#include <Conic_arc_2.h>

Collaboration diagram for _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >:

Classes
struct	Extra_data
Public Types
typedef Rat_kernel_	Rat_kernel
typedef Alg_kernel_	Alg_kernel
typedef Nt_traits_	Nt_traits
typedef _Conic_arc_2 < Rat_kernel, Alg_kernel, Nt_traits >	Self
typedef Rat_kernel::FT	Rational
typedef Rat_kernel::Point_2	Rat_point_2
typedef Rat_kernel::Segment_2	Rat_segment_2
typedef Rat_kernel::Circle_2	Rat_circle_2
typedef Nt_traits::Integer	Integer
typedef Alg_kernel::FT	Algebraic
typedef Alg_kernel::Point_2	Point_2
typedef _Conic_point_2 < Alg_kernel >	Conic_point_2
Public Member Functions
Construction and destruction functions.
	_Conic_arc_2 ()
	_Conic_arc_2 (const Self &arc)
	_Conic_arc_2 (const Rational &r, const Rational &s, const Rational &t, const Rational &u, const Rational &v, const Rational &w)
	_Conic_arc_2 (const Rational &r, const Rational &s, const Rational &t, const Rational &u, const Rational &v, const Rational &w, const Orientation &orient, const Point_2 &source, const Point_2 &target)
	_Conic_arc_2 (const Rat_segment_2 &seg)
	_Conic_arc_2 (const Rat_circle_2 &circ)
	_Conic_arc_2 (const Rat_circle_2 &circ, const Orientation &orient, const Point_2 &source, const Point_2 &target)
	_Conic_arc_2 (const Rat_point_2 &p1, const Rat_point_2 &p2, const Rat_point_2 &p3)
	_Conic_arc_2 (const Rat_point_2 &p1, const Rat_point_2 &p2, const Rat_point_2 &p3, const Rat_point_2 &p4, const Rat_point_2 &p5)
	_Conic_arc_2 (const Rational &r, const Rational &s, const Rational &t, const Rational &u, const Rational &v, const Rational &w, const Orientation &orient, const Point_2 &app_source, const Rational &r_1, const Rational &s_1, const Rational &t_1, const Rational &u_1, const Rational &v_1, const Rational &w_1, const Point_2 &app_target, const Rational &r_2, const Rational &s_2, const Rational &t_2, const Rational &u_2, const Rational &v_2, const Rational &w_2)
virtual	~_Conic_arc_2 ()
const Self &	operator= (const Self &arc)
Get the arc properties.
bool	is_valid () const
const Integer &	r () const
const Integer &	s () const
const Integer &	t () const
const Integer &	u () const
const Integer &	v () const
const Integer &	w () const
bool	is_x_monotone () const
bool	is_y_monotone () const
bool	is_full_conic () const
const Point_2 &	source () const
const Point_2 &	target () const
Orientation	orientation () const
Bbox_2	bbox () const
Modifying functions.
void	set_source (const Point_2 &ps)
void	set_target (const Point_2 &pt)
Compute points on the arc.
int	vertical_tangency_points (Point_2 *vpts) const
int	horizontal_tangency_points (Point_2 *hpts) const
int	points_at_x (const Point_2 &p, Point_2 *ps) const
int	points_at_y (const Point_2 &p, Point_2 *ps) const
Protected Types
enum	{ IS_VALID = 1, IS_FULL_CONIC = 2 }
Protected Member Functions
Auxiliary functions.
Sign	_sign_of_extra_data (const Algebraic &px, const Algebraic &py) const
bool	_is_on_supporting_conic (const Point_2 &p) const
bool	_is_between_endpoints (const Point_2 &p) const
bool	_is_strictly_between_endpoints (const Point_2 &p) const
int	_conic_vertical_tangency_points (Point_2 *ps) const
int	_conic_horizontal_tangency_points (Point_2 *ps) const
int	_conic_get_y_coordinates (const Algebraic &x, Algebraic *ys) const
int	_conic_get_x_coordinates (const Algebraic &y, Algebraic *xs) const
int	_solve_quadratic_equation (const Algebraic &A, const Algebraic &B, const Algebraic &C, Algebraic &x_minus, Algebraic &x_plus) const
Protected Attributes
Integer	_r
Integer	_s
Integer	_t
Integer	_u
Integer	_v
Integer	_w
Orientation	_orient
int	_info
Conic_point_2	_source
Conic_point_2	_target
Extra_data *	_extra_data_P

