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()); } }
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_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()); } }