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;
}
Face_index_observer (Arrangement_2& arr) :
CGAL::Arr_observer<Arrangement_2> (arr),
n_faces (0)
{
CGAL_precondition (arr.is_empty());
arr.unbounded_face()->set_data (0);
n_faces++;
}
int main (int argc, char *argv[])
{
// Get the name of the input file from the command line, or use the default
// fan_grids.dat file if no command-line parameters are given.
const char * filename = (argc > 1) ? argv[1] : "fan_grids.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 segments from the file.
// The input file format should be (all coordinate values are integers):
// <n> // number of segments.
// <sx_1> <sy_1> <tx_1> <ty_1> // source and target of segment #1.
// <sx_2> <sy_2> <tx_2> <ty_2> // source and target of segment #2.
// : : : :
// <sx_n> <sy_n> <tx_n> <ty_n> // source and target of segment #n.
std::list<Segment_2> segments;
unsigned int n;
in_file >> n;
unsigned int i;
for (i = 0; i < n; ++i) {
int sx, sy, tx, ty;
in_file >> sx >> sy >> tx >> ty;
segments.push_back (Segment_2 (Point_2 (Number_type(sx), Number_type(sy)),
Point_2 (Number_type(tx), Number_type(ty))));
}
in_file.close();
// Construct the arrangement by aggregately inserting all segments.
Arrangement_2 arr;
CGAL::Timer timer;
std::cout << "Performing aggregated insertion of "
<< n << " segments." << std::endl;
timer.start();
insert (arr, segments.begin(), segments.end());
timer.stop();
// Print the arrangement dimensions.
std::cout << "V = " << arr.number_of_vertices()
<< ", E = " << arr.number_of_edges()
<< ", F = " << arr.number_of_faces() << std::endl;
std::cout << "Construction took " << timer.time()
<< " seconds." << std::endl;
return 0;
}
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) {}
}
bool test(const Arrangement_2& arr)
{
if (arr.number_of_vertices() != 0) {
std::cerr << "(A) Number of vertices (" << arr.number_of_vertices()
<< ") not 0!" << std::endl;
return false;
}
// Check the validity more thoroughly.
if (! CGAL::is_valid(arr)) {
std::cerr << "The arrangement is NOT valid!" << std::endl;
return false;
}
return true;
}
bool test_ray(Arrangement_2& arr, Face_handle f)
{
Segment_2 s1(Point_2(0, 0), Point_2(1, 0));
Halfedge_handle eh1 =
arr.insert_in_face_interior(X_monotone_curve_2(s1), f);
Vertex_handle vh = eh1->target();
Ray_2 ray(Point_2(1, 0), Point_2(2, 0));
Halfedge_handle eh2 =
arr.insert_from_left_vertex(X_monotone_curve_2(ray), vh);
// Remove the edges
arr.remove_edge(eh2);
arr.remove_edge(eh1);
if (!::test(arr)) return false;
return true;
}
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;
}
int main ()
{
Arrangement_2 arr;
// Construct an arrangement of seven intersecting line segments.
insert (arr, Segment_2 (Point_2 (1, 1), Point_2 (7, 1)));
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 faces to indices.
CGAL::Arr_face_index_map<Arrangement_2> index_map (arr);
// Perform breadth-first search from the unbounded face, and use the BFS
// visitor to associate each arrangement face with its discover time.
Discover_time_bfs_visitor<CGAL::Arr_face_index_map<Arrangement_2> >
bfs_visitor (index_map);
Arrangement_2::Face_handle uf = arr.unbounded_face();
boost::breadth_first_search (Dual_arrangement_2 (arr), uf,
boost::vertex_index_map (index_map).
visitor (bfs_visitor));
// Print the results:
Arrangement_2::Face_iterator fit;
for (fit = arr.faces_begin(); fit != arr.faces_end(); ++fit)
{
std::cout << "Discover time " << fit->data() << " for ";
if (fit != uf)
{
std::cout << "face ";
print_ccb<Arrangement_2> (fit->outer_ccb());
}
else
std::cout << "the unbounded face." << std::endl;
}
return (0);
}
int main ()
{
// Construct the arrangement containing two intersecting triangles.
