Intersection Intersection;
 
   // Type of indexes to characterize the lowest dimensional face of the input
   // complex on which a vertex lie
@@ -217,10 +212,10 @@ class Poisson_mesh_domain_3
    */
   template<typename Bounding_object, typename CGAL_NP_TEMPLATE_PARAMETERS>
   static Poisson_mesh_domain_3 create_Poisson_mesh_domain(const Function& function,
-                                                           const Bounding_object& bounding_object,
-                                                           const CGAL_NP_CLASS& np = parameters::default_values()
+                                                          const Bounding_object& bounding_object,
+                                                          const CGAL_NP_CLASS& np = parameters::default_values()
 #ifndef DOXYGEN_RUNNING
-                                                           ,typename std::enable_if<!is_named_function_parameter<Function>>::type* = nullptr
+                                                          ,typename std::enable_if<!is_named_function_parameter<Function>>::type* = nullptr
 #endif
 )
   {
@@ -277,15 +272,14 @@ class Poisson_mesh_domain_3
    */
   struct Construct_intersection
   {
-    Construct_intersection(const Poisson_mesh_domain_3& domain)
-      : r_domain_(domain) {}
+    Construct_intersection(const Poisson_mesh_domain_3& domain) : domain_(domain) {}
 
     Intersection operator()(const Segment_3& s) const
     {
 #ifndef CGAL_MESH_3_NO_LONGER_CALLS_DO_INTERSECT_3
       CGAL_precondition(r_domain_.do_intersect_surface_object()(s) != std::nullopt);
 #endif // NOT CGAL_MESH_3_NO_LONGER_CALLS_DO_INTERSECT_3
-      return this->operator()(s.source(),s.target());
+      return this->operator()(s.source(), s.target());
     }
 
     Intersection operator()(const Ray_3& r) const
@@ -305,6 +299,9 @@ class Poisson_mesh_domain_3
      * because it drives bisection cuts.
      * Indeed, the returned point is the first intersection of `[a,b]`
      * with a subdomain surface.
+     *
+     * The difference from the Labeled_mesh_domain_3::Construct_intersection is that
+     * the underlying Delaunay triangulation in the Poisson function is used for the bisection.
      */
     Intersection operator()(const Point_3& a, const Point_3& b) const
     {
@@ -323,8 +320,8 @@ class Poisson_mesh_domain_3
       typename Function::Cell_handle c1, c2;
       bool c1_is_inf, c2_is_inf;
 
-      std::tie(value_at_p1, c1, c1_is_inf) = r_domain_.poisson_function.special_func(p1);
-      std::tie(value_at_p2, c2, c2_is_inf) = r_domain_.poisson_function.special_func(p2);
+      std::tie(value_at_p1, c1, c1_is_inf) = domain_.poisson_function.special_func(p1);
+      std::tie(value_at_p2, c2, c2_is_inf) = domain_.poisson_function.special_func(p2);
 
       Subdomain_index label_at_p1 = (value_at_p1 < 0) ? 1 : 0;
       Subdomain_index label_at_p2 = (value_at_p2 < 0) ? 1 : 0;
@@ -343,19 +340,19 @@ class Poisson_mesh_domain_3
             std::cout << "Intersection(): c1 == c2 and inf!" << std::endl;
             return Intersection();
           } else {
-            const Surface_patch_index sp_index = r_domain_.make_surface_index(label_at_p1, label_at_p2);
-            const Index index = r_domain_.index_from_surface_patch_index(sp_index);
+            const Surface_patch_index sp_index = domain_.make_surface_index(label_at_p1, label_at_p2);
+            const Index index = domain_.index_from_surface_patch_index(sp_index);
             return Intersection(Point_3(ORIGIN + ((value_at_p2 * (p1 - ORIGIN)) - (value_at_p1 * (p2 - ORIGIN))) /
                                                   (value_at_p2 - value_at_p1)), index, 2);
           }
         }
         mid = midpoint(p1, p2);
         // If the two points are enough close, then we return midpoint
-        if ( squared_distance(p1, p2) < r_domain_.squared_error_bound_ )
+        if ( squared_distance(p1, p2) < domain_.squared_error_bound_ )
         {
           CGAL_assertion(value_at_p1 * value_at_p2 <= 0);
-          const Surface_patch_index sp_index = r_domain_.make_surface_index(label_at_p1, label_at_p2);
-          const Index index = r_domain_.index_from_surface_patch_index(sp_index);
+          const Surface_patch_index sp_index = domain_.make_surface_index(label_at_p1, label_at_p2);
+          const Index index = domain_.index_from_surface_patch_index(sp_index);
           return Intersection(mid, index, 2);
         }
 