Detailed Description

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>
class _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >

Representation of a conic arc -- a bounded segment that lies on a conic curve, the loci of all points satisfying the equation: r*x^2 + s*y^2 + t*xy + u*x + v*y +w = 0

The class is templated with three parameters: Rat_kernel A kernel that provides the input objects or coefficients. Rat_kernel::FT should be an integral or a rational type. Alg_kernel A geometric kernel, where Alg_kernel::FT is the number type for the coordinates of arrangement vertices, which are algebraic numbers of degree up to 4 (preferably it is CORE::Expr). Nt_traits A traits class for performing various operations on the integer, rational and algebraic types.

Member Typedef Documentation

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

typedef Alg_kernel_ _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::Alg_kernel

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

typedef Alg_kernel::FT _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::Algebraic

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

typedef _Conic_point_2<Alg_kernel> _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::Conic_point_2

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

typedef Nt_traits::Integer _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::Integer

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

typedef Nt_traits_ _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::Nt_traits

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

typedef Alg_kernel::Point_2 _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::Point_2

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

typedef Rat_kernel::Circle_2 _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::Rat_circle_2

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

typedef Rat_kernel_ _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::Rat_kernel

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

typedef Rat_kernel::Point_2 _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::Rat_point_2

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

typedef Rat_kernel::Segment_2 _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::Rat_segment_2

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

typedef Rat_kernel::FT _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::Rational

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

typedef _Conic_arc_2<Rat_kernel, Alg_kernel, Nt_traits> _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::Self

Member Enumeration Documentation

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

anonymous enum [protected]

Enumerator:

IS_VALID
IS_FULL_CONIC

Constructor & Destructor Documentation

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

_Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_Conic_arc_2 ( ) [inline]

Default constructor.

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

_Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_Conic_arc_2 ( const Self & arc ) [inline]

Copy constructor.

Parameters:

arc	The copied arc.

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

_Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_Conic_arc_2	(	const Rational &	r,
		const Rational &	s,
		const Rational &	t,
		const Rational &	u,
		const Rational &	v,
		const Rational &	w
	)		`[inline]`

Construct a conic arc which is the full conic: C: r*x^2 + s*y^2 + t*xy + u*x + v*y + w = 0

Precondition:: The conic C must be an ellipse (so 4rs - t^2 > 0).

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

_Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_Conic_arc_2	(	const Rational &	r,
		const Rational &	s,
		const Rational &	t,
		const Rational &	u,
		const Rational &	v,
		const Rational &	w,
		const Orientation &	orient,
		const Point_2 &	source,
		const Point_2 &	target
	)		`[inline]`

Construct a conic arc which lies on the conic: C: r*x^2 + s*y^2 + t*xy + u*x + v*y + w = 0

Parameters:

orient	The orientation of the arc (clockwise or counterclockwise).
source	The source point.
target	The target point.

Precondition:: The source and the target must be on the conic boundary and must not be the same.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

_Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_Conic_arc_2 ( const Rat_segment_2 & seg ) [inline]

Construct a conic arc from the given line segment.

Parameters:

seg	The line segment with rational endpoints.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

_Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_Conic_arc_2 ( const Rat_circle_2 & circ ) [inline]

Set a circular arc that corresponds to a full circle.

Parameters:

circ	The circle (with rational center and rational squared radius).

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

_Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_Conic_arc_2	(	const Rat_circle_2 &	circ,
		const Orientation &	orient,
		const Point_2 &	source,
		const Point_2 &	target
	)		`[inline]`

Set a circular arc that lies on the given circle: C: (x - x0)^2 + (y - y0)^2 = R^2

Parameters:

orient	The orientation of the circle.
source	The source point.
target	The target point.

Precondition:: The source and the target must be on the conic boundary and must not be the same.

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

_Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_Conic_arc_2	(	const Rat_point_2 &	p1,
		const Rat_point_2 &	p2,
		const Rat_point_2 &	p3
	)		`[inline]`

Construct a circular arc from the given three points.

Parameters:

p1	The arc source.
p2	A point in the interior of the arc.
p3	The arc target.

Precondition:: The three points must not be collinear.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

_Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_Conic_arc_2	(	const Rat_point_2 &	p1,
		const Rat_point_2 &	p2,
		const Rat_point_2 &	p3,
		const Rat_point_2 &	p4,
		const Rat_point_2 &	p5
	)		`[inline]`

Construct a conic arc from the given five points, specified by the points p1, p2, p3, p4 and p5.

