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;
}