Exemple #1
0
int main ()
{
  // Construct an arrangement of four polylines named A--D.
  Arrangement_2    arr;

  Point_2          points1[5] = {Point_2(0,0), Point_2(2,4), Point_2(3,3),
                                 Point_2(4,4), Point_2(6,0)};
  insert (arr, Curve_2 (Polyline_2 (points1, points1 + 5), "A"));

  Point_2          points2[3] = {Point_2(1,5), Point_2(3,3), Point_2(5,5)};
  insert (arr, Curve_2 (Polyline_2 (points2, points2 + 3), "B"));

  Point_2          points3[4] = {Point_2(1,0), Point_2(2,2),
                                 Point_2(4,2), Point_2(5,0)};
  insert (arr, Curve_2 (Polyline_2 (points3, points3 + 4), "C"));

  Point_2          points4[2] = {Point_2(0,2), Point_2(6,2)};
  insert (arr, Curve_2 (Polyline_2 (points4, points4 + 2), "D"));

  // Print all edges that correspond to an overlapping polyline.
  Arrangement_2::Edge_iterator    eit;

  for (eit = arr.edges_begin(); eit != arr.edges_end(); ++eit) {
    if (eit->curve().data().length() > 1) {
      std::cout << "[" << eit->curve() << "]  "
                << "named: " << eit->curve().data() << std::endl;

      // Rename the curve associated with the edge.
      arr.modify_edge (eit, X_monotone_curve_2 (eit->curve(), "overlap"));
    }
  }
  return 0;
}
void CriticalCurves::setParameters(double radius_1, double radius_2, Arrangements_2 insets_1, Arrangements_2 insets_2)
{
    Arrangement_2_iterator inset_1 = insets_1.begin();
    Arrangement_2_iterator inset_2 = insets_2.begin();

    while (inset_1 != insets_1.end() && inset_2 != insets_2.end())
    {
        Arrangement_2 arrangement;

        // Add the curves of the inset.
        for (Edge_iterator edge = inset_1->edges_begin(); edge != inset_1->edges_end(); ++edge)
        {
            insert(arrangement, edge->curve());
        }

        // Add the critical curves of type I.
        for (Edge_iterator edge = inset_2->edges_begin(); edge != inset_2->edges_end(); ++edge)
        {
            if (CGAL::COLLINEAR == edge->curve().orientation())
            {
                // Displaced a segment.
                Nt_traits nt_traits;
                Algebraic_ft factor = nt_traits.convert(Rational(radius_1) + Rational(radius_2));
                Conic_point_2 source = edge->curve().source();
                Conic_point_2 target = edge->curve().target();
                Algebraic_ft delta_x = target.x() - source.x();
                Algebraic_ft delta_y = target.y() - source.y();
                Algebraic_ft length = nt_traits.sqrt(delta_x * delta_x + delta_y * delta_y);
                Algebraic_ft translation_x = factor * delta_y / length;
                Algebraic_ft translation_y = - factor * delta_x / length;
                Conic_point_2 point_1(source.x() + translation_x, source.y() + translation_y);
                Conic_point_2 point_2(target.x() + translation_x, target.y() + translation_y);
                Algebraic_ft a = - delta_y;
                Algebraic_ft b = delta_x;
                Algebraic_ft c = factor * length - (source.y() * target.x() - source.x() * target.y());
                X_monotone_curve_2 x_monotone_curve(a, b, c, point_1, point_2);
                insert(arrangement, x_monotone_curve);
            }
            else
            {
                // Displaces an arc.
                Rational two(2);
                Rational four(4);

                Rational r = edge->curve().r();
                Rational s = edge->curve().s();
                Rational t = edge->curve().t();
                Rational u = edge->curve().u();
                Rational v = edge->curve().v();
                Rational w = edge->curve().w();

                Nt_traits nt_traits;
                Rational x_center = - u / (two * r);
                Rational y_center = - v / (two * r);
                Rat_point_2 rat_center(x_center, y_center);
                Conic_point_2 center(nt_traits.convert(x_center), nt_traits.convert(y_center));

                Rational radius = Rational(radius_1) + two * Rational(radius_2);

                Algebraic_ft coefficient = nt_traits.convert(radius / Rational(radius_2));

                Conic_point_2 source_1 = edge->curve().source();
                Algebraic_ft x_source_2 = center.x() + coefficient * (source_1.x() - center.x());
                Algebraic_ft y_source_2 = center.y() + coefficient * (source_1.y() - center.y());
                Conic_point_2 source_2(x_source_2, y_source_2);

                Conic_point_2 target_1 = edge->curve().target();
                Algebraic_ft x_target_2 = center.x() + coefficient * (target_1.x() - center.x());
                Algebraic_ft y_target_2 = center.y() + coefficient * (target_1.y() - center.y());
                Conic_point_2 target_2(x_target_2, y_target_2);

                Rat_circle_2 circle(rat_center, radius * radius);

                Conic_arc_2 conic_arc(circle, CGAL::COUNTERCLOCKWISE, source_2, target_2);

                insert(arrangement, conic_arc);
            }
        }

        // Add the critical curves of type II.
        for (Edge_iterator edge = inset_2->edges_begin(); edge != inset_2->edges_end(); ++edge)
        {
            double x = CGAL::to_double(edge->curve().source().x());
            double y = CGAL::to_double(edge->curve().source().y());
            double radius = radius_1 + radius_2;
            Rat_point_2 center(x, y);
            Rat_circle_2 circle(center, radius * radius);
            Conic_arc_2 conic_arc(circle);
            insert(arrangement, conic_arc);
        }

        // Remove the curves which are not include in the inset.
        Objects objects;
        Face_handle face;
        for (Edge_iterator edge = arrangement.edges_begin(); edge != arrangement.edges_end(); ++edge)
        {
            CGAL::zone(*inset_1, edge->curve(), std::back_inserter(objects));
            for (Object_iterator object = objects.begin(); object != objects.end(); ++object)
            {
                if (assign(face, *object))
                {
                    if (face->is_unbounded())
                    {
                        remove_edge(arrangement, edge);
                        break;
                    }
                }
            }
            objects.clear();
        }

        // Print essential information on the standard input.
        std::cout << "Arrangement:" << std::endl;
        std::cout << "  Number of vertices: " << arrangement.number_of_vertices() << std::endl;
        std::cout << "  Number of edges   : " << arrangement.number_of_edges() << std::endl;
        std::cout << "  Number of face    : " << arrangement.number_of_faces() << std::endl;

        this->critical_curves.push_back(arrangement);

        ++inset_1;
        ++inset_2;
    }

    // Commit changes.
    emit(criticalCurvesChanged());
    return;
}
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;
}