@@ -363,7 +360,7 @@ class Poisson_mesh_domain_3
         FT value_at_mid;
         typename Function::Cell_handle c_at_mid;
         bool c_is_inf;
-        std::tie(value_at_mid, c_at_mid, c_is_inf) = r_domain_.poisson_function.special_func(mid);
+        std::tie(value_at_mid, c_at_mid, c_is_inf) = domain_.poisson_function.special_func(mid);
         Subdomain_index label_at_mid = (value_at_mid < 0) ? 1 : 0;
 
         // Else we must go on
@@ -371,7 +368,7 @@ class Poisson_mesh_domain_3
         // change p2 if f(p1)!=f(p2).
         // That allows us to find the first intersection from a of [a,b] with
         // a surface.
-        if(label_at_p1 != label_at_mid && !(r_domain_.null(label_at_p1) && r_domain_.null(label_at_mid)))
+        if(label_at_p1 != label_at_mid && !(domain_.null(label_at_p1) && domain_.null(label_at_mid)))
         {
           p2 = mid;
           value_at_p2 = value_at_mid;
@@ -390,16 +387,15 @@ class Poisson_mesh_domain_3
     template<typename Query>
     Intersection clip_to_segment(const Query& query) const
     {
-      const auto clipped = CGAL::intersection(query, r_domain_.bbox_);
-      if(clipped)
-        if(const Segment_3* s = std::get_if<Segment_3>(&*clipped))
+      const auto clipped = CGAL::intersection(query, domain_.bbox_);
+      if (clipped)
+        if (const Segment_3* s = std::get_if<Segment_3>(&*clipped))
           return this->operator()(*s);
 
       return Intersection();
     }
 
-  private:
-    const Poisson_mesh_domain_3& r_domain_;
+    const Poisson_mesh_domain_3& domain_;
   };
 
   // Returns Construct_intersection object

From a8cd0902a8fa26b536971436ab385e971a2df0c1 Mon Sep 17 00:00:00 2001
From: Sven Oesau <sven.oesau@geometryfactory.com>
Date: Thu, 17 Apr 2025 15:46:21 +0200
Subject: [PATCH 20/21] integrating reviews

---
 Mesh_3/include/CGAL/Labeled_mesh_domain_3.h            |  6 +-----
 .../Poisson_surface_reconstruction_3.txt               |  4 ++--
 .../include/CGAL/Poisson_mesh_domain_3.h               | 10 ++++------
 3 files changed, 7 insertions(+), 13 deletions(-)

diff --git a/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h b/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h
index 5ad1060e6c5..a9284359d4a 100644
--- a/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h
+++ b/Mesh_3/include/CGAL/Labeled_mesh_domain_3.h
@@ -1131,11 +1131,7 @@ class Labeled_mesh_domain_3
   /*
    * Returns a point in the intersection of the primitive `type`
    * with some boundary surface.
-   * `Type1` is either `Segment_3`, `Ray_3` or `Line_3`.
-   * The integer `dimension` is set to the dimension of the lowest
-   * dimensional face in the input complex containing the returned point, and
-   * `index` is set to the index to be stored at a mesh vertex lying
-   * on this face.
+   * `Type` is either `Segment_3`, `Ray_3` or `Line_3`.
    */
   struct Construct_intersection
   {
diff --git a/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt b/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
index 184e087e3a7..d37c3273547 100644
--- a/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
+++ b/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
@@ -119,9 +119,9 @@ The following example reads a point set, creates a Poisson implicit function and
 The computed implicit functions can be iso-contoured to reconstruct a
 surface by using the \ref PkgMesh3 :
 
