Document GH variations

Surface_mesh_simplification/doc/Surface_mesh_simplification/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_plane_policies.h

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+namespace CGAL {
+namespace Surface_mesh_simplification {
+
+/*!
+\ingroup PkgSurfaceMeshSimplificationRef
+
+The class `GarlandHeckbert_plane_policies` regroups the cost and placement policies
+based on the Garland-Heckbert "Classic Plane" strategy
+(Section \ref SurfaceMeshSimplificationGarlandHeckbertStrategy).
+This class implements the original Garland-Heckbert quadric error metric strategy,
+as described in their seminal paper \cgalCite{gh-ssqem-97}.
+
+Both the cost and the placement policies must be used together as they internally use
+and share information associating quadrics to vertices.
+Note however, that they may still be wrapped with behavior modifying classes
+such as `Constrained_placement` or `Bounded_normal_change_placement`.
+
+\tparam TriangleMesh is the type of surface mesh being simplified, and must be a model
+                     of the `MutableFaceGraph` and `HalfedgeListGraph` concepts.
+\tparam GeomTraits must be a model of `Kernel`. If you have passed a traits class in the optional
+                   named parameters in the call to `edge_collapse()`, the types must be identical.
+
+These policies depend on the third party \ref thirdpartyEigen library.
+
+\sa `GarlandHeckbert_probabilistic_plane_policies`
+\sa `GarlandHeckbert_triangle_policies`
+\sa `GarlandHeckbert_probabilistic_triangle_policies`
+*/
+template <typename TriangleMesh, typename GeomTraits>
+class GarlandHeckbert_plane_policies
+{
+public:
+  /// The type of the Garland Heckbert cost functor, a model of the concept `GetCost`
+  typedef unspecified_type Get_cost;
+
+  /// The type of the Garland Heckbert placement functor, a model of the concept `GetPlacement`
+  typedef unspecified_type Get_placement;
+
+  /// \name Creation
+  /// @{
+
+  /*!
+  Initializes the Garland-Heckbert Plane policies.
+  */
+  GarlandHeckbert_plane_policies(TriangleMesh& tmesh);
+
+  /// @}
+
+  /// \name Accessors
+  /// @{
+
+  const Get_cost& get_cost() const;
+  const Get_placement& get_placement() const;
+
+  /// @}
+
+};
+
+} // namespace Surface_mesh_simplification
+} // namespace CGAL

Surface_mesh_simplification/doc/Surface_mesh_simplification/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_probabilistic_plane_policies.h

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+namespace CGAL {
+namespace Surface_mesh_simplification {
+
+/*!
+\ingroup PkgSurfaceMeshSimplificationRef
+
+The class `GarlandHeckbert_probabilistic_plane_policies` regroups the cost and placement policies
+based on the "Probabilistic Plane" strategy of Trettner and Kobbelt \cgalCite{tk-frqmpq-20}.
+This policy enhances the original Garland-Heckbert quadric error metrics,
+by adding notions of variance (i.e., noise) to the positions of the vertices and the normals of faces.
+Compared to the "classic" plane strategy, this strategy sacrifices tightness to the input
+for speed and quality of the result (Section \ref SurfaceMeshSimplificationGarlandHeckbertStrategy).
+
+Both the cost and the placement policies must be used together as they internally use
+and share information associating quadrics to vertices.
+Note however, that they may still be wrapped with behavior modifying classes
+such as `Constrained_placement` or `Bounded_normal_change_placement`.
+
+\tparam TriangleMesh is the type of surface mesh being simplified, and must be a model
+                     of the `MutableFaceGraph` and `HalfedgeListGraph` concepts.
+\tparam GeomTraits must be a model of `Kernel`. If you have passed a traits class in the optional
+                   named parameters in the call to `edge_collapse()`, the types must be identical.
+
+These policies depend on the third party \ref thirdpartyEigen library.
+
+\sa `GarlandHeckbert_plane_policies`
+\sa `GarlandHeckbert_triangle_policies`
+\sa `GarlandHeckbert_probabilistic_triangle_policies`
+*/
+template <typename TriangleMesh, typename GeomTraits>
+class GarlandHeckbert_probabilistic_plane_policies
+{
+public:
+  /// The type of the Garland Heckbert cost functor, a model of the concept `GetCost`
+  typedef unspecified_type Get_cost;
+
+  /// The type of the Garland Heckbert placement functor, a model of the concept `GetPlacement`
+  typedef unspecified_type Get_placement;
+
+  /// \name Creation
+  /// @{
+
+  /*!
+  Initializes the Garland-Heckbert Probabilistic Plane policies.
+  */
+  GarlandHeckbert_probabilistic_plane_policies(TriangleMesh& tmesh);
+
+  /// @}
+
+  /// \name Accessors
+  /// @{
+
+  const Get_cost& get_cost() const;
+  const Get_placement& get_placement() const;
+
+  /// @}
+};
+
+} // namespace Surface_mesh_simplification
+} // namespace CGAL

