You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
66 lines
2.6 KiB
66 lines
2.6 KiB
12 months ago
|
// Special procedures for the ``generic'' algorithm, i.e. going through the param
|
||
|
|
// of a quadric of inertia (2,2)
|
||
|
|
|
||
|
|
#ifndef _qi_inter_with_22_
|
||
|
|
#define _qi_inter_with_22_
|
||
|
|
|
||
|
|
/** QI */
|
||
|
|
#include <libqi/kernel/QIHompoly.h>
|
||
|
|
#include <libqi/kernel/QIQsicStruct.h>
|
||
|
|
|
||
|
|
using namespace std;
|
||
|
|
using namespace rpl;
|
||
|
|
|
||
|
|
// Enter namespace QI
|
||
|
|
namespace QI {
|
||
|
|
|
||
|
|
// Input : initial quadrics q1, q2
|
||
|
|
// determinental equation of the pencil : det_p
|
||
|
|
// a quadric 22 : q
|
||
|
|
// case_flag = 0 if the intersection is a smooth quartic, 2 real affinely finite
|
||
|
|
// = 1 " 1 real affinely finite
|
||
|
|
// = 2 " 2 real affinely infinite
|
||
|
|
// = 3 if intersection is a cubic and a line secant
|
||
|
|
// = 4 " non-secant
|
||
|
|
// = 5 if intersection is two real skew lines
|
||
|
|
// Output : Compute the Parameterization s1 + sqrt(xi) s2 of a quadric 22 in the pencil
|
||
|
|
// and the Associated biquadratic equation poly1 + sqrt(xi) poly2 = 0
|
||
|
|
// Call smooth_quartic(...) or cubic_line(...) for computing the intersection curve
|
||
|
|
quad_inter <bigint> intersection_with_quadric22(const bigint_matrix &q1,
|
||
|
|
const bigint_matrix &q2,
|
||
|
|
const hom_polynomial <bigint> &det_p,
|
||
|
|
const bigint_matrix &q,
|
||
|
|
const unsigned int case_flag,
|
||
|
|
const int opt_level,
|
||
|
|
ostream &s);
|
||
|
|
|
||
|
|
// Input : initial quadrics q1, q2
|
||
|
|
// determinental equation of the pencil : det_p
|
||
|
|
// a quadric 22 q
|
||
|
|
// Output : a quadric 22 quadric_sol and a point on it point_sol
|
||
|
|
// the determinant a^2.b of the quadric 22 in the form [a,b]
|
||
|
|
void find_quadric_22_and_point(const bigint_matrix &q1, const bigint_matrix &q2,
|
||
|
|
const hom_polynomial <bigint> &det_p,
|
||
|
|
const bigint_matrix &q_cp,
|
||
|
|
bigint_matrix &quadric_sol,
|
||
|
|
math_vector <bigint> &point_sol,
|
||
|
|
bigint &det_R,
|
||
|
|
math_vector <bigint> &det_sol,
|
||
|
|
const int opt_level, ostream &s);
|
||
|
|
|
||
|
|
// Input: a matrix q of inertia 2,2
|
||
|
|
// a point on it and the determinant of q in the form [a,b] such that det(q)=a^2. b
|
||
|
|
// Output : Parameterization of the quadric : s1 + sqrt(det_q[1]) s2
|
||
|
|
// If det_q[1]=1 then s2=[0,0,0,0]
|
||
|
|
void find_parameterization_quadric_22(const math_matrix <bigint> &q_cp,
|
||
|
|
const math_vector <bigint> &point_on_q,
|
||
|
|
const math_vector <bigint> &det_q_cp,
|
||
|
|
const bigint &det_R,
|
||
|
|
surface_param <bigint> &s1,
|
||
|
|
surface_param <bigint> &s2,
|
||
|
|
const int opt_level, ostream &s);
|
||
|
|
|
||
|
|
} // end of namespace QI
|
||
|
|
|
||
|
|
#endif
|