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;
}
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;
}
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()
{
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()
{
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 ()
{
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;
}
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 ()
{
// 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);
}