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Sign_2 revised

This commit is contained in:
Pavel Emeliyanenko 2007-10-21 13:38:15 +00:00
parent a9af048652
commit bda42a3b66
1 changed files with 73 additions and 22 deletions
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95
Algebraic_kernel_d/include/CGAL/Algebraic_curve_kernel_2.h
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@ -632,7 +632,7 @@ public:
* computes the sign of a bivariate polynomial \c p evaluated at the root
* \c r of a system of two bivariate polynomial equations
*
* return the value convertible into \c CGAL::Sign
* returns a value convertible to \c CGAL::Sign
*/
struct Sign_at_2 :
public Binary_function< Polynomial_2, Xy_coordinate_2, Sign > {
@ -650,8 +650,9 @@ public:
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());
typename Curve_analysis_2::Curve_vertical_line_1
cv_line = ca_2.vertical_line_for_x(r.x()),
cv_line_r = ca_2r.vertical_line_for_x(r.x());
// fast check for the presence of vertical line at r.x()
if(cv_line.covers_line())
@ -665,6 +666,8 @@ public:
// get an y-position of the point r
int idx = cpv_line.get_event_of_curve(r.arcno(), 1);
std::pair<int, int> ipair;
X_coordinate_1 boundary_x;
if(cpv_line.is_event()) {
if(cpv_line.is_intersection()) {
ipair = cpv_line.get_curves_at_event(idx);
@ -674,34 +677,76 @@ public:
}
// 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..))");
}
if(cv_line_r.is_event())
CGAL_error("you're lucky )) this is not an easy \
case..");
//std::cout << "sign at event of curve p\n";
// this is an event of curve p but not of r.curve() ->
// shift to the left of r.x() otherwise we would find
// arc-numbers of p at event point (r.arcno() is valid
// over curve-pair interval)
cpv_line = cpa_2.vertical_line_of_interval(
cpv_line.get_index());
// recompute vertical line of p and y-position of r
// (however y-position of r.arcno() should not change
// since it can only happen at 2-curve event or at event
// of g)
idx = cpv_line.get_event_of_curve(r.arcno(), 1);
// need cv-line over interval ?
cv_line = ca_2.vertical_line_of_interval(
cv_line.get_index());
boundary_x = cpv_line.x();
} else if(cv_line_r.is_event()) {
// std::cout << "sign at event of curve r: cpv_line x: "
// << cpv_line.x() << "\n";
// 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
}
// an event arcno
// need to recompute boundary_x (but leave cpv_line
// unchanged otherwise r.arcno() is not valid)
boundary_x = cpa_2.vertical_line_of_interval(
cpv_line.get_index()).x();
}
} else {
// 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
boundary_x = cpv_line.x();
// std::cout << "sign over curve pair interval\n";
}
// obtain vertical line at exact rational x
cv_line = ca_2.vertical_line_at_exact_x(
X_coordinate_1(boundary_x.low()));
int arcno_low = -1, arcno_high = -1;
int arcno_low = -1, arcno_high = -1, i = idx;
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);
// arcno_low and arcno_high are consecutive event indices of
// curve p at r.x()
while(i-- > 0) {
ipair = cpv_line.get_curves_at_event(i);
if(ipair.first != -1) {
arcno_low = ipair.first;
xy1 = cv_line.get_algebraic_real_2(arcno_low);
break;
}
}
i = idx;
while(i++ < cpv_line.number_of_events() - 1) {
ipair = cpv_line.get_curves_at_event(i);
if(ipair.first != -1) {
arcno_high = ipair.first;
xy2 = cv_line.get_algebraic_real_2(arcno_high);
break;
}
}
// std::cout << "arcno_low : " << arcno_low << "; arcno_high: " <<
// arcno_high << "\n";
if(arcno_low != -1) {
boundary_y = (arcno_high != -1 ?
@ -713,11 +758,17 @@ public:
boundary_y = (arcno_high != -1 ?
typename Traits::Lower_boundary()(xy2) : Boundary(0));
}
X_coordinate_1 boundary_x = cv_line.x();
// if(arcno_low != -1&& arcno_high!=-1) {
// std::cout << xy1 << "; " << xy2 << "\n";
// }
//
if(boundary_x.low() != boundary_x.high())
std::cout << "oops very bizarre error occurred..\n";
// std::cout << "target pt: " <<
// NiX::to_double(boundary_x.low()) << "; " <<
// NiX::to_double(boundary_y) << "\n";
NiX::Polynomial<Boundary> poly =
NiX::substitute_x(p.f(), boundary_x.low());