Add functions to compute discrete curvatures

Installation/CHANGES.md

@@ -3,6 +3,10 @@
 
 ## [Release 6.1](https://github.com/CGAL/cgal/releases/tag/v6.1)
 
+### [Polygon Mesh Processing](https://doc.cgal.org/6.1/Manual/packages.html#PkgPolygonMeshProcessing)
+- Added the function `CGAL::Polygon_mesh_processing::discrete_mean_curvature` and `CGAL::Polygon_mesh_processing::discrete_Guassian_curvature` to evaluate the discrete curvature at a vertex of a mesh.
+- Added the function `CGAL::Polygon_mesh_processing::angle_sum` to compute the sum of the angles around a vertex.
+
 ### [Algebraic Kernel](https://doc.cgal.org/6.1/Manual/packages.html#PkgAlgebraicKernelD)
 
 -   **Breaking change**: Classes based on the RS Library are no longer provided.

Kernel_23/include/CGAL/Kernel/function_objects.h

@@ -965,22 +965,14 @@ namespace CommonKernelFunctors {
      typename K::Compute_scalar_product_3 scalar_product =
        k.compute_scalar_product_3_object();
 
-     double product = CGAL::sqrt(to_double(scalar_product(u,u)) * to_double(scalar_product(v,v)));
+     double product = to_double(approximate_sqrt(scalar_product(u,u) * scalar_product(v,v)));
 
      if(product == 0)
        return 0;
 
      // cosine
      double dot = to_double(scalar_product(u,v));
-     double cosine = dot / product;
-
-     if(cosine > 1.){
-       cosine = 1.;
-     }
-     if(cosine < -1.){
-       cosine = -1.;
-     }
-
+     double cosine = std::clamp(dot / product, -1., 1.);
      return std::acos(cosine) * 180./CGAL_PI;
    }
 

Lab/demo/Lab/Color_map.h

@@ -23,9 +23,9 @@ compute_color_map(QColor base_color,
                   std::size_t nb_of_colors,
                   Output_color_iterator out)
 {
-  qreal hue = base_color.hueF();
-  const qreal step = (static_cast<qreal>(1)) / nb_of_colors;
+  const qreal step = (static_cast<qreal>(0.85)) / nb_of_colors;
 
+  qreal hue = base_color.hueF();
   qreal h = (hue == -1) ? 0 : hue;
   for(std::size_t i=0; i<nb_of_colors; ++i)
   {

Lab/demo/Lab/Plugins/Display/Display_property_plugin.cpp

@@ -22,6 +22,7 @@
 #include <CGAL/Polygon_mesh_processing/compute_normal.h>
 #include <CGAL/Polygon_mesh_processing/measure.h>
 #include <CGAL/Polygon_mesh_processing/triangulate_faces.h>
+#include <CGAL/Polygon_mesh_processing/curvature.h>
 #include <CGAL/Polygon_mesh_processing/interpolated_corrected_curvatures.h>
 
 #include <QAbstractItemView>
@@ -350,11 +351,11 @@ private Q_SLOTS:
   template<typename ValueType>
   void displayMapLegend(const std::vector<ValueType>& values)
   {
-    const std::size_t size = (std::min)(color_map.size(), std::size_t(1024));
+    const std::size_t size = (std::min)(color_map.size(), std::size_t(4096));
 
     const int text_height = 20;
     const int height = text_height * static_cast<int>(size) + text_height;
-    const int width = 140;
+    const int width = 200;
     const int cell_width = width / 3;
     const int top_margin = 15;
     const int left_margin = 5;
@@ -381,13 +382,13 @@ private Q_SLOTS:
                        tick_height,
                        color);
 
-      QRect text_rect(left_margin + cell_width + 10, drawing_height - top_margin - j, 50, text_height);
-      painter.drawText(text_rect, Qt::AlignCenter, QObject::tr("%1").arg(values[i], 0, 'f', 3, QLatin1Char(' ')));
+      QRect text_rect(left_margin + cell_width + 10, drawing_height - top_margin - j, 100, text_height);
+      painter.drawText(text_rect, Qt::AlignCenter, QObject::tr("%1").arg(values[i], 0, 'f', 6, QLatin1Char(' ')));
     }
 
     if(color_map.size() > size)
     {
-      QRect text_rect(left_margin + cell_width + 10, 0, 50, text_height);
+      QRect text_rect(left_margin + cell_width + 10, 0, 100, text_height);
       painter.drawText(text_rect, Qt::AlignCenter, QObject::tr("[...]"));
     }
 