Arrangement_2 arr;
Face_index_observer obs (arr);
Segment_2 s1 (Point_2(4, 1), Point_2(7, 6));
Segment_2 s2 (Point_2(1, 6), Point_2(7, 6));
Segment_2 s3 (Point_2(4, 1), Point_2(1, 6));
Segment_2 s4 (Point_2(1, 3), Point_2(7, 3));
Segment_2 s5 (Point_2(1, 3), Point_2(4, 8));
Segment_2 s6 (Point_2(4, 8), Point_2(7, 3));
insert_non_intersecting_curve (arr, s1);
insert_non_intersecting_curve (arr, s2);
insert_non_intersecting_curve (arr, s3);
insert (arr, s4);
insert (arr, s5);
insert (arr, s6);
// Go over all arrangement faces and print the index of each face and it
// outer boundary. The face index is stored in its data field in our case.
Arrangement_2::Face_const_iterator fit;
Arrangement_2::Ccb_halfedge_const_circulator curr;
std::cout << arr.number_of_faces() << " faces:" << std::endl;
for (fit = arr.faces_begin(); fit != arr.faces_end(); ++fit) {
std::cout << "Face no. " << fit->data() << ": ";
if (fit->is_unbounded())
std::cout << "Unbounded." << std::endl;
else {
curr = fit->outer_ccb();
std::cout << curr->source()->point();
do {
std::cout << " --> " << curr->target()->point();
++curr;
} while (curr != fit->outer_ccb());
std::cout << std::endl;
}
}
return 0;
}
int main (int argc, char *argv[])
{
// Get the name of the input file from the command line, or use the default
// Bezier.dat file if no command-line parameters are given.
const char *filename = (argc > 1) ? argv[1] : "Bezier.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 curves from the input file.
unsigned int n_curves;
std::list<Bezier_curve_2> curves;
Bezier_curve_2 B;
unsigned int k;
in_file >> n_curves;
for (k = 0; k < n_curves; k++) {
// Read the current curve (specified by its control points).
in_file >> B;
curves.push_back (B);
std::cout << "B = {" << B << "}" << std::endl;
}
// Construct the arrangement.
Arrangement_2 arr;
insert (arr, curves.begin(), curves.end());
// Print the arrangement size.
std::cout << "The arrangement size:" << std::endl
<< " V = " << arr.number_of_vertices()
<< ", E = " << arr.number_of_edges()
<< ", F = " << arr.number_of_faces() << std::endl;
return 0;
}
int main()
{
// Construct the arrangement of five intersecting segments.
Arrangement_2 arr;
Walk_pl pl(arr);
Segment_2 s1(Point_2(1, 0), Point_2(2, 4));
Segment_2 s2(Point_2(5, 0), Point_2(5, 5));
Segment_2 s3(Point_2(1, 0), Point_2(5, 3));
Segment_2 s4(Point_2(0, 2), Point_2(6, 0));
Segment_2 s5(Point_2(3, 0), Point_2(5, 5));
insert_non_intersecting_curve(arr, s1, pl);
insert_non_intersecting_curve(arr, s2, pl);
insert(arr, s3, pl);
insert(arr, s4, pl);
insert(arr, s5, pl);
// Print the size of the arrangement.
std::cout << "The arrangement size:" << std::endl
<< " V = " << arr.number_of_vertices()
<< ", E = " << arr.number_of_edges()
<< ", F = " << arr.number_of_faces() << std::endl;
// Perform a point-location query on the resulting arrangement and print
// the boundary of the face that contains it.
Point_2 q(4, 1);
Walk_pl::result_type obj = pl.locate(q);
Arrangement_2::Face_const_handle f;
CGAL_assertion_code(bool success =) CGAL::assign(f, obj);
CGAL_assertion(success);
std::cout << "The query point (" << q << ") is located in: ";
print_face<Arrangement_2>(f);
return 0;
}
int main()
{
// Step(a) - construct a triangular face.
