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Filters for the y()-function

This commit is contained in:
Michael Kerber 2007-12-12 16:21:11 +00:00
parent 65f4870ef5
commit ab20fb2cb7
2 changed files with 40 additions and 14 deletions
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5
Algebraic_kernel_d/include/CGAL/Algebraic_curve_kernel_2.h
View File

@ -451,6 +451,11 @@ public:
Comparison_result operator()(const Xy_coordinate_2& xy1,
const Xy_coordinate_2& xy2) const {
// It is easier if the x coordinates are equal!
if(Compare_x_2()(xy1.x(),xy2.x()) == CGAL::EQUAL) {
return Compare_xy_2()(xy1,xy2);
}
return (Compare_x_2()(xy1.y(), xy2.y()));
}
};

49
Algebraic_kernel_d/include/CGAL/Algebraic_curve_kernel_2/Xy_coordinate_2.h
View File

@ -264,33 +264,55 @@ public:
* and using get_approximation_y() instead whenever approximations suffice.
*/
X_coordinate_1 y() const {
std::cout << "y() starts" << std::endl;
typedef typename Algebraic_curve_kernel_2::Polynomial_2::Polynomial_2
Polynomial_2;
Polynomial_2 f = curve().f();
typedef typename Polynomial_2::NT Polynomial_1;
// This will be the defining polynomial of y
Polynomial_1 y_pol;
// Filter: If we know that the point is critical, we can use
// the resultant of f and f_y with respect to x as polynomial
int i;
bool is_event;
bool point_is_certainly_critical = false;
curve().x_to_index(x(),i,is_event);
if(is_event) {
typename Curve_2::Event1_info ev_info = curve().event_info(i);
if(ev_info.num_arcs_left(arcno()) != 1 ||
ev_info.num_arcs_left(arcno()) != 1) {
point_is_certainly_critical = true;
y_pol = NiX::make_square_free(
NiX::resultant
(transpose_bivariate_polynomial(f),
transpose_bivariate_polynomial(NiX::diff(f))));
}
}
if(! point_is_certainly_critical) {
Polynomial_2 r(x().polynomial());
y_pol = NiX::make_square_free(
NiX::resultant(transpose_bivariate_polynomial(f),
transpose_bivariate_polynomial(r) ));
}
typename NiX::Real_roots<X_coordinate_1,
NiX::Descartes<Polynomial_1, Boundary> > real_roots;
Polynomial_2 r(x().polynomial());
Polynomial_2 f = curve().f();
std::cout << "res.." << std::flush;
Polynomial_1 y_pol
= NiX::make_square_free(
NiX::resultant(transpose_bivariate_polynomial(f),
transpose_bivariate_polynomial(r)));
std::cout << "done, degree=" << y_pol.degree() << std::endl;
std::vector<X_coordinate_1> y_roots;
std::cout << "roots.." << std::flush;
real_roots(y_pol,
std::back_inserter(y_roots));
std::cout << "done" << std::endl;
Boundary_interval y_iv = get_approximation_y();
typename std::vector<X_coordinate_1>::const_iterator it
= y_roots.begin();
std::cout << "Loop starts" << std::endl;
while(it != y_roots.end()) {
if(it->high() < y_iv.lower()) {
it++;
@ -302,7 +324,6 @@ public:
refine_y();
y_iv = get_approximation_y();
}
std::cout << "Loop ends" << std::endl;
CGAL_assertion(it!=y_roots.end());
return X_coordinate_1( y_pol, it->low(), it->high() );
}