@@ -463,13 +464,17 @@ private Q_SLOTS:
                                           "Largest Angle Per Face",
                                           "Scaled Jacobian",
                                           "Face Area",
+                                          "Discrete Mean Curvature",
+                                          "Discrete Gaussian Curvature",
                                           "Interpolated Corrected Mean Curvature",
                                           "Interpolated Corrected Gaussian Curvature"});
       property_simplex_types = { Property_simplex_type::FACE,
                                  Property_simplex_type::FACE,
                                  Property_simplex_type::FACE,
                                  Property_simplex_type::FACE,
                                  Property_simplex_type::VERTEX,
+                                 Property_simplex_type::VERTEX,
+                                 Property_simplex_type::VERTEX,
                                  Property_simplex_type::VERTEX };
       detectSMScalarProperties(*(sm_item->face_graph()));
     }
@@ -516,12 +521,12 @@ private Q_SLOTS:
 
       // Curvature property-specific slider
       const std::string& property_name = dock_widget->propertyBox->currentText().toStdString();
-      const bool is_curvature_property = (property_name == "Interpolated Corrected Mean Curvature" ||
-                                          property_name == "Interpolated Corrected Gaussian Curvature");
-      dock_widget->expandingRadiusLabel->setVisible(is_curvature_property);
-      dock_widget->expandingRadiusSlider->setVisible(is_curvature_property);
-      dock_widget->expandingRadiusLabel->setEnabled(is_curvature_property);
-      dock_widget->expandingRadiusSlider->setEnabled(is_curvature_property);
+      const bool is_interpolated_curvature_property = (property_name == "Interpolated Corrected Mean Curvature" ||
+                                                       property_name == "Interpolated Corrected Gaussian Curvature");
+      dock_widget->expandingRadiusLabel->setVisible(is_interpolated_curvature_property);
+      dock_widget->expandingRadiusSlider->setVisible(is_interpolated_curvature_property);
+      dock_widget->expandingRadiusLabel->setEnabled(is_interpolated_curvature_property);
+      dock_widget->expandingRadiusSlider->setEnabled(is_interpolated_curvature_property);
     }
     else // no or broken property
     {
@@ -570,6 +575,16 @@ private Q_SLOTS:
     {
       displayArea(sm_item);
     }
+    else if(property_name == "Discrete Mean Curvature")
+    {
+      displayDiscreteCurvatureMeasure(sm_item, MEAN_CURVATURE);
+      sm_item->setRenderingMode(Gouraud);
+    }
+    else if(property_name == "Discrete Gaussian Curvature")
+    {
+      displayDiscreteCurvatureMeasure(sm_item, GAUSSIAN_CURVATURE);
+      sm_item->setRenderingMode(Gouraud);
+    }
     else if(property_name == "Interpolated Corrected Mean Curvature")
     {
       displayInterpolatedCurvatureMeasure(sm_item, MEAN_CURVATURE);
@@ -682,6 +697,8 @@ private Q_SLOTS:
     removeDisplayPluginProperty(item, "f:display_plugin_largest_angle");
     removeDisplayPluginProperty(item, "f:display_plugin_scaled_jacobian");
     removeDisplayPluginProperty(item, "f:display_plugin_area");
+    removeDisplayPluginProperty(item, "v:display_plugin_discrete_mean_curvature");
+    removeDisplayPluginProperty(item, "v:display_plugin_discrete_Gaussian_curvature");
     removeDisplayPluginProperty(item, "v:display_plugin_interpolated_corrected_mean_curvature");
     removeDisplayPluginProperty(item, "v:display_plugin_interpolated_corrected_Gaussian_curvature");
   }
@@ -864,6 +881,35 @@ private Q_SLOTS:
     displaySMProperty<face_descriptor>("f:display_plugin_area", *sm);
   }
 
+private:
+  void displayDiscreteCurvatureMeasure(Scene_surface_mesh_item* sm_item,
+                                       CurvatureType mu_index)
+  {
+    SMesh* sm = sm_item->face_graph();
+    if(sm == nullptr)
+      return;
+
+    if(mu_index != MEAN_CURVATURE && mu_index != GAUSSIAN_CURVATURE)
+      return;
+
+    std::string vdc_name = (mu_index == MEAN_CURVATURE) ? "v:display_plugin_discrete_mean_curvature"
+                                                        : "v:display_plugin_discrete_Gaussian_curvature";
+
+    bool not_initialized;
+    SMesh::Property_map<vertex_descriptor, double> vdc;
+    std::tie(vdc, not_initialized) = sm->add_property_map<vertex_descriptor, double>(vdc_name, 0);
+
+    if(not_initialized)
+    {
+      if(mu_index == MEAN_CURVATURE)
+        PMP::discrete_mean_curvatures(*sm, vdc);
+      else
+        PMP::discrete_Gaussian_curvatures(*sm, vdc);
+    }
+
+    displaySMProperty<vertex_descriptor>(vdc_name, *sm);
+  }
+
 private Q_SLOTS:
   void setExpandingRadius()
   {
@@ -1131,6 +1177,10 @@ private Q_SLOTS:
         zoomToSimplexWithPropertyExtremum(faces(mesh), mesh, "f:display_plugin_scaled_jacobian", extremum);
       else if(property_name == "Face Area")
         zoomToSimplexWithPropertyExtremum(faces(mesh), mesh, "f:display_plugin_area", extremum);
+      else if(property_name == "Discrete Mean Curvature")
+        zoomToSimplexWithPropertyExtremum(vertices(mesh), mesh, "v:display_plugin_discrete_mean_curvature", extremum);
+      else if(property_name == "Discrete Gaussian Curvature")
+        zoomToSimplexWithPropertyExtremum(vertices(mesh), mesh, "v:display_plugin_discrete_Gaussian_curvature", extremum);
       else if(property_name == "Interpolated Corrected Mean Curvature")
         zoomToSimplexWithPropertyExtremum(vertices(mesh), mesh, "v:display_plugin_interpolated_corrected_mean_curvature", extremum);
       else if(property_name == "Interpolated Corrected Gaussian Curvature")
@@ -1470,6 +1520,8 @@ isSMPropertyScalar(const std::string& name,
      name == "f:display_plugin_largest_angle" ||
      name == "f:display_plugin_scaled_jacobian" ||
      name == "f:display_plugin_area" ||
+     name == "v:display_plugin_discrete_mean_curvature" ||
+     name == "v:display_plugin_discrete_Gaussian_curvature" ||
      name == "v:display_plugin_interpolated_corrected_mean_curvature" ||
      name == "v:display_plugin_interpolated_corrected_Gaussian_curvature")
     return false;