Surface_mesh_simplification/doc/Surface_mesh_simplification/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_probabilistic_triangle_policies.h

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+namespace CGAL {
+namespace Surface_mesh_simplification {
+
+/*!
+\ingroup PkgSurfaceMeshSimplificationRef
+
+The class `GarlandHeckbert_probabilistic_triangle_policies` regroups the cost and placement policies
+based on the "Probabilistic Triangle" strategy of Trettner and Kobbelt \cgalCite{tk-frqmpq-20}.
+This policy enhances the original Garland-Heckbert quadric error metrics,
+by adding notions of variance (i.e., noise) to the positions of the vertices and the normals of faces.
+Compared to the "classic" triangle strategy, this strategy sacrifices tightness to the input
+for speed and quality of the result (Section \ref SurfaceMeshSimplificationGarlandHeckbertStrategy).
+
+Both the cost and the placement policies must be used together as they internally use
+and share information associating quadrics to vertices.
+Note however, that they may still be wrapped with behavior modifying classes
+such as `Constrained_placement` or `Bounded_normal_change_placement`.
+
+\tparam TriangleMesh is the type of surface mesh being simplified, and must be a model
+                     of the `MutableFaceGraph` and `HalfedgeListGraph` concepts.
+\tparam GeomTraits must be a model of `Kernel`. If you have passed a traits class in the optional
+                   named parameters in the call to `edge_collapse()`, the types must be identical.
+
+These policies depend on the third party \ref thirdpartyEigen library.
+
+\sa `GarlandHeckbert_plane_policies`
+\sa `GarlandHeckbert_probabilistic_plane_policies`
+\sa `GarlandHeckbert_triangle_policies`
+*/
+template <typename TriangleMesh, typename GeomTraits>
+class GarlandHeckbert_probabilistic_triangle_policies
+{
+public:
+  /// The type of the Garland Heckbert cost functor, a model of the concept `GetCost`
+  typedef unspecified_type Get_cost;
+
+  /// The type of the Garland Heckbert placement functor, a model of the concept `GetPlacement`
+  typedef unspecified_type Get_placement;
+
+  /// \name Creation
+  /// @{
+
+  /*!
+  Initializes the Garland-Heckbert "Probabilistic Triangle" policies.
+  */
+  GarlandHeckbert_probabilistic_triangle_policies(TriangleMesh& tmesh);
+
+  /// @}
+
+  /// \name Accessors
+  /// @{
+
+  const Get_cost& get_cost() const;
+  const Get_placement& get_placement() const;
+
+  /// @}
+};
+
+} // namespace Surface_mesh_simplification
+} // namespace CGAL

Surface_mesh_simplification/doc/Surface_mesh_simplification/CGAL/Surface_mesh_simplification/Policies/Edge_collapse/GarlandHeckbert_triangle_policies.h

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+namespace CGAL {
+namespace Surface_mesh_simplification {
+
+/*!
+\ingroup PkgSurfaceMeshSimplificationRef
+
+The class `GarlandHeckbert_triangle_policies` regroups the cost and placement policies
+using the triangle-based Garland-Heckbert strategy (Section \ref SurfaceMeshSimplificationGarlandHeckbertStrategy).
+This strategy considers distances to triangular faces, rather than the supporting planes of the faces
+as in `GarlandHeckbert_plane_policies`.
+
+Both the cost and the placement policies must be used together as they internally use
+and share information associating quadrics to vertices.
+Note however, that they may still be wrapped with behavior modifying classes
+such as `Constrained_placement` or `Bounded_normal_change_placement`.
+
+\tparam TriangleMesh is the type of surface mesh being simplified, and must be a model
+                     of the `MutableFaceGraph` and `HalfedgeListGraph` concepts.
+\tparam GeomTraits must be a model of `Kernel`. If you have passed a traits class in the optional
+                   named parameters in the call to `edge_collapse()`, the types must be identical.
+
+These policies depend on the third party \ref thirdpartyEigen library.
+
+\sa `GarlandHeckbert_probabilistic_plane_policies`
+\sa `GarlandHeckbert_probabilistic_triangle_policies`
+*/
+template <typename TriangleMesh, typename GeomTraits>
+class GarlandHeckbert_triangle_policies
+{
+public:
+  /// The type of the Garland Heckbert cost functor, a model of the concept `GetCost`
+  typedef unspecified_type Get_cost;
+
+  /// The type of the Garland Heckbert placement functor, a model of the concept `GetPlacement`
+  typedef unspecified_type Get_placement;
+
+  /// \name Creation
+  /// @{
+
+  /*!
+  Initializes the Garland-Heckbert Triangle policies.
+  */
+  GarlandHeckbert_triangle_policies(TriangleMesh& tmesh);
+
+  /// @}
+
+  /// \name Accessors
+  /// @{
+
+  const Get_cost& get_cost() const;
+  const Get_placement& get_placement() const;
+
+  /// @}
+};
+
+} // namespace Surface_mesh_simplification
+} // namespace CGAL