void
arrangement::keep_arc(Arrangement_2::Edge_iterator &e, Arrangement_2 ©, Walk_pl &walk_pl)
{
e->set_data("none");
Conic_point_2 p;
// if it is a segment
if (e->curve().orientation() == CGAL::COLLINEAR)
{
Conic_point_2 source = e->curve().source();
Conic_point_2 target = e->curve().target();
double x = CGAL::to_double((target.x() + source.x()) /2);
double y = CGAL::to_double((target.y() + source.y()) /2);
Rational x_(x);
Rational y_(y);
p = Conic_point_2(x_,y_);
}
else // if it is an arc
{
int n = 2;
approximated_point_2* points = new approximated_point_2[n + 1];
e->curve().polyline_approximation(n, points); // there is 3 points
p = Conic_point_2(Rational(points[1].first),Rational(points[1].second));
}
Arrangement_2::Vertex_handle v = insert_point(copy, p, walk_pl);
try
{
if (v->face()->data() != 1)
nonCriticalRegions.remove_edge(e, false, false);
copy.remove_isolated_vertex(v);
}
catch (const std::exception exn) {}
}
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;
}
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;
}
void
arrangement::compute_ACScell()
{
/*
for (int i = 0; i < (int)convolutions.size(); ++i)
for (Arrangement_2::Edge_iterator edge = convolutions[i].edges_begin(); edge != convolutions[i].edges_end(); ++edge)
{
convolution_r_all = Arrangement_2(convolutions[i]);
insert(convolution_r_all, edge->curve());
Arrangement_2::Edge_iterator e = convolution_r_all.edges_end();
e->set_data(edge->data());
}
*/
/*
std::cout << "edge label convo : ";
for (Arrangement_2::Edge_iterator edge = convolution_r_all.edges_begin(); edge != convolution_r_all.edges_end(); ++edge)
std::cout << edge->data() << " ";
std::cout << std::endl;
*/
for (int i = 0; i < (int)point_in_faces.size(); ++i)
{
// do a copy
Arrangement_2 copy(convolutions[0]);
Observer observer(copy);
// add a circle
Rat_point_2 center(point_in_faces[i][0], point_in_faces[i][1]);
Rat_circle_2 circle(center, r1r2 * r1r2);
Conic_curve_2 conic_arc(circle);
insert(copy, conic_arc);
// then add rho label for arc
for (Arrangement_2::Edge_iterator edge = copy.edges_begin(); edge != copy.edges_end(); ++edge)
{
if (edge->data().compare("") == 0)
{
edge->set_data("rho_");
edge->twin()->set_data("rho_");
}
}
Walk_pl walk_pl(copy);
std::vector<std::vector<double> > points;
compute_pointInCells(copy, points);
for (int j = 0; j < (int)points.size(); ++j)
{
double _x = point_in_faces[i][0] - points[j][0];
double _y = point_in_faces[i][1] - points[j][1];
if (r1r2 < sqrt(_x * _x + _y * _y))
{
Rational x_(points[j][0]);
Rational y_(points[j][1]);
Conic_point_2 p(x_,y_);
Arrangement_2::Vertex_handle v = insert_point(copy, p, walk_pl);
try
{
ACScell cell(i);
Arrangement_2::Ccb_halfedge_circulator first_outer_ccb = v->face()->outer_ccb();
Arrangement_2::Ccb_halfedge_circulator outer_ccb = v->face()->outer_ccb();
do
{
// for retrieving ACScell Begin and End
insert(cell.arr, outer_ccb->curve());
// then continue
cell.addLabel(outer_ccb->data());
++outer_ccb;
} while (outer_ccb != first_outer_ccb);
ACScells.push_back(cell);
}
catch (const std::exception exn) {}
}
}
}
// clean ACScells
for (int i = 0; i < (int)ACScells.size(); ++i)
ACScells[i].cleanLabels();
// compute ACScells id
int cpt = 0;
int previous = 0;
for (int i = 0; i < (int)ACScells.size(); ++i)
{
if (previous != ACScells[i].NCR)
{
cpt = 0;
previous = ACScells[i].NCR;
}
ACScells[i].id = std::to_string(ACScells[i].NCR) + "." + std::to_string(cpt);
++cpt;
}
}
void
arrangement::compute_criticalCurves_type_II()
{
for (int i = 0; i < (int) convolutions_o.size(); ++i)
{
// for all convolution arrangements
Arrangement_2::Edge_iterator first = convolutions_o[i].edges_begin();
Arrangement_2::Edge_iterator previous = convolutions_o[i].edges_begin();
bool flag = true;
Arrangement_2 copy(convolutions_o[i]);
Walk_pl walk_pl(copy);
for (Arrangement_2::Edge_iterator edge = convolutions_o[i].edges_begin(); edge != convolutions_o[i].edges_end(); ++edge)
{
if (flag)
{
++edge;
flag = false;
