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Co-authored-by: Mael <mael.rouxel.labbe@geometryfactory.com>

Kernel_23/doc/Kernel_23/CGAL/Kernel/global_functions.h

@@ -622,7 +622,7 @@ const CGAL::Point_3<Kernel>&r);
 /// \ingroup kernel_global_function
 /*!
 compares the angles \f$ \theta_1\f$ and \f$ \theta_2\f$, where
-\f$ \theta_1\f$ is the angle, in \f$ [0, \pi]\f$, of the triangle
+\f$ \theta_1\f$ is the angle in \f$ [0, \pi]\f$ of the triangle
 \f$ (a, b, c)\f$ at the vertex `b`, and \f$ \theta_2\f$ is
 the angle in \f$ [0, \pi]\f$ such that \f$ cos(\theta_2) = cosine\f$.
 \pre `a!=b && c!=b`.

Kernel_23/doc/Kernel_23/Concepts/FunctionObjectConcepts.h

@@ -759,7 +759,7 @@ public:
 
   /*!
   compares the angles \f$ \theta_1\f$ and \f$ \theta_2\f$, where
-  \f$ \theta_1\f$ is the angle, in \f$ [0, \pi]\f$, of the triangle
+  \f$ \theta_1\f$ is the angle in \f$ [0, \pi]\f$ of the triangle
   \f$ (a, b, c)\f$ at the vertex `b`, and \f$ \theta_2\f$ is
   the angle in \f$ [0, \pi]\f$ such that \f$ cos(\theta_2) = cosine\f$.
   \pre `a!=b && c!=b`.

Polygon_mesh_processing/doc/Polygon_mesh_processing/Polygon_mesh_processing.txt

@@ -153,18 +153,22 @@ algorithm while preserving the detected sharp edges
 is given in \ref Polygon_mesh_processing/delaunay_remeshing_example.cpp
 
 \paragraph Decimate Remeshing of (Almost) Planar Patches
-If a triangulated surface mesh uses a lot of triangles to describe some planar regions of a model, it is possible to simplify
-those parts using the function `CGAL::Polygon_mesh_processing::remesh_planar_patches()`.
-For simply connected patches, it is even possible to not retriangulate them.
-The coplanarity and collinearty tests being exact, almost coplanar patches will not be detected by default. It is possible to specify a
-threshold on the angle between adjacent faces (resp. segments) so that they are considered coplanar (resp. collinear). However, this
-coplanarity and collinearity tolerance is only local and there is no global control (think of the classical example of a circle arc
-densely sampled: 3 consecutive points are seen as almost collinear while all the points on the arc are not). To circumvent this situation,
-we also provide the function `CGAL::Polygon_mesh_processing::remesh_almost_planar_patches()` that expects the segmentation into
-planar patches and corners to be provided. The function `CGAL::Polygon_mesh_processing::region_growing_of_planes_on_faces()`
-uses the region growing algorithm to detect planar regions in a mesh with global and local criteria. Similarly, the function
-`CGAL::Polygon_mesh_processing::detect_corners_of_regions()` can be used to detect corner vertices on the border of the planar
-regions detected by running the region growing algorithm on border segments of the patch.
+When many triangles are used to describe a planar region of a model, one might wish to simplify the mesh
+in this region to use few elements, or even a single large polygonal face when the region makes up a simply connected patch.
+This can be achieved using the function `CGAL::Polygon_mesh_processing::remesh_planar_patches()`.
+This function performs the detection of the planar regions, using geometric predicates for coplanarity and
+collinearity checks. If these tests are performed exactly, the planar regions can be unexpectedly small due to the
+input in fact not being perfectly planar. To palliate this, it is possible to specify a threshold on the angle
+between adjacent faces (resp. segments) such that they are considered coplanar (resp. collinear).
+However, this tolerance threshold is only local and there is no global control, which can have undesired effects, such as in the classic example of a densely sampled circle arc where all points are eventually found
+to be almost collinear). To circumvent this situation, we provide the function
+ `CGAL::Polygon_mesh_processing::remesh_almost_planar_patches()` , which expects the segmentation into
+planar patches and corners to be provided by the user. Such segmentation can be obtained using the function
+ `CGAL::Polygon_mesh_processing::region_growing_of_planes_on_faces()`, which
+uses the region growing algorithm to detect planar regions in a mesh with global and local criteria.
+Similarly, the function `CGAL::Polygon_mesh_processing::detect_corners_of_regions()` can be used
+to detect corner vertices on the border of the planar regions detected by running the region growing
+algorithm on border segments of the patch.
 
 
 \cgalFigureBegin{decimate_cheese, decimate_cheese.png, decimate_colors.png}

Polygon_mesh_processing/examples/Polygon_mesh_processing/remesh_planar_patches.cpp

@@ -22,6 +22,7 @@ int main()
 
   // triangulate faces;
   PMP::triangulate_faces(sm);
+  std::cout << "Input mesh has " << faces(sm).size() << " faces" << std::endl;
   assert(faces(sm).size()==12);
 
   Surface_mesh::Property_map<Surface_mesh::Edge_index, bool> ecm =
@@ -32,16 +33,17 @@ int main()
 
   // create a remeshed version of the cube with many elements
   PMP::isotropic_remeshing(faces(sm), 0.1, sm, CGAL::parameters::edge_is_constrained_map(ecm));
-  std::ofstream("cube_remeshed.off") << sm;
+  CGAL::IO::write_polygon_mesh("cube_remeshed.off", sm, CGAL::parameters::stream_precision(17));
   assert(faces(sm).size()>100);
 
   // decimate the mesh
   Surface_mesh out;
   PMP::remesh_planar_patches(sm, out);
-  std::ofstream("cube_decimated.off") << out;
+  CGAL::IO::write_polygon_mesh("cube_decimated.off", out, CGAL::parameters::stream_precision(17));
 
   // we should be back to 12 faces
+  std::cout << "Output mesh has " << faces(out).size() << " faces" << std::endl;
   assert(faces(out).size()==12);
 
-  return 0;
+  return EXIT_SUCCESS;
 }

Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/remesh_planar_patches.h

@@ -27,12 +27,13 @@
 
 #include <CGAL/Named_function_parameters.h>
 #include <CGAL/boost/graph/properties.h>
-#include <unordered_map>
+
 #include <boost/dynamic_bitset.hpp>
 #include <boost/iterator/function_output_iterator.hpp>
 #include <boost/container/small_vector.hpp>
 
 #include <algorithm>
+#include <unordered_map>
 
 namespace CGAL{
 
@@ -1290,8 +1291,8 @@ bool decimate_meshes_with_common_interfaces_impl(TriangleMeshRange& meshes,
  *  \ingroup PMP_meshing_grp
  *  generates a new triangle mesh `tm_out` with the minimal number of triangles while preserving the shape as `tm_in`.
  *  In practice, this means that connected components of edge incident faces belonging to the same plane are
- *  first extracted (each such connected component is called a *patch*). Then the connected components of vertex
- *  connected patch border edges belonging to the same line are extracted. Endpoints of such components and
+ *  first extracted (each such connected component is called a *patch*). Then, the connected components of
+ *  vertex-connected patch border edges belonging to the same line are extracted. Endpoints of such components and
  *  vertices incident to more than two patches (or two patches + one mesh boundary) are called *corners*.
  *  `tm_out` contains the 2D constrained Delaunay triangulation of each patch using only corner vertices
  *  on the boundary of the patch.