Polygon_mesh_processing/doc/Polygon_mesh_processing/PackageDescription.txt

@@ -25,7 +25,7 @@
 /// \ingroup PkgPolygonMeshProcessingRef
 
 /// \defgroup PMP_measure_grp Geometric Measure Functions
-/// Functions to compute lengths of edges and borders, areas of faces and patches, as well as volumes of closed meshes.
+/// Functions to compute discrete curvatures, lengths of edges and borders, areas of faces and patches, volumes of closed meshes.
 /// \ingroup PkgPolygonMeshProcessingRef
 
 /// \defgroup PMP_orientation_grp Orientation Functions
@@ -239,6 +239,11 @@ The page \ref bgl_namedparameters "Named Parameters" describes their usage.
 - `CGAL::Polygon_mesh_processing::sample_triangle_mesh()`
 
 \cgalCRPSection{Geometric Measure Functions}
+- \link PMP_measure_grp `CGAL::Polygon_mesh_processing::angle_sum()` \endlink
+- \link PMP_measure_grp `CGAL::Polygon_mesh_processing::discrete_Gaussian_curvatures()` \endlink
+- \link PMP_measure_grp `CGAL::Polygon_mesh_processing::discrete_Gaussian_curvature()` \endlink
+- \link PMP_measure_grp `CGAL::Polygon_mesh_processing::discrete_mean_curvature()` \endlink
+- \link PMP_measure_grp `CGAL::Polygon_mesh_processing::discrete_mean_curvatures()` \endlink
 - \link PMP_measure_grp `CGAL::Polygon_mesh_processing::edge_length()` \endlink
 - \link PMP_measure_grp `CGAL::Polygon_mesh_processing::squared_edge_length()` \endlink
 - \link PMP_measure_grp `CGAL::Polygon_mesh_processing::face_area()` \endlink
@@ -248,7 +253,6 @@ The page \ref bgl_namedparameters "Named Parameters" describes their usage.
 - \link PMP_measure_grp `CGAL::Polygon_mesh_processing::face_border_length()` \endlink
 - \link PMP_measure_grp `CGAL::Polygon_mesh_processing::longest_border()` \endlink
 - \link PMP_measure_grp `CGAL::Polygon_mesh_processing::centroid()` \endlink
-- \link PMP_measure_grp `CGAL::Polygon_mesh_processing::match_faces()` \endlink
 
 \cgalCRPSection{Feature Detection Functions}
 - `CGAL::Polygon_mesh_processing::sharp_edges_segmentation()`

Polygon_mesh_processing/doc/Polygon_mesh_processing/Polygon_mesh_processing.txt

@@ -1225,6 +1225,17 @@ compute the curvatures on a specific vertex.
 
 \cgalExample{Polygon_mesh_processing/interpolated_corrected_curvatures_vertex.cpp}
 
+\subsection DCurvartures Discrete Curvatures
+
+The package also provides methods to compute the standard, non-interpolated discrete mean and Gaussian
+curvatures on triangle meshes, based on the work of Meyer et al. \cgalCite{cgal:mdsb-ddgot-02}.
+These curvatures are computed at each vertex of the mesh, and are based on the angles of the incident
+triangles. The functions are:
+- `CGAL::Polygon_mesh_processing::discrete_mean_curvature()`
+- `CGAL::Polygon_mesh_processing::discrete_mean_curvatures()`
+- `CGAL::Polygon_mesh_processing::discrete_Gaussian_curvature()`
+- `CGAL::Polygon_mesh_processing::discrete_Gaussian_curvatures()`
+
 ****************************************
 \section PMPSlicer Slicer