Arrangement_2 arr;
Segment_2 s1(Point_2(667, 1000), Point_2(4000, 5000));
Segment_2 s2(Point_2(4000, 0), Point_2(4000, 5000));
Segment_2 s3(Point_2(667, 1000), Point_2(4000, 0));
Halfedge_handle e1 = arr.insert_in_face_interior(s1, arr.unbounded_face());
Vertex_handle v1 = e1->source();
Vertex_handle v2 = e1->target();
Halfedge_handle e2 = arr.insert_from_right_vertex(s2, v2);
Vertex_handle v3 = e2->target();
arr.insert_at_vertices(s3, v3, v1);
// Step (b) - create additional two faces inside the triangle.
Point_2 p1(4000, 3666), p2(4000, 1000);
Segment_2 s4(Point_2(4000, 5000), p1);
Segment_2 s5(p1, p2);
Segment_2 s6(Point_2(4000, 0), p2);
Halfedge_handle e4 = arr.split_edge(e2, s4, Segment_2(Point_2(4000, 0), p1));
Vertex_handle w1 = e4->target();
Halfedge_handle e5 = arr.split_edge(e4->next(), s5, s6);
Vertex_handle w2 = e5->target();
Halfedge_handle e6 = e5->next();
Segment_2 s7(p1, Point_2(3000, 2666));
Segment_2 s8(p2, Point_2(3000, 1333));
Segment_2 s9(Point_2(3000, 2666), Point_2(2000, 1666));
Segment_2 s10(Point_2(3000, 1333), Point_2(2000, 1666));
Segment_2 s11(Point_2(3000, 1333), Point_2(3000, 2666));
Halfedge_handle e7 = arr.insert_from_right_vertex(s7, w1);
Vertex_handle v4 = e7->target();
Halfedge_handle e8 = arr.insert_from_right_vertex(s8, w2);
Vertex_handle v5 = e8->target();
Vertex_handle v6 =
arr.insert_in_face_interior(Point_2(2000, 1666), e8->face());
arr.insert_at_vertices(s9, v4, v6);
arr.insert_at_vertices(s10, v5, v6);
arr.insert_at_vertices(s11, v4, v5);
// Step(c) - remove and merge faces to form a single hole in the traingle.
arr.remove_edge(e7);
arr.remove_edge(e8);
e5 = arr.merge_edge(e5, e6, Segment_2(e5->source()->point(),
e6->target()->point()));
e2 = arr.merge_edge(e4, e5, s2);
print_arrangement(arr);
return 0;
}
int main ()
{
Arrangement_2 arr;
Point_2 ps[N_POINTS];
Vertex_handle vhs[N_POINTS];
bool valid;
int k;
ps[0] = Point_2 (2, 2);
ps[1] = Point_2 (2, 7);
ps[2] = Point_2 (4, 9);
ps[3] = Point_2 (4, 5);
ps[4] = Point_2 (5, 3);
ps[5] = Point_2 (7, 1);
ps[6] = Point_2 (7, 5);
ps[7] = Point_2 (7, 7);
ps[8] = Point_2 (9, 3);
ps[9] = Point_2 (9, 6);
for (k = 0; k < N_POINTS; k++)
{
vhs[k] = insert_point (arr, ps[k]);
}
arr.insert_from_left_vertex (Segment_2 (Point_2 (2, 7), Point_2 (4, 7)),
vhs[1]);
TEST_VALIDITY(1);
arr.insert_from_right_vertex (Segment_2 (Point_2 (6, 6), Point_2 (7, 5)),
vhs[6]);
TEST_VALIDITY(2);
arr.insert_at_vertices (Segment_2 (Point_2 (7, 1), Point_2 (9, 3)),
vhs[5], vhs[8]);
TEST_VALIDITY(3);
arr.insert_at_vertices (Segment_2 (Point_2 (7, 5), Point_2 (9, 3)),
vhs[6], vhs[8]);
TEST_VALIDITY(4);
arr.insert_from_right_vertex (Segment_2 (Point_2 (1, 1), Point_2 (2, 7)),
vhs[1]);
TEST_VALIDITY(5);
insert_non_intersecting_curve (arr,
Segment_2 (Point_2 (1, 1), Point_2 (7, 1)));
TEST_VALIDITY(6);
insert_non_intersecting_curve (arr,
Segment_2 (Point_2 (4, 7), Point_2 (6, 6)));
TEST_VALIDITY(7);
insert_non_intersecting_curve (arr,
Segment_2 (Point_2 (2, 7), Point_2 (3, 3)));
TEST_VALIDITY(8);
insert_non_intersecting_curve (arr,
Segment_2 (Point_2 (3, 3), Point_2 (7, 1)));
TEST_VALIDITY(9);
arr.insert_at_vertices (Segment_2 (Point_2 (7, 5), Point_2 (9, 6)),
vhs[6], vhs[9]);
TEST_VALIDITY(10);
std::cout << "Arrangement size:"
<< " V = " << arr.number_of_vertices()
<< " (" << arr.number_of_isolated_vertices() << " isolated)"
<< ", E = " << arr.number_of_edges()
<< ", F = " << arr.number_of_faces() << std::endl;
// Check the validity more thoroughly.
