Added merdians

Arrangement_on_surface_2/examples/Arrangement_on_surface_2/spherical_insert.cpp

@@ -2,6 +2,8 @@
 // Constructing an arrangement of arcs of great circles.
 
 #include <list>
+#include <cmath>
+#include <cstdio>
 
 #include <CGAL/Exact_predicates_exact_constructions_kernel.h>
 #include <CGAL/Arrangement_on_surface_2.h>
@@ -11,42 +13,62 @@
 
 #include "arr_print.h"
 
-typedef CGAL::Exact_predicates_exact_constructions_kernel         Kernel;
-typedef CGAL::Arr_geodesic_arc_on_sphere_traits_2<Kernel>         Geom_traits;
-typedef Geom_traits::Point_2                                      Point;
-typedef Geom_traits::Curve_2                                      Curve;
-typedef CGAL::Arr_spherical_topology_traits_2<Geom_traits>        Topol_traits;
-typedef CGAL::Arrangement_on_surface_2<Geom_traits, Topol_traits> Arrangement;
+using Kernel = CGAL::Exact_predicates_exact_constructions_kernel;
+using Geom_traits = CGAL::Arr_geodesic_arc_on_sphere_traits_2<Kernel>;
+using Point = Geom_traits::Point_2;
+using X_monotone_curve = Geom_traits::X_monotone_curve_2;
+using Topol_traits = CGAL::Arr_spherical_topology_traits_2<Geom_traits>;
+using Arrangement = CGAL::Arrangement_on_surface_2<Geom_traits, Topol_traits>;
 
-int main() {
+int main(int argc, char* argv[]) {
   // Construct the arrangement from 12 geodesic arcs.
   Geom_traits traits;
   Arrangement arr(&traits);
 
   auto ctr_p = traits.construct_point_2_object();
-  auto ctr_cv = traits.construct_curve_2_object();
+  auto ctr_xcv = traits.construct_x_monotone_curve_2_object();
 
   // Observe that the identification curve is a meridian that contains the
   // point (-11, 7, 0). The curve (-1,0,0),(0,1,0) intersects the identification
   // curve.
 
-  std::list<Curve> arcs;
-
-  arcs.push_back(ctr_cv(ctr_p(1, 0, 0), ctr_p(0, 0, -1)));
-  arcs.push_back(ctr_cv(ctr_p(1, 0, 0), ctr_p(0, 0, 1)));
-  arcs.push_back(ctr_cv(ctr_p(0, 1, 0), ctr_p(0, 0, -1)));
-  arcs.push_back(ctr_cv(ctr_p(0, 1, 0), ctr_p(0, 0, 1)));
-  arcs.push_back(ctr_cv(ctr_p(-1, 0, 0), ctr_p(0, 0, -1)));
-  arcs.push_back(ctr_cv(ctr_p(-1, 0, 0), ctr_p(0, 0, 1)));
-  arcs.push_back(ctr_cv(ctr_p(0, -1, 0), ctr_p(0, 0, -1)));
-  arcs.push_back(ctr_cv(ctr_p(0, -1, 0), ctr_p(0, 0, 1)));
-  arcs.push_back(ctr_cv(ctr_p(1, 0, 0), ctr_p(0, 1, 0)));
-  arcs.push_back(ctr_cv(ctr_p(1, 0, 0), ctr_p(0, -1, 0)));
-  arcs.push_back(ctr_cv(ctr_p(-1, 0, 0), ctr_p(0, 1, 0)));
-  arcs.push_back(ctr_cv(ctr_p(-1, 0, 0), ctr_p(0, -1, 0)));
+  std::list<X_monotone_curve> arcs;
+
+  arcs.push_back(ctr_xcv(ctr_p(1, 0, 0), ctr_p(0, 0, -1)));
+  arcs.push_back(ctr_xcv(ctr_p(1, 0, 0), ctr_p(0, 0, 1)));
+  arcs.push_back(ctr_xcv(ctr_p(0, 1, 0), ctr_p(0, 0, -1)));
+  arcs.push_back(ctr_xcv(ctr_p(0, 1, 0), ctr_p(0, 0, 1)));
+  arcs.push_back(ctr_xcv(ctr_p(-1, 0, 0), ctr_p(0, 0, -1)));
+  arcs.push_back(ctr_xcv(ctr_p(-1, 0, 0), ctr_p(0, 0, 1)));
+  arcs.push_back(ctr_xcv(ctr_p(0, -1, 0), ctr_p(0, 0, -1)));
+  arcs.push_back(ctr_xcv(ctr_p(0, -1, 0), ctr_p(0, 0, 1)));
+  arcs.push_back(ctr_xcv(ctr_p(1, 0, 0), ctr_p(0, 1, 0)));
+  arcs.push_back(ctr_xcv(ctr_p(1, 0, 0), ctr_p(0, -1, 0)));
+  arcs.push_back(ctr_xcv(ctr_p(-1, 0, 0), ctr_p(0, 1, 0)));
+  arcs.push_back(ctr_xcv(ctr_p(-1, 0, 0), ctr_p(0, -1, 0)));
+
+  // Construct meridians
+  std::size_t num_meridians(16);
+  if (argc > 1) sscanf(argv[1], "%zu", &num_meridians);
+
+  if (num_meridians > 0) {
+    auto np = ctr_p(0, 0, 1);
+    auto sp = ctr_p(0, 0, -1);
+    using FT = Kernel::FT;
+    using Direction_3 = Kernel::Direction_3;
+    auto delta = 2.0 * CGAL_PI / num_meridians;
+    FT z(0);
+    for (auto i = 0; i < num_meridians; ++i) {
+      auto alpha = delta * i;
+      FT x(std::sin(alpha));
+      FT y(std::cos(alpha));
+      Direction_3 normal(x, y, z);
+      arcs.push_back(ctr_xcv(sp, np, normal));
+    }
+  }
 
   CGAL::insert(arr, arcs.begin(), arcs.end());
-  print_arrangement_size(arr);          // print the arrangement size
+  print_arrangement_size(arr);
   // print_arrangement(arr);
   CGAL::draw(arr, "Aos", true);