}
if (previous->data().compare(edge->data()) != 0)
{
// add critical curve type II in the copy
double x = CGAL::to_double(edge->curve().source().x());
double y = CGAL::to_double(edge->curve().source().y());
double radius = r1r2;
Rat_point_2 center(x, y);
Rat_circle_2 circle(center, radius * radius);
Conic_curve_2 conic_arc(circle);
insert(nonCriticalRegions, conic_arc);
}
previous = edge;
}
if (previous->data().compare(first->data()) != 0)
{
// add critical curve type II in the copy
double x = CGAL::to_double(first->curve().source().x());
double y = CGAL::to_double(first->curve().source().y());
double radius = r1r2;
Rat_point_2 center(x, y);
Rat_circle_2 circle(center, radius * radius);
Conic_curve_2 conic_arc(circle);
insert(nonCriticalRegions, conic_arc);
}
// keep only wanted curves and put it in the arrangement
for (Arrangement_2::Edge_iterator e = nonCriticalRegions.edges_begin(); e != nonCriticalRegions.edges_end(); ++e)
if ((e->data().compare("") == 0))
keep_arc(e, copy, walk_pl);
for (Arrangement_2::Edge_iterator edge = convolutions_o[i].edges_begin(); edge != convolutions_o[i].edges_end(); ++edge)
insert(nonCriticalRegions, edge->curve());
}
}
void
arrangement::compute_criticalCurves_type_I()
{
double radius_1 = ((double)manipulator_diametre)/2.0;
double radius_2 = ((double)target_diametre)/2.0;
for (int i = 0; i < (int) convolutions_o.size(); ++i)
{
Arrangement_2 copy(convolutions_o[i]);
Walk_pl walk_pl(copy);
// Add the critical curves of type I.
for (Arrangement_2::Edge_iterator edge = convolutions_o[i].edges_begin(); edge != convolutions_o[i].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(nonCriticalRegions, x_monotone_curve);
}
else
{
// Displaces an arc.
Rational two(2);
Rational r = edge->curve().r();
Rational u = edge->curve().u();
Rational v = edge->curve().v();
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_curve_2 conic_arc(circle, CGAL::CLOCKWISE, source_2, target_2);
insert(nonCriticalRegions, conic_arc);
}
}
// keep only wanted curves and put it in the arrangement
for (Arrangement_2::Edge_iterator e = nonCriticalRegions.edges_begin(); e != nonCriticalRegions.edges_end(); ++e)
if ((e->data().compare("") == 0))
keep_arc(e, copy, walk_pl);
for (Arrangement_2::Edge_iterator edge = convolutions_o[i].edges_begin(); edge != convolutions_o[i].edges_end(); ++edge)
insert(nonCriticalRegions, edge->curve());
}
}
void
arrangement::compute_convolutionLabels()
{
// initialize variables
int compteur_wall = 0;
int compteur_arc = 0;
std::vector<std::string > labels;
for (int i = 0; i < (int) env_points.size(); ++i)
labels.push_back("none");
double r = manipulator_diametre/2;
// compute labels for robot convolution
for (int i = 0; i < (int) convolutions.size(); ++i)
{
for (Arrangement_2::Edge_iterator edge = convolutions[i].edges_begin(); edge != convolutions[i].edges_end(); ++edge)
{
if (edge->curve().orientation() == CGAL::COLLINEAR) // if it is a segment
{
edge->set_data("w"+std::to_string(compteur_wall));
edge->twin()->set_data("w"+std::to_string(compteur_wall++));
}
else // if it is an arc
{
std::string l = getLabel(labels, edge->curve(), compteur_arc, r);
edge->set_data(l);
edge->twin()->set_data(l);
}
}
}
// compute labels for object convolution (usefull just to clean critical curves 2)
compteur_wall = 0;
compteur_arc = 0;
labels.clear();
for (int i = 0; i < (int) env_points.size(); ++i)
labels.push_back("none");
r = target_diametre/2;
for (int i = 0; i < (int) convolutions_o.size(); ++i)
{
for (Arrangement_2::Edge_iterator edge = convolutions_o[i].edges_begin(); edge != convolutions_o[i].edges_end(); ++edge)
{
if (edge->curve().orientation() == CGAL::COLLINEAR) // if it is a segment
{
edge->set_data("w"+std::to_string(compteur_wall));
edge->twin()->set_data("w"+std::to_string(compteur_wall++));
}
else // if it is an arc
{
std::string l = getLabel(labels, edge->curve(), compteur_arc, r);
edge->set_data(l);
edge->twin()->set_data(l);
}
}
}
}