valid = is_valid(arr);
std::cout << "Arrangement is "
<< (valid ? "valid." : "NOT valid!") << std::endl;
return (0);
}
int main()
{
std::list<Curve_2> curves;
// Create a circle centered at the origin with squared radius 2.
Kernel::Point_2 c1 = Kernel::Point_2(0, 0);
Circle_2 circ1 = Circle_2(c1, CGAL::Exact_rational(2));
curves.push_back(Curve_2(circ1));
// Create a circle centered at (2,3) with radius 3/2 - note that
// as the radius is rational we use a different curve constructor.
Kernel::Point_2 c2 = Kernel::Point_2(2, 3);
curves.push_back(Curve_2(c2, CGAL::Exact_rational(3, 2)));
// Create a segment of the line (y = x) with rational endpoints.
Kernel::Point_2 s3 = Kernel::Point_2(-2, -2);
Kernel::Point_2 t3 = Kernel::Point_2(2, 2);
Segment_2 seg3 = Segment_2(s3, t3);
curves.push_back(Curve_2(seg3));
// Create a line segment with the same supporting line (y = x), but
// having one endpoint with irrational coefficients.
CoordNT sqrt_15 = CoordNT(0, 1, 15); // = sqrt(15)
Point_2 s4 = Point_2(3, 3);
Point_2 t4 = Point_2(sqrt_15, sqrt_15);
curves.push_back(Curve_2(seg3.supporting_line(), s4, t4));
// Create a circular arc that correspond to the upper half of the
// circle centered at (1,1) with squared radius 3. We create the
// circle with clockwise orientation, so the arc is directed from
// (1 - sqrt(3), 1) to (1 + sqrt(3), 1).
Kernel::Point_2 c5 = Kernel::Point_2(1, 1);
Circle_2 circ5 = Circle_2(c5, 3, CGAL::CLOCKWISE);
CoordNT one_minus_sqrt_3 = CoordNT(1, -1, 3);
CoordNT one_plus_sqrt_3 = CoordNT(1, 1, 3);
Point_2 s5 = Point_2(one_minus_sqrt_3, CoordNT(1));
Point_2 t5 = Point_2(one_plus_sqrt_3, CoordNT(1));
curves.push_back(Curve_2(circ5, s5, t5));
// Create a circular arc of the unit circle, directed clockwise from
// (-1/2, sqrt(3)/2) to (1/2, sqrt(3)/2). Note that we orient the
// supporting circle accordingly.
Kernel::Point_2 c6 = Kernel::Point_2(0, 0);
CoordNT sqrt_3_div_2 = CoordNT(CGAL::Exact_rational(0),
CGAL::Exact_rational(1,2),
CGAL::Exact_rational(3));
Point_2 s6 = Point_2(CGAL::Exact_rational(-1, 2), sqrt_3_div_2);
Point_2 t6 = Point_2(CGAL::Exact_rational(1, 2), sqrt_3_div_2);
curves.push_back(Curve_2(c6, 1, CGAL::CLOCKWISE, s6, t6));
// Create a circular arc defined by two endpoints and a midpoint,
// all having rational coordinates. This arc is the upper-right
// quarter of a circle centered at the origin with radius 5.
