Exemple #1
0
int main()
{
  Arrangement_2   arr;

  // Construct an arrangement of seven intersecting line segments.
  // We keep a handle for the vertex v_0 that corresponds to the point (1,1).
  Arrangement_2::Halfedge_handle  e =
    insert_non_intersecting_curve (arr, Segment_2 (Point_2 (1, 1),
                                                   Point_2 (7, 1)));
  Arrangement_2::Vertex_handle    v0 = e->source();
  insert (arr, Segment_2 (Point_2 (1, 1), Point_2 (3, 7)));
  insert (arr, Segment_2 (Point_2 (1, 4), Point_2 (7, 1)));
  insert (arr, Segment_2 (Point_2 (2, 2), Point_2 (9, 3)));
  insert (arr, Segment_2 (Point_2 (2, 2), Point_2 (4, 4)));
  insert (arr, Segment_2 (Point_2 (7, 1), Point_2 (9, 3)));
  insert (arr, Segment_2 (Point_2 (3, 7), Point_2 (9, 3)));

  // Create a mapping of the arrangement vertices to indices.
  Arr_vertex_index_map index_map(arr);

  // Perform Dijkstra's algorithm from the vertex v0.
  Edge_length_func edge_length;

  boost::vector_property_map<double, Arr_vertex_index_map> dist_map(static_cast<unsigned int>(arr.number_of_vertices()), index_map);



  boost::dijkstra_shortest_paths(arr, v0,
                                 boost::vertex_index_map(index_map).
                                 weight_map(edge_length).
                                 distance_map(dist_map));

  // Print the results:
  Arrangement_2::Vertex_iterator      vit;

  std::cout << "The distances of the arrangement vertices from ("
            << v0->point() << ") :" << std::endl;
  for (vit = arr.vertices_begin(); vit != arr.vertices_end(); ++vit)
    std::cout << "(" << vit->point() << ") at distance "
              << dist_map[vit] << std::endl;

  return 0;
}
Exemple #2
0
int main(int argc, char *argv[])
{
  // Get the name of the input file from the command line, or use the default
  // points.dat file if no command-line parameters are given.
  const char * filename = (argc > 1) ? argv[1] : "coll_points.dat";

  // Open the input file.
  std::ifstream     in_file(filename);

  if (! in_file.is_open()) {
    std::cerr << "Failed to open " << filename << " ..." << std::endl;
    return (1);
  }

  // Read the points from the file, and consturct their dual lines.
  std::vector<Point_2>           points;
  std::list<X_monotone_curve_2>  dual_lines;

  unsigned int n;
  in_file >> n;
  points.resize(n);
  unsigned int k;
  for (k = 0; k < n; ++k) {
    int px, py;
    in_file >> px >> py;
    points[k] = Point_2(px, py);

    // The line dual to the point (p_x, p_y) is y = p_x*x - p_y,
    // or: p_x*x - y - p_y = 0:
    Line_2 dual_line = Line_2(CGAL::Exact_rational(px),
                              CGAL::Exact_rational(-1),
                              CGAL::Exact_rational(-py));

    // Generate the x-monotone curve based on the line and the point index.
    dual_lines.push_back(X_monotone_curve_2(dual_line, k));
  }
  in_file.close();

  // Construct the dual arrangement by aggragately inserting the lines.
  Arrangement_2 arr;

  insert(arr, dual_lines.begin(), dual_lines.end());

  // Look for vertices whose degree is greater than 4.
  Arrangement_2::Vertex_const_iterator vit;
  Arrangement_2::Halfedge_around_vertex_const_circulator circ;
  size_t d;

  for (vit = arr.vertices_begin(); vit != arr.vertices_end(); ++vit) {
    if (vit->degree() > 4) {
      // There should be vit->degree()/2 lines intersecting at the current
      // vertex. We print their primal points and their indices.
      circ = vit->incident_halfedges();
      for (d = 0; d < vit->degree() / 2; d++) {
        k = circ->curve().data();     // The index of the primal point.
        std::cout << "Point no. " << k+1 << ": (" << points[k] << "), ";
        ++circ;
      }
      std::cout << "are collinear." << std::endl;
    }
  }
  return 0;
}
int main ()
{
  // Construct an arrangement containing three RED line segments.
  Arrangement_2     arr;
  Landmarks_pl      pl (arr);

  Segment_2         s1 (Point_2(-1, -1), Point_2(1, 3));
  Segment_2         s2 (Point_2(2, 0), Point_2(3, 3));
  Segment_2         s3 (Point_2(0, 3), Point_2(2, 5));

  insert (arr, Colored_segment_2 (s1, RED), pl);
  insert (arr, Colored_segment_2 (s2, RED), pl);
  insert (arr, Colored_segment_2 (s3, RED), pl);

  // Insert three BLUE line segments.
  Segment_2         s4 (Point_2(-1, 3), Point_2(4, 1));
  Segment_2         s5 (Point_2(-1, 0), Point_2(4, 1));
  Segment_2         s6 (Point_2(-2, 1), Point_2(1, 4));

  insert (arr, Colored_segment_2 (s4, BLUE), pl);
  insert (arr, Colored_segment_2 (s5, BLUE), pl);
  insert (arr, Colored_segment_2 (s6, BLUE), pl);

  // Go over all vertices and print just the ones corresponding to intersection
  // points between RED segments and BLUE segments. Note that we skip endpoints
  // of overlapping sections.
  Arrangement_2::Vertex_const_iterator   vit;
  Segment_color                          color;

  for (vit = arr.vertices_begin(); vit != arr.vertices_end(); ++vit) {
    // Go over the incident halfedges of the current vertex and examine their
    // colors.
    bool       has_red = false;
    bool       has_blue = false;

    Arrangement_2::Halfedge_around_vertex_const_circulator  eit, first;

    eit = first = vit->incident_halfedges();
    do {
      // Get the color of the current half-edge.
      if (eit->curve().data().size() == 1) {
        color = eit->curve().data().front();

        if (color == RED)
          has_red = true;
        else if (color == BLUE)
          has_blue = true;
      }

      ++eit;
    } while (eit != first);

    // Print the vertex only if incident RED and BLUE edges were found.
    if (has_red && has_blue)
    {
      std::cout << "Red-blue intersection at (" << vit->point() << ")"
                << std::endl;
    }
  }

  // Locate the edges that correspond to a red-blue overlap.
  Arrangement_2::Edge_iterator   eit;

  for (eit = arr.edges_begin(); eit != arr.edges_end(); ++eit)
  {
    // Go over the incident edges of the current vertex and examine their
    // colors.
    bool       has_red = false;
    bool       has_blue = false;

    Traits_2::Data_container::const_iterator       dit;

    for (dit = eit->curve().data().begin(); dit != eit->curve().data().end();
         ++dit)
    {
      if (*dit == RED)
        has_red = true;
      else if (*dit == BLUE)
        has_blue = true;
    }

    // Print the edge only if it corresponds to a red-blue overlap.
    if (has_red && has_blue)
      std::cout << "Red-blue overlap at [" << eit->curve() << "]"  << std::endl;
  }
  return 0;
}