Add an example of interior wrapping

Alpha_wrap_2/examples/Alpha_wrap_2/CMakeLists.txt

@@ -12,3 +12,4 @@ create_single_source_cgal_program("polyline_wrap_2.cpp")
 create_single_source_cgal_program("polygon_wrap_2.cpp")
 create_single_source_cgal_program("triangle_soup_wrap_2.cpp")
 create_single_source_cgal_program("mixed_inputs_wrap_2.cpp")
+create_single_source_cgal_program("wrap_from_cavity_2.cpp")

Alpha_wrap_2/examples/Alpha_wrap_2/wrap_from_cavity_2.cpp

@@ -0,0 +1,84 @@
+#include <CGAL/Exact_predicates_inexact_constructions_kernel.h>
+
+#include <CGAL/alpha_wrap_2.h>
+#include <CGAL/Multipolygon_with_holes_2.h>
+#include <CGAL/Polygon_repair/repair.h>
+
+#include <CGAL/Real_timer.h>
+#include <CGAL/IO/WKT.h>
+
+#include <fstream>
+#include <iostream>
+#include <string>
+#include <vector>
+
+using K = CGAL::Exact_predicates_inexact_constructions_kernel;
+using Point_2 = K::Point_2;
+
+using Multipolygon = CGAL::Multipolygon_with_holes_2<K>;
+using Polygon_with_holes = Multipolygon::Polygon_with_holes_2;
+using Polygon = Polygon_with_holes::Polygon_2;
+
+int main(int argc, char** argv)
+{
+  std::cout.precision(17);
+  std::cerr.precision(17);
+
+  // Read the input multipolygon
+  const std::string filename = argc > 1 ? argv[1] : CGAL::data_file_path("wkt/issue.wkt");
+  std::ifstream in(filename);
+  Multipolygon mp_in;
+  if(!in || !CGAL::IO::read_multi_polygon_WKT(in, mp_in))
+  {
+    std::cerr << "Can't read input file " << filename << std::endl;
+    return EXIT_FAILURE;
+  }
+
+  std::cout << mp_in.polygons_with_holes().size() << " input polygons" << std::endl;
+
+  // Compute the alpha and offset values
+  const double relative_alpha = (argc > 2) ? std::stod(argv[2]) : 10.;
+  const double relative_offset = (argc > 3) ? std::stod(argv[3]) : 300.;
+
+  CGAL::Bbox_2 bbox = mp_in.bbox();
+  const double diag_length = std::sqrt(CGAL::square(bbox.xmax() - bbox.xmin()) +
+                                       CGAL::square(bbox.ymax() - bbox.ymin()));
+  const double alpha = diag_length / relative_alpha;
+  const double offset = diag_length / relative_offset;
+  std::cout << "absolute alpha = " << alpha << " absolute offset = " << offset << std::endl;
+
+  // Set up seed points
+  //
+  // There is no limit on how many seeds can be used.
+  // However, the algorithm automatically determines whether a seed can be used
+  // to initialize the refinement based on a few conditions (distance to the offset, value of alpha, etc.)
+  // See internal function Alpha_wrap_3::initialize_from_cavities() for more information
+  std::vector<Point_2> seeds = {
+    // the center of the bbox
+    Point_2((bbox.xmin() + bbox.xmax()) / 2.0, (bbox.ymin() + bbox.ymax()) / 2.0),
+
+    // a point outside the bounding box
+    Point_2(bbox.xmax() + 10 * (alpha + offset),
+            bbox.ymax() + 10 * (alpha + offset))
+  };
+
+  // Construct the wrap using the seed point
+  CGAL::Real_timer t;
+  t.start();
+
+  Multipolygon wrap;
+  CGAL::alpha_wrap_2(mp_in, alpha, offset, wrap, CGAL::parameters::seed_points(std::ref(seeds)));
+
+  t.stop();
+  std::cout << "Result: " << wrap.polygons_with_holes().size() << " polygons" << std::endl;
+  std::cout << "Took " << t.time() << " s." << std::endl;
+
+  // Save the result
+  std::ofstream out("cavity_wrap.wkt");
+  out.precision(std::numeric_limits<double>::max_digits10);
+  CGAL::IO::write_multi_polygon_WKT(out, wrap);
+
+  std::cout << "Done." << std::endl;
+
+  return EXIT_SUCCESS;
+}