Kernel::Point_2 s7 = Kernel::Point_2(0, 5);
Kernel::Point_2 mid7 = Kernel::Point_2(3, 4);
Kernel::Point_2 t7 = Kernel::Point_2(5, 0);
curves.push_back(Curve_2(s7, mid7, t7));
// Construct the arrangement of the curves.
Arrangement_2 arr;
insert(arr, curves.begin(), curves.end());
// Print the size of the arrangement.
std::cout << "The arrangement size:" << std::endl
<< " V = " << arr.number_of_vertices()
<< ", E = " << arr.number_of_edges()
<< ", F = " << arr.number_of_faces() << std::endl;
return 0;
}
int main ()
{
// Construct the initial arrangement.
Arrangement_2 arr;
Segment_2 segs[N_SEGMENTS];
Halfedge_handle hhs[N_SEGMENTS];
bool valid;
int k;
segs[0] = Segment_2 (Point_2 (5, 9), Point_2 (5, 11));
segs[1] = Segment_2 (Point_2 (5, 9), Point_2 (7, 9));
segs[2] = Segment_2 (Point_2 (5, 11), Point_2 (7, 9));
segs[3] = Segment_2 (Point_2 (7, 6), Point_2 (9, 7));
segs[4] = Segment_2 (Point_2 (9, 7), Point_2 (7, 9));
segs[5] = Segment_2 (Point_2 (5, 9), Point_2 (7, 6));
segs[6] = Segment_2 (Point_2 (10, 11), Point_2 (8, 13));
segs[7] = Segment_2 (Point_2 (8, 13), Point_2 (11, 12));
segs[8] = Segment_2 (Point_2 (10, 11), Point_2 (11, 12));
segs[9] = Segment_2 (Point_2 (1, 20), Point_2 (5, 1));
segs[10] = Segment_2 (Point_2 (5, 1), Point_2 (12, 6));
segs[11] = Segment_2 (Point_2 (1, 20), Point_2 (12, 6));
segs[12] = Segment_2 (Point_2 (13, 13), Point_2 (13, 15));
segs[13] = Segment_2 (Point_2 (13, 15), Point_2 (15, 12));
segs[14] = Segment_2 (Point_2 (13, 13), Point_2 (15, 12));
segs[15] = Segment_2 (Point_2 (11, 12), Point_2 (13, 13));
segs[16] = Segment_2 (Point_2 (1, 20), Point_2 (11, 17));
segs[17] = Segment_2 (Point_2 (11, 17), Point_2 (20, 13));
segs[18] = Segment_2 (Point_2 (12, 6), Point_2 (20, 13));
segs[19] = Segment_2 (Point_2 (15, 12), Point_2 (20, 13));
segs[20] = Segment_2 (Point_2 (5, 1), Point_2 (20, 1));
segs[21] = Segment_2 (Point_2 (20, 1), Point_2 (20, 13));
segs[22] = Segment_2 (Point_2 (15, 5), Point_2 (17, 3));
segs[23] = Segment_2 (Point_2 (13, 3), Point_2 (17, 3));
segs[24] = Segment_2 (Point_2 (12, 6), Point_2 (13, 3));
segs[25] = Segment_2 (Point_2 (17, 3), Point_2 (20, 1));
for (k = 0; k < N_SEGMENTS; k++)
{
hhs[k] = insert_non_intersecting_curve (arr, segs[k]);
}
valid = arr.is_valid();
std::cout << "Arrangement size:"
<< " V = " << arr.number_of_vertices()
<< ", E = " << arr.number_of_edges()
<< ", F = " << arr.number_of_faces() << std::endl;
std::cout << "The arrangement is "
<< (valid ? "valid." : "NOT valid!") << std::endl;
if (! valid)
return (1);
// Remove some edges.
int del_indices[N_REMOVE] = {25, 23, 22, 1, 3, 11, 19, 15, 4, 24};
for (k = 0; k < N_REMOVE; k++)
{
arr.remove_edge (hhs[del_indices[k]]);
valid = arr.is_valid();
std::cout << " Removed " << k+1 << " segment(s), arrangement is "
<< (valid ? "valid." : "NOT valid!") << std::endl;
if (! valid)
return (1);
}
std::cout << "Final arrangement size:"
<< " V = " << arr.number_of_vertices()
<< ", E = " << arr.number_of_edges()
<< ", F = " << arr.number_of_faces() << std::endl;
// Check the validity more thoroughly.