Parameters:

p1	The source point of the given arc.
p2,p3,p4	Points lying on the conic arc, between p1 and p5.
p5	The target point of the given arc.

Precondition:: No three points are collinear.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

_Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_Conic_arc_2	(	const Rational &	r,
		const Rational &	s,
		const Rational &	t,
		const Rational &	u,
		const Rational &	v,
		const Rational &	w,
		const Orientation &	orient,
		const Point_2 &	app_source,
		const Rational &	r_1,
		const Rational &	s_1,
		const Rational &	t_1,
		const Rational &	u_1,
		const Rational &	v_1,
		const Rational &	w_1,
		const Point_2 &	app_target,
		const Rational &	r_2,
		const Rational &	s_2,
		const Rational &	t_2,
		const Rational &	u_2,
		const Rational &	v_2,
		const Rational &	w_2
	)		`[inline]`

Construct a conic arc which lies on the conic: C: r*x^2 + s*y^2 + t*xy + u*x + v*y + w = 0 The source and the target are specified by the intersection of the conic with: C_1: r_1*x^2 + s_1*y^2 + t_1*xy + u_1*x + v_1*y + w_1 = 0 C_2: r_2*x^2 + s_2*y^2 + t_2*xy + u_2*x + v_2*y + w_2 = 0 The user must also specify the source and the target with approximated coordinates. The actual intersection points that best fits the source (or the target) will be selected.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

virtual _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::~_Conic_arc_2 ( ) [inline, virtual]

Destructor.

Member Function Documentation

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

int _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_conic_get_x_coordinates	(	const Algebraic &	y,
		Algebraic *	xs
	)		const `[inline, protected]`

Find the x coordinates of the underlying conic at a given y coordinate.

Parameters:

y	The y coordinate.
xs	The output x coordinates.

Precondition:: The vector xs must be allocated at the size of 2.

Returns:: The number of x coordinates computed (either 0, 1 or 2).

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

int _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_conic_get_y_coordinates	(	const Algebraic &	x,
		Algebraic *	ys
	)		const `[inline, protected]`

Find the y coordinates of the underlying conic at a given x coordinate.

Parameters:

x	The x coordinate.
ys	The output y coordinates.

Precondition:: The vector ys must be allocated at the size of 2.

Returns:: The number of y coordinates computed (either 0, 1 or 2).

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

int _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_conic_horizontal_tangency_points ( Point_2 * ps ) const [inline, protected]

Find the horizontal tangency points of the undelying conic.

Parameters:

ps	The output points of horizontal tangency. This area must be allocated at the size of 2.

Returns:: The number of horizontal tangency points.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

int _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_conic_vertical_tangency_points ( Point_2 * ps ) const [inline, protected]

Find the vertical tangency points of the undelying conic.

Parameters:

ps	The output points of vertical tangency. This area must be allocated at the size of 2.

Returns:: The number of vertical tangency points.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

bool _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_is_between_endpoints ( const Point_2 & p ) const [inline, protected]

Check whether the given point is between the source and the target. The point is assumed to be on the conic's boundary.

Parameters:

p	The query point.

Returns:: (true) if the point is between the two endpoints, (false) if it is not.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

bool _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_is_on_supporting_conic ( const Point_2 & p ) const [inline, protected]

Check whether the given point lies on the supporting conic of the arc.

Parameters:

p	The query point.

Returns:: (true) if p lies on the supporting conic; (false) otherwise.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

bool _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_is_strictly_between_endpoints ( const Point_2 & p ) const [inline, protected]

Check whether the given point is strictly between the source and the target (but not any of them). The point is assumed to be on the conic's boundary.

Parameters:

p	The query point.

Returns:: (true) if the point is strictly between the two endpoints, (false) if it is not.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

Sign _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_sign_of_extra_data	(	const Algebraic &	px,
		const Algebraic &	py
	)		const `[inline, protected]`

Evaluate the sign of (a*x + b*y + c) stored with the extra data field at a given point.

Parameters:

px	The x-coordinate of query point.
py	The y-coordinate of query point.

Returns:: The sign of (a*x + b*y + c).

