SPAR/AIModule/BWTA/vendors/CGAL/CGAL/Arr_geometry_traits/Conic_intersections_2.h File Reference

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Functions
template<class Nt_traits >
CGAL_BEGIN_NAMESPACE int	_compute_resultant_roots (Nt_traits &nt_traits, const typename Nt_traits::Integer &r1, const typename Nt_traits::Integer &s1, const typename Nt_traits::Integer &t1, const typename Nt_traits::Integer &u1, const typename Nt_traits::Integer &v1, const typename Nt_traits::Integer &w1, const int &deg1, const typename Nt_traits::Integer &r2, const typename Nt_traits::Integer &s2, const typename Nt_traits::Integer &t2, const typename Nt_traits::Integer &u2, const typename Nt_traits::Integer &v2, const typename Nt_traits::Integer &w2, const int &deg2, typename Nt_traits::Algebraic *xs)
template<class Nt_traits >
int	_compute_resultant_roots (Nt_traits &nt_traits, const typename Nt_traits::Algebraic &r, const typename Nt_traits::Algebraic &s, const typename Nt_traits::Algebraic &t, const typename Nt_traits::Algebraic &u, const typename Nt_traits::Algebraic &v, const typename Nt_traits::Algebraic &w, const int &deg1, const typename Nt_traits::Algebraic &A, const typename Nt_traits::Algebraic &B, const typename Nt_traits::Algebraic &C, typename Nt_traits::Algebraic *xs)

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Detailed Description

Implementation of functions related to the intersection of conics curves.

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Function Documentation

template<class Nt_traits >

CGAL_BEGIN_NAMESPACE int _compute_resultant_roots	(	Nt_traits &	nt_traits,
		const typename Nt_traits::Integer &	r1,
		const typename Nt_traits::Integer &	s1,
		const typename Nt_traits::Integer &	t1,
		const typename Nt_traits::Integer &	u1,
		const typename Nt_traits::Integer &	v1,
		const typename Nt_traits::Integer &	w1,
		const int &	deg1,
		const typename Nt_traits::Integer &	r2,
		const typename Nt_traits::Integer &	s2,
		const typename Nt_traits::Integer &	t2,
		const typename Nt_traits::Integer &	u2,
		const typename Nt_traits::Integer &	v2,
		const typename Nt_traits::Integer &	w2,
		const int &	deg2,
		typename Nt_traits::Algebraic *	xs
	)

Compute the roots of the resultants of the two bivariate polynomials: C1: r1*x^2 + s1*y^2 + t1*xy + u1*x + v1*y + w1 = 0 C2: r2*x^2 + s2*y^2 + t2*xy + u2*x + v2*y + w2 = 0

Parameters:

deg1	The degree of the first curve.
deg2	The degree of the second curve.
xs	Output: The real-valued roots of the polynomial, sorted in an ascending order.

Precondition:

xs must be a vector of size 4.

Returns:

The number of distinct roots found.

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template<class Nt_traits >

int _compute_resultant_roots	(	Nt_traits &	nt_traits,
		const typename Nt_traits::Algebraic &	r,
		const typename Nt_traits::Algebraic &	s,
		const typename Nt_traits::Algebraic &	t,
		const typename Nt_traits::Algebraic &	u,
		const typename Nt_traits::Algebraic &	v,
		const typename Nt_traits::Algebraic &	w,
		const int &	deg1,
		const typename Nt_traits::Algebraic &	A,
		const typename Nt_traits::Algebraic &	B,
		const typename Nt_traits::Algebraic &	C,
		typename Nt_traits::Algebraic *	xs
	)

Compute the roots of the resultants of the two bivariate polynomials: C1: r*x^2 + s*y^2 + t*xy + u*x + v*y + w = 0 C2: A*x + B*y + C = 0

Parameters:

deg1	The degree of the first curve.
xs	Output: The real-valued roots of the polynomial, sorted in an ascending order.

Precondition:

xs must be a vector of size 4.

Returns:

The number of distinct roots found.

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