valid = is_valid(arr);
std::cout << "Arrangement is "
<< (valid ? "valid." : "NOT valid!") << std::endl;
return (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;
}
void
arrangement::compute_pointInCells(Arrangement_2 &arr, std::vector<std::vector<double> > &points)
{
Walk_pl walk_pl(arr);
int cpt = 0;
for (Arrangement_2::Face_iterator face = arr.faces_begin(); face != arr.faces_end(); ++face)
{
if (face->is_unbounded())
face->set_data(-1);
else
{
// set data to each face
face->set_data(cpt++);
// find a point in this face
Arrangement_2::Ccb_halfedge_circulator previous = face->outer_ccb();
Arrangement_2::Ccb_halfedge_circulator first_edge = face->outer_ccb();
Arrangement_2::Ccb_halfedge_circulator edge = face->outer_ccb();
++edge;
do
{
std::vector<double> p1 = getPointMiddle(previous);
std::vector<double> p2 = getPointMiddle(edge);
std::vector<double> m;
m.push_back((p1[0]+p2[0])/2);
m.push_back((p1[1]+p2[1])/2);
Rational x_(m[0]);
Rational y_(m[1]);
Conic_point_2 p(x_,y_);
Arrangement_2::Vertex_handle v = insert_point(arr, p, walk_pl);
try
{
if (v->face()->data() == (cpt-1))
{
bool flag = false;
// test if it is not in holes and not in unbounded face
for (int i = 0; i < (int) convolutions_o.size(); ++i)
{
Walk_pl wpl(convolutions_o[i]);
Arrangement_2::Vertex_handle t = insert_point(convolutions_o[i], p, wpl);
if (t->face()->data() == 1)
{
convolutions_o[i].remove_isolated_vertex(t);
break;
}
else if (t->face()->data() == 2 || t->face()->data() == 0)
{
flag = true;
convolutions_o[i].remove_isolated_vertex(t);
break;
}
}
// then continue
if (!flag)
points.push_back(m);
else
{
--cpt;
face->set_data(-1);
}
arr.remove_isolated_vertex(v);
break;
}
arr.remove_isolated_vertex(v);
}
catch (const std::exception exn) {}
previous = edge;
++edge;
} while (edge != first_edge);
}
}
}
int main()
{
Arrangement_2 arr;
// Construct an arrangement of five linear objects.
std::vector<X_monotone_curve_2> curves;
curves.push_back(Ray_2(Point_2(0, 0), Point_2(0, 1)));
curves.push_back(Ray_2(Point_2(0, 0), Point_2(1, 0)));
curves.push_back(Ray_2(Point_2(0, 0), Point_2(0, -1)));
curves.push_back(Ray_2(Point_2(0, 0), Point_2(-1, 0)));
curves.push_back(Ray_2(Point_2(0, 0), Point_2(1, 1)));
curves.push_back(Ray_2(Point_2(0, 0), Point_2(1, -1)));
curves.push_back(Ray_2(Point_2(0, 0), Point_2(-1, 1)));
curves.push_back(Ray_2(Point_2(0, 0), Point_2(-1, -1)));
std::vector<Halfedge_handle> hhs(curves.size());
for (size_t i = 0; i < curves.size(); i++)
hhs[i] = insert_non_intersecting_curve(arr, curves[i]);
bool valid = arr.is_valid();
std::cout << "Arrangement size:"
<< " V = " << arr.number_of_vertices()
<< ", E = " << arr.number_of_edges()
<< ", F = " << arr.number_of_faces() << std::endl;
std::cout << "The arrangement is "
<< (valid ? "valid." : "NOT valid!") << std::endl;
if (! valid) return (1);
// Remove the edges.
for (size_t i = 0; i < hhs.size(); i++) {
arr.remove_edge(hhs[i]);
bool valid = arr.is_valid();
std::cout << " Removed " << i+1 << " curve(s), arrangement is "
<< (valid ? "valid." : "NOT valid!") << std::endl;
if (! valid) return (1);
}
std::cout << "Final arrangement size:"
<< " V = " << arr.number_of_vertices()
<< ", E = " << arr.number_of_edges()
<< ", F = " << arr.number_of_faces() << std::endl;
if (!::test(arr)) return 1;
/* Construct another arrangement of a segment connected to a ray.
