Add a first example in Surface_mesh_topology package.

Surface_mesh_topology/examples/Surface_mesh_topology/basic_example_surface_mesh_topology.cpp

@@ -0,0 +1,59 @@
+#include <CGAL/Linear_cell_complex_for_combinatorial_map.h>
+#include <CGAL/Linear_cell_complex_constructors.h>
+#include <CGAL/Surface_mesh_curve_topology.h>
+
+#include <CGAL/Path_generators.h>
+#include <CGAL/Path_on_surface.h>
+
+/* If you want to use a viewer, you can use qglviewer. Enable only if CGAL
+   was compile with Qt5. */
+#include <CGAL/draw_lcc_with_paths.h>
+
+typedef CGAL::Linear_cell_complex_for_combinatorial_map<2,3> LCC_3_cmap;
+
+///////////////////////////////////////////////////////////////////////////////
+int main()
+{
+  LCC_3_cmap lcc;
+  if (!CGAL::load_off(lcc, "data/double-torus-example.off"))
+  {
+    std::cout<<"ERROR reading file data/double-torus-example.off"<<std::endl;
+    exit(EXIT_FAILURE);
+  }
+
+  CGAL::Surface_mesh_curve_topology<LCC_3_cmap> smct(lcc);
+
+  CGAL::Path_on_surface<LCC_3_cmap> p1(lcc); // A first path
+  p1.push_back_by_index(14); // Its starting dart
+  for (int i=0; i<7; ++i)
+  { p1.extend_positive_turn(2); } // Extend the path
+  
+  CGAL::Path_on_surface<LCC_3_cmap> p2(lcc); // A second path
+  std::vector<std::size_t> indices={56,59,303,305,314,335,206,202}; // All the indices of the darts
+  for (int i=0; i<indices.size(); ++i)
+  { p2.push_back_by_index(indices[i]); }
+
+  CGAL::Path_on_surface<LCC_3_cmap> p3(lcc); // A third path
+  p3.push_back_by_index(470); // Its starting dart
+  for (int i=0; i<15; ++i)
+  { p3.extend_positive_turn(2); } // Extend the path
+  
+  bool res1=smct.is_contractible(p1);
+  std::cout<<"First path p1 "<<(res1?"IS":"IS NOT")<<" contractible."<<std::endl;
+  
+  bool res2=smct.are_freely_homotopic(p1, p2);
+  std::cout<<"The two paths p1 and p2 "<<(res2?"ARE":"ARE NOT")<<" homotopic."<<std::endl;
+
+  bool res3=smct.are_freely_homotopic(p1, p3);
+  std::cout<<"The two paths p1 and p3 "<<(res3?"ARE":"ARE NOT")<<" homotopic."<<std::endl;
+
+#ifdef CGAL_USE_BASIC_VIEWER
+  std::vector<CGAL::Path_on_surface<LCC_3_cmap> > paths;
+  paths.push_back(p1);
+  paths.push_back(p2);  
+  paths.push_back(p3);  
+  CGAL::draw(lcc, paths); // Enable only if CGAL was compiled with Qt5
+#endif // CGAL_USE_BASIC_VIEWER
+  
+  return EXIT_SUCCESS;
+}