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

int _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_solve_quadratic_equation	(	const Algebraic &	A,
		const Algebraic &	B,
		const Algebraic &	C,
		Algebraic &	x_minus,
		Algebraic &	x_plus
	)		const `[inline, protected]`

Solve the given quadratic equation: Ax^2 + B*x + C = 0.

Parameters:

x_minus	The root obtained from taking -sqrt(discriminant).
x_plus	The root obtained from taking -sqrt(discriminant).

Returns:: The number of disticnt solutions to the equation.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

Bbox_2 _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::bbox ( ) const [inline]

Get a bounding box for the conic arc.

Returns:: The bounding box.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

int _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::horizontal_tangency_points ( Point_2 * hpts ) const [inline]

Calculate the horizontal tangency points of the arc.

Parameters:

hpts	The horizontal tangency points.

Precondition:: The hpts vector should be allocated at the size of 2.

Returns:: The number of horizontal tangency points.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

bool _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::is_full_conic ( ) const [inline]

Check whether the arc represents a full conic curve.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

bool _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::is_valid ( ) const [inline]

Check if the arc is valid.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

bool _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::is_x_monotone ( ) const [inline]

Check whether the arc is x-monotone.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

bool _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::is_y_monotone ( ) const [inline]

Check whether the arc is y-monotone.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

const Self& _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::operator= ( const Self & arc ) [inline]

Assignment operator.

Parameters:

arc	The copied arc.

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

Orientation _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::orientation ( ) const [inline]

Get the orientation of the arc.

Returns:: The orientation.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

int _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::points_at_x	(	const Point_2 &	p,
		Point_2 *	ps
	)		const `[inline]`

Find all points on the arc with a given x-coordinate.

Parameters:

p	A placeholder for the x-coordinate.
ps	The point on the arc at x(p).

Precondition:: The vector ps should be allocated at the size of 2.

Returns:: The number of points found.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

int _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::points_at_y	(	const Point_2 &	p,
		Point_2 *	ps
	)		const `[inline]`

Find all points on the arc with a given y-coordinate.

Parameters:

p	A placeholder for the y-coordinate.
ps	The point on the arc at x(p).

Precondition:: The vector ps should be allocated at the size of 2.

Returns:: The number of points found.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

const Integer& _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::r ( ) const [inline]

Get the coefficients of the underlying conic.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

const Integer& _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::s ( ) const [inline]

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

void _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::set_source ( const Point_2 & ps ) [inline]

Set the source point of the conic arc.

Parameters:

ps	The new source point.

Precondition:: The arc is not a full conic curve. ps must lie on the supporting conic curve.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

void _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::set_target ( const Point_2 & pt ) [inline]

Set the target point of the conic arc.

Parameters:

pt	The new source point.

Precondition:: The arc is not a full conic curve. pt must lie on the supporting conic curve.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

const Point_2& _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::source ( ) const [inline]

Get the arc's source.

Returns:: The source point.

Precondition:: The arc does not represent a full conic curve.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

const Integer& _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::t ( ) const [inline]

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

const Point_2& _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::target ( ) const [inline]

Get the arc's target.

Returns:: The target point.

Precondition:: The arc does not represent a full conic curve.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

const Integer& _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::u ( ) const [inline]

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

const Integer& _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::v ( ) const [inline]

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

int _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::vertical_tangency_points ( Point_2 * vpts ) const [inline]

Calculate the vertical tangency points of the arc.

Parameters:

vpts	The vertical tangency points.

Precondition:: The vpts vector should be allocated at the size of 2.

Returns:: The number of vertical tangency points.

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template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

const Integer& _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::w ( ) const [inline]

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Member Data Documentation

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

Extra_data* _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_extra_data_P [protected]

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

int _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_info [protected]

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

Orientation _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_orient [protected]

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

Integer _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_r [protected]

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

Integer _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_s [protected]

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

Conic_point_2 _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_source [protected]

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

Integer _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_t [protected]

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

Conic_point_2 _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_target [protected]

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

Integer _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_u [protected]

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

Integer _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_v [protected]

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>

Integer _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >::_w [protected]

The documentation for this class was generated from the following file:

SPAR/AIModule/BWTA/vendors/CGAL/CGAL/Arr_geometry_traits/Conic_arc_2.h

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Detailed Description

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_> class _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<class Rat_kernel_, class Alg_kernel_, class Nt_traits_>
class _Conic_arc_2< Rat_kernel_, Alg_kernel_, Nt_traits_ >