Added new examples.

.gitattributes

@@ -1044,7 +1044,14 @@ Minkowski_sum_2/doc_tex/Minkowski_sum_2/fig/onecyc_out.fig -text
 Minkowski_sum_2/doc_tex/Minkowski_sum_2/fig/sum_triangles.fig -text
 Minkowski_sum_2/doc_tex/Minkowski_sum_2/fig/sum_triangles.pstex -text
 Minkowski_sum_2/doc_tex/Minkowski_sum_2/fig/sum_triangles.pstex_t -text
+Minkowski_sum_2/examples/Minkowski_sum_2/ex_approx_offset.C -text
+Minkowski_sum_2/examples/Minkowski_sum_2/ex_exact_offset.C -text
+Minkowski_sum_2/examples/Minkowski_sum_2/ex_sum_by_decomposition.C -text
 Minkowski_sum_2/examples/Minkowski_sum_2/ex_sum_triangles.C -text
+Minkowski_sum_2/examples/Minkowski_sum_2/ex_sum_with_holes.C -text
+Minkowski_sum_2/examples/Minkowski_sum_2/ms_rational_nt.h -text
+Minkowski_sum_2/examples/Minkowski_sum_2/rooms_star.dat -text
+Minkowski_sum_2/examples/Minkowski_sum_2/spiked.dat -text
 Modifier/doc_tex/Modifier/idraw/modifier.eps -text
 Modifier/doc_tex/Modifier/idraw/modifier.pdf -text svneol=unset#unset
 Modifier/doc_tex/Modifier/modifier.gif -text svneol=unset#unset

Minkowski_sum_2/examples/Minkowski_sum_2/ex_approx_offset.C

@@ -0,0 +1,56 @@
+//! \file examples/Minkowski_sum_2/ex_approx_offset.C
+// Computing the approximated offset of a polygon.
+
+#include "ms_rational_nt.h"
+#include <CGAL/Lazy_exact_nt.h>
+#include <CGAL/Cartesian.h>
+#include <CGAL/approximated_offset_2.h>
+#include <CGAL/offset_polygon_2.h>
+#include <CGAL/Timer.h>
+#include <iostream>
+
+typedef CGAL::Lazy_exact_nt<Number_type>           Lazy_exact_nt;
+typedef CGAL::Cartesian<Lazy_exact_nt>             Kernel;
+typedef CGAL::Polygon_2<Kernel>                    Polygon_2;
+
+typedef CGAL::Gps_circle_segment_traits_2<Kernel>  Gps_traits_2;
+typedef Gps_traits_2::Polygon_2                    Offset_polygon_2;
+typedef Gps_traits_2::Polygon_with_holes_2         Offset_polygon_with_holes_2;
+
+int main ()
+{
+  // Open the input file.
+  std::ifstream    in_file ("spiked.dat");
+
+  if (! in_file.is_open())
+  {
+    std::cerr << "Failed to open the input file." << std::endl;
+    return (1);
+  }
+
+  // Read the input polygon.
+  Polygon_2        P;
+
+  in_file >> P;
+  in_file.close();
+
+  std::cout << "Read an input polygon with " 
+            << P.size() << " vertices." << std::endl;
+
+  // Approximate the offset polygon.
+  const Number_type            radius = 5;
+  const double                 err_bound = 0.00001;
+  Offset_polygon_with_holes_2  offset;
+  CGAL::Timer                  timer;
+
+  timer.start();
+  offset = approximated_offset_2 (P, radius, err_bound);
+  timer.stop();
+
+  std::cout << "The offset polygon has "
+            << offset.outer_boundary().size() << " vertices, "
+            << offset.number_of_holes() << " holes." << std::endl;
+  std::cout << "Offset computation took " 
+            << timer.time() << " seconds." << std::endl;
+  return (0);
+}