-`make_mesh_3()` with the `surface_only()` parameter for using parallel Mesh_3
+`make_mesh_3()` with the `surface_only()` parameter to only mesh the surface
 
-The parameter `Tag` affects the behavior of `make_mesh_3()`:
+The following `Tag` parameters affect the behavior of `make_mesh_3()`:
 - `Manifold_tag`: the output mesh is guaranteed to be a manifold surface without boundary.
 - `Manifold_with_boundary_tag`: the output mesh is guaranteed to be manifold and may have boundaries.
 - `Non_manifold_tag`: the output mesh has no guarantee and hence is outputted as a polygon soup.
diff --git a/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h b/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h
index a88fa7d5412..d852e182b8e 100644
--- a/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h
+++ b/Poisson_surface_reconstruction_3/include/CGAL/Poisson_mesh_domain_3.h
@@ -30,7 +30,7 @@ namespace CGAL {
 
 \tparam BGT is a geometric traits class that provides
     the basic operations to implement intersection tests and intersection computations through a bisection
-    method.This parameter must be instantiated with a model of the concept `BisectionGeometricTraits_3`.
+    method. This parameter must be instantiated with a model of the concept `BisectionGeometricTraits_3`.
 
 \cgalModels{MeshDomain_3}
 
@@ -39,7 +39,9 @@ namespace CGAL {
 */
 template<class BGT>
 class Poisson_mesh_domain_3
+#ifndef DOXYGEN_RUNNING
     : public Labeled_mesh_domain_3<BGT>
+#endif
 {
 public:
   using Base = Labeled_mesh_domain_3<BGT>;
@@ -264,11 +266,7 @@ class Poisson_mesh_domain_3
   /*
    * Returns a point in the intersection of the primitive `type`
    * with some boundary surface.
-   * `Type1` is either `Segment_3`, `Ray_3` or `Line_3`.
-   * The integer `dimension` is set to the dimension of the lowest
-   * dimensional face in the input complex containing the returned point, and
-   * `index` is set to the index to be stored at a mesh vertex lying
-   * on this face.
+   * `Type` is either `Segment_3`, `Ray_3` or `Line_3`.
    */
   struct Construct_intersection
   {

From 5feb75062c2a58b114862773deaeea97f38d0863 Mon Sep 17 00:00:00 2001
From: Mael <mael.rouxel.labbe@geometryfactory.com>
Date: Fri, 18 Apr 2025 12:49:56 +0200
Subject: [PATCH 21/21] Rephrase

---
 .../Poisson_surface_reconstruction_3.txt                    | 6 ++----
 1 file changed, 2 insertions(+), 4 deletions(-)

diff --git a/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt b/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
index d37c3273547..bbdee6e662e 100644
--- a/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
+++ b/Poisson_surface_reconstruction_3/doc/Poisson_surface_reconstruction_3/Poisson_surface_reconstruction_3.txt
@@ -115,11 +115,9 @@ The following example reads a point set, creates a Poisson implicit function and
 
 \subsection Poisson_surface_reconstruction_3Contouring Contouring
 
-
 The computed implicit functions can be iso-contoured to reconstruct a
-surface by using the \ref PkgMesh3 :
-
-`make_mesh_3()` with the `surface_only()` parameter to only mesh the surface
+surface by using the \ref PkgMesh3 component, and in particular the function
+`make_mesh_3()` with the `surface_only()` parameter to only mesh the surface.
 
 The following `Tag` parameters affect the behavior of `make_mesh_3()`:
 - `Manifold_tag`: the output mesh is guaranteed to be a manifold surface without boundary.