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Sign_2 predicate added

This commit is contained in:
Pavel Emeliyanenko 2007-10-18 12:40:29 +00:00
parent 2259365505
commit 5836bca0b9
1 changed files with 84 additions and 19 deletions
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103
Algebraic_kernel_d/include/CGAL/Algebraic_curve_kernel_2.h
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@ -30,6 +30,8 @@
#include <CGAL/Algebraic_curve_kernel_2/Curve_pair_vertical_line_1.h>
#include <CGAL/Algebraic_curve_kernel_2/Curve_pair_analysis_2.h>
#include <CGAL/Algebraic_curve_kernel_2/Algebraic_real_traits.h>
#include <CGAL/Algebraic_curve_kernel_2/LRU_hashed_map.h>
#include <algorithm>
@ -277,6 +279,10 @@ public:
//! type of a curve point
typedef CGALi::Xy_coordinate_2<Self> Xy_coordinate_2;
//! type of algebraic real traits
typedef CGALi::Algebraic_real_traits<Xy_coordinate_2,
Internal_curve_pair_2> Algebraic_real_traits;
//! \brief comparison of x-coordinates
struct Compare_x_2 :
public Binary_function<X_coordinate_1, X_coordinate_1,
@ -638,25 +644,84 @@ public:
// Algebraic_surface_3_z_at_xy_isolator_traits_base.h
if(p.id() == r.curve().id()) // point lies on the same curve
return CGAL::ZERO;
// Curve_pair_2 cp = Self::get_curve_pair_cache()
// (std::make_pair(p, r.curve()));
// typename Self::Curve_pair_analysis_2 cpa_2(cp);
// this is to keep compiler happy ))
typename Self::Curve_pair_analysis_2 cpa_2(
(Curve_analysis_2(p)),(Curve_analysis_2(r.curve())));
typename Self::Curve_pair_analysis_2::Curve_pair_vertical_line_1
cpv_line = cpa_2.vertical_line_at_exact_x(r.x());
// check only if there is an intersection of both curve along this line
if(cpv_line.is_event() && cpv_line.is_intersection()) {
// get an y-position of the point r
int idx = cpv_line.get_event_of_curve(r.arcno(), 1);
std::pair<int, int> ipair = cpv_line.get_curves_at_event(idx);
if(ipair.first != -1&&ipair.second != -1)
return CGAL::ZERO; // intersection of both curves
typedef typename Self::Curve_analysis_2 Curve_analysis_2;
typedef typename Self::Curve_pair_analysis_2 Curve_pair_analysis_2;
Curve_analysis_2 ca_2(p), ca_2r(r.curve());
Curve_pair_analysis_2 cpa_2(ca_2, ca_2r);
typename Curve_analysis_2::Curve_vertical_line_1 cv_line =
ca_2.vertical_line_for_x(r.x());
// fast check for the presence of vertical line at r.x()
if(cv_line.covers_line())
return CGAL::ZERO;
// in case there is no event at this x-coordinate, vertical
// line at some rational x over an interval is returned
typename Curve_pair_analysis_2::Curve_pair_vertical_line_1
cpv_line = cpa_2.vertical_line_for_x(r.x());
// get an y-position of the point r
int idx = cpv_line.get_event_of_curve(r.arcno(), 1);
std::pair<int, int> ipair;
if(cpv_line.is_event()) {
if(cpv_line.is_intersection()) {
ipair = cpv_line.get_curves_at_event(idx);
// easy case: there is a 2-curve intersection at this x
if(ipair.first != -1&&ipair.second != -1)
return CGAL::ZERO; // intersection of both curves
}
// check if there is an event of curve p at r.x()
if(cv_line.is_event()) {
CGAL_error("this is not an easy case..))");
}
// this is an event of r.curve() -> therefore cpv_line.x()
// is given as algebraic real (not rational) and r.arcno() is
// an event arcno
}
// otherwise compute the sign..
return CGAL::SMALLER;
// there is no event at r.x() of curve p hence we're free to
// pick up any rational boundary over an interval to compute the
// sign at
int arcno_low = -1, arcno_high = -1;
typedef typename Self::Algebraic_real_traits Traits;
typedef typename Traits::Boundary Boundary;
Boundary boundary_y;
Xy_coordinate_2 xy1, xy2;
// idx-1 and idx+1 are consecutive event indices over r.x()
if(idx > 0) {
ipair = cpv_line.get_curves_at_event(idx-1);
arcno_low = ipair.first;
xy1 = cv_line.get_algebraic_real_2(arcno_low);
}
if(idx < cv_line.number_of_events() - 1) {
ipair = cpv_line.get_curves_at_event(idx+1);
arcno_high = ipair.first;
xy2 = cv_line.get_algebraic_real_2(arcno_high);
}
if(arcno_low != -1) {
boundary_y = (arcno_high != -1 ?
typename Traits::Boundary_between()(xy1, xy2) :
typename Traits::Upper_boundary()(xy1));
} else {
// if arcno_high == -1 pick up arbitrary rational since the
// curve p does not cross vertical line at r.x()
boundary_y = (arcno_high != -1 ?
typename Traits::Lower_boundary()(xy2) : Boundary(0));
}
X_coordinate_1 boundary_x = cv_line.x();
if(boundary_x.low() != boundary_x.high())
std::cout << "oops very bizarre error occurred..\n";
NiX::Polynomial<Boundary> poly =
NiX::substitute_x(p.f(), boundary_x.low());
return poly.sign_at(boundary_y);
}
};
CGAL_Algebraic_Kernel_pred(Sign_at_2, sign_at_2_object);
@ -689,7 +754,7 @@ public:
OutputIteratorRoots roots, OutputIteratorMult mults) const
{
// these tests are quite expensive... do we really need them ??
/*CGAL_precondition_code (
CGAL_precondition_code (
typename Self::Has_finite_number_of_self_intersections_2
not_self_overlapped;
typename Self::Has_finite_number_of_intersections_2
@ -697,7 +762,7 @@ public:
CGAL_precondition(not_self_overlapped(p1) &&
not_self_overlapped(p2));
CGAL_precondition(do_not_overlap(p1, p2));
);*/
);
typename Self::Curve_pair_analysis_2 cpa_2(
(Curve_analysis_2(p1)),(Curve_analysis_2(p2)));
typename Self::Curve_pair_analysis_2::Curve_pair_vertical_line_1