Minkowski_sum_2/examples/Minkowski_sum_2/ex_exact_offset.C

@@ -0,0 +1,73 @@
+//! \file examples/Minkowski_sum_2/ex_exact_offset.C
+// Computing the exact offset of a polygon.
+#include <CGAL/basic.h>
+
+#ifndef CGAL_USE_CORE
+#include <iostream>
+int main ()
+{
+  std::cout << "Sorry, this example needs CORE ..." << std::endl; 
+  return (0);
+}
+#else
+
+#include <CGAL/Cartesian.h>
+#include <CGAL/CORE_algebraic_number_traits.h>
+#include <CGAL/Arr_conic_traits_2.h>
+#include <CGAL/offset_polygon_2.h>
+#include <CGAL/Timer.h>
+#include <iostream>
+
+typedef CGAL::CORE_algebraic_number_traits     Nt_traits;
+typedef Nt_traits::Rational                    Rational;
+typedef Nt_traits::Algebraic                   Algebraic;
+typedef CGAL::Cartesian<Rational>              Rat_kernel;
+typedef CGAL::Cartesian<Algebraic>             Alg_kernel;
+typedef CGAL::Arr_conic_traits_2<Rat_kernel,
+                                 Alg_kernel,
+                                 Nt_traits>    Conic_traits_2;
+typedef CGAL::Polygon_2<Rat_kernel>            Polygon_2;
+
+typedef CGAL::Gps_traits_2<Conic_traits_2>     Gps_traits_2;
+typedef Gps_traits_2::Polygon_2                Offset_polygon_2;
+typedef Gps_traits_2::Polygon_with_holes_2     Offset_polygon_with_holes_2;
+
+int main ()
+{
+  // Open the input file.
+  std::ifstream    in_file ("spiked.dat");
+
+  if (! in_file.is_open())
+  {
+    std::cerr << "Failed to open the input file." << std::endl;
+    return (1);
+  }
+
+  // Read the input polygon.
+  Polygon_2        P;
+
+  in_file >> P;
+  in_file.close();
+
+  std::cout << "Read an input polygon with " 
+            << P.size() << " vertices." << std::endl;
+
+  // Compute the offset polygon.
+  Conic_traits_2               traits;
+  const Rational               radius = 5;
+  Offset_polygon_with_holes_2  offset;
+  CGAL::Timer                  timer;
+
+  timer.start();
+  offset = offset_polygon_2 (traits, P, radius);
+  timer.stop();
+
+  std::cout << "The offset polygon has "
+            << offset.outer_boundary().size() << " vertices, "
+            << offset.number_of_holes() << " holes." << std::endl;
+  std::cout << "Offset computation took " 
+            << timer.time() << " seconds." << std::endl;
+  return (0);
+}
+
+#endif

Minkowski_sum_2/examples/Minkowski_sum_2/ex_sum_by_decomposition.C

@@ -0,0 +1,43 @@
+//! \file examples/Minkowski_sum_2/ex_sum_by_decomposition.C
+// Computing the Minkowski sum of two non-convex polygons read from a file
+// using the small-side angle-bisector decomposition strategy.
+
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+#include <CGAL/minkowski_sum_2.h>
+#include <CGAL/Small_side_angle_bisector_decomposition.h>
+#include <iostream>
+#include <fstream>
+
+#include "print_utils.h"
+
+typedef CGAL::Exact_predicates_exact_constructions_kernel  Kernel;
+typedef Kernel::Point_2                               Point_2;
+typedef CGAL::Polygon_2<Kernel>                       Polygon_2;
+typedef CGAL::Polygon_with_holes_2<Kernel>            Polygon_with_holes_2;
+
+int main ()
+{
+  // Open the input file.
+  std::ifstream    in_file ("rooms_star.dat");
+
+  if (! in_file.is_open())
+  {
+    std::cerr << "Failed to open the input file." << std::endl;
+    return (1);
+  }
+
+  // Read the two polygons from the file and compute their Minkowski sum.
+  Polygon_2   P, Q;
+
+  in_file >> P >> Q;
+  in_file.close();
+
+  // Compute the Minkowski sum using the decomposition approach.
+  CGAL::Small_side_angle_bisector_decomposition<Kernel>  ssab_decomp;
+
+  Polygon_with_holes_2  sum = minkowski_sum_2 (P, Q, ssab_decomp);
+
+  std::cout << "P (+) Q = "; print_polygon_with_holes (sum);
+  
+  return (0);
+}

Minkowski_sum_2/examples/Minkowski_sum_2/ex_sum_triangles.C

@@ -1,14 +1,13 @@
 //! \file examples/Minkowski_sum_2/ex_sum_triangles.C
 // Computing the Minkowski sum of two triangles.
 