* First remove the ray, then remove the segment.
*
* o---------------o
* | |
* | |
* | |
* | o--o----|
* | |
* | |
* | |
* o---------------o
*/
if (!test_ray(arr, arr.unbounded_face())) return 1;
/* Construct another arrangement of a segment connected to a ray.
* First remove the ray, then remove the segment.
*
* o---------------o
* | |
* | |
* | |
* | o--o----|
* | |
* o---------------o
* | |
* o---------------o
*/
Line_2 l1(Point_2(0, -1), Point_2(1, -1));
Halfedge_handle eh1 =
arr.insert_in_face_interior(X_monotone_curve_2(l1), arr.unbounded_face());
if (!test_ray(arr, eh1->face())) return 1;
arr.remove_edge(eh1);
/* Construct another arrangement of a segment connected to a ray.
* First remove the ray, then remove the segment.
*
* o-----o---------o
* | | |
* | | |
* | | |
* | | o--o----|
* | | |
* | | |
* | | |
* o-----o---------o
*/
Line_2 l2(Point_2(-1, 0), Point_2(-1, 1));
Halfedge_handle eh2 =
arr.insert_in_face_interior(X_monotone_curve_2(l2), arr.unbounded_face());
if (!test_ray(arr, eh2->twin()->face())) return 1;
arr.remove_edge(eh2);
return 0;
}
int main ()
{
CGAL::set_pretty_mode(std::cout); // for nice printouts.
// Traits class object
AK1 ak1;
Traits_2 traits(&ak1);
// constructor for rational functions
Traits_2::Construct_curve_2 construct = traits.construct_curve_2_object();
// a polynomial representing x .-)
Polynomial_1 x = CGAL::shift(Polynomial_1(1),1);
// container storing all arcs
std::vector<Traits_2::Curve_2> arcs;
// Create the rational functions (y = 1 / x), and (y = -1 / x).
Polynomial_1 P1(1);
Polynomial_1 minusP1(-P1);
Polynomial_1 Q1 = x;
arcs.push_back(construct(P1, Q1));
arcs.push_back(construct(minusP1, Q1));
// Create a bounded segments of the parabolas (y = -4*x^2 + 3) and
// (y = 4*x^2 - 3), defined over [-sqrt(3)/2, sqrt(3)/2].
Polynomial_1 P2 = -4*x*x+3;
Polynomial_1 minusP2 = -P2;
std::vector<std::pair<Alg_real_1,int> > roots;
// [-sqrt(3)/2, sqrt(3)/2]
traits.algebraic_kernel_d_1()->solve_1_object()(P2, std::back_inserter(roots));
arcs.push_back(construct(P2, roots[0].first, roots[1].first));
arcs.push_back(construct(minusP2, roots[0].first, roots[1].first));
// Create the rational function (y = 1 / 2*x) for x > 0, and the
// rational function (y = -1 / 2*x) for x < 0.
Polynomial_1 P3(1);
Polynomial_1 minusP3(-P3);
Polynomial_1 Q3 = 2*x;
arcs.push_back(construct(P3, Q3, Alg_real_1(0), true));
arcs.push_back(construct(minusP3, Q3, Alg_real_1(0), false));
// Construct the arrangement of the six arcs.
//Arrangement_2 arr(&traits);
Arrangement_2 arr;
insert(arr, arcs.begin(), arcs.end());
// Print the arrangement size.
std::cout << "The arrangement size:" << std::endl
<< " V = " << arr.number_of_vertices()
<< " (plus " << arr.number_of_vertices_at_infinity()
<< " at infinity)"
<< ", E = " << arr.number_of_edges()
<< ", F = " << arr.number_of_faces()
<< " (" << arr.number_of_unbounded_faces() << " unbounded)"
<< std::endl << std::endl;
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;
}