+#include "ms_rational_nt.h"
 #include <CGAL/Cartesian.h>
-#include <CGAL/Polygon_2.h>
 #include <CGAL/minkowski_sum_2.h>
 #include <iostream>
 
 #include "print_utils.h"
 
-typedef int                                         Number_type;
 typedef CGAL::Cartesian<Number_type>                Kernel;
 typedef Kernel::Point_2                             Point_2;
 typedef CGAL::Polygon_2<Kernel>                     Polygon_2;

Minkowski_sum_2/examples/Minkowski_sum_2/ex_sum_with_holes.C

@@ -0,0 +1,39 @@
+//! \file examples/Minkowski_sum_2/ex_sum_with_holes.C
+// Computing the Minkowski sum of two non-convex polygons read from a file.
+
+#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
+#include <CGAL/minkowski_sum_2.h>
+#include <iostream>
+#include <fstream>
+
+#include "print_utils.h"
+
+typedef CGAL::Exact_predicates_exact_constructions_kernel  Kernel;
+typedef Kernel::Point_2                               Point_2;
+typedef CGAL::Polygon_2<Kernel>                       Polygon_2;
+typedef CGAL::Polygon_with_holes_2<Kernel>            Polygon_with_holes_2;
+
+int main ()
+{
+  // Open the input file.
+  std::ifstream    in_file ("rooms_star.dat");
+
+  if (! in_file.is_open())
+  {
+    std::cerr << "Failed to open the input file." << std::endl;
+    return (1);
+  }
+
+  // Read the two polygons from the file and compute their Minkowski sum.
+  Polygon_2   P, Q;
+
+  in_file >> P >> Q;
+  in_file.close();
+
+  // Compute and print the Minkowski sum.
+  Polygon_with_holes_2  sum = minkowski_sum_2 (P, Q);
+
+  std::cout << "P (+) Q = "; print_polygon_with_holes (sum);
+  
+  return (0);
+}

Minkowski_sum_2/examples/Minkowski_sum_2/ms_rational_nt.h

@@ -0,0 +1,23 @@
+#ifndef CGAL_MS_RATIONAL_NT_H
+#define CGAL_MS_RATIONAL_NT_H
+
+#include <CGAL/basic.h>
+
+#ifdef CGAL_USE_GMP
+
+  // GMP is installed. Use the GMP rational number-type. 
+  #include <CGAL/Gmpq.h>
+
+  typedef CGAL::Gmpq                                    Number_type;
+
+#else
+
+  // GMP is not installed. Use CGAL's exact rational number-type.
+  #include <CGAL/MP_Float.h>
+  #include <CGAL/Quotient.h>
+
+  typedef CGAL::Quotient<CGAL::MP_Float>                Number_type;
+
+#endif
+
+#endif

Minkowski_sum_2/examples/Minkowski_sum_2/rooms_star.dat

@@ -0,0 +1,37 @@
+26
+0/1 8/1
+0/1 0/1
+17/1 0/1
+17/1 18/1
+0/1 18/1
+0/1 9/1
+6/1 9/1
+6/1 10/1
+1/1 10/1
+1/1 17/1
+8/1 17/1
+8/1 14/1
+9/1 14/1
+9/1 17/1
+16/1 17/1
+16/1 10/1
+9/1 10/1
+8/1 9/1
+16/1 9/1
+16/1 1/1
+9/1 1/1
+9/1 8/1
+8/1 8/1
+8/1 1/1
+1/1 1/1
+1/1 8/1
+
+8
+0/1 -3/1
+1/1 -1/1
+3/1 0/1
+1/1 1/1
+0/1 3/1
+-1/1 1/1
+-3/1 0/1
+-1/1 -1/1

Minkowski_sum_2/examples/Minkowski_sum_2/spiked.dat

@@ -0,0 +1,65 @@
+64
+100/1 -10/1
+100/1 500/1
+500/1 498/1
+110/1 495/1
+110/1 450/1
+500/1 448/1
+110/1 445/1
+110/1 400/1
+500/1 398/1
+110/1 395/1
+110/1 350/1
+500/1 348/1
+110/1 345/1
+110/1 300/1
+500/1 298/1
+110/1 295/1
+110/1 250/1
+500/1 248/1
+110/1 245/1
+110/1 200/1
+500/1 198/1
+110/1 195/1
+110/1 150/1
+500/1 148/1
+110/1 145/1
+110/1 100/1
+500/1 98/1
+110/1 95/1
+110/1 50/1
+500/1 48/1
+110/1 45/1
+110/1 0/1
+600/1 0/1
+602/1 500/1
+605/1 0/1
+610/1 0/1
+612/1 500/1
+615/1 0/1
+620/1 0/1
+622/1 500/1
+625/1 0/1
+630/1 0/1
+632/1 500/1
+635/1 0/1
+640/1 0/1
+642/1 500/1
+645/1 0/1
+650/1 0/1
+652/1 500/1
+655/1 0/1
+660/1 0/1
+662/1 500/1
+665/1 0/1
+670/1 0/1
+672/1 500/1
+675/1 0/1
+680/1 0/1
+682/1 500/1
+685/1 0/1
+690/1 0/1
+692/1 500/1
+695/1 0/1
+700/1 0/1
+700/1 -10/1