#include <Conic_x_monotone_arc_2.h>

Classes
struct	Less_conic_pair
Public Types
typedef Conic_arc_	Conic_arc_2
typedef _Conic_x_monotone_arc_2 < Conic_arc_2 >	Self
typedef Conic_arc_2::Alg_kernel	Alg_kernel
typedef Conic_arc_2::Algebraic	Algebraic
typedef Conic_arc_2::Point_2	Point_2
typedef Conic_arc_2::Conic_point_2	Conic_point_2
typedef Conic_point_2::Conic_id	Conic_id
typedef std::pair< Conic_id, Conic_id >	Conic_pair
typedef std::pair < Conic_point_2, unsigned int >	Intersection_point_2
typedef std::list < Intersection_point_2 >	Intersection_list
typedef std::map< Conic_pair, Intersection_list, Less_conic_pair >	Intersection_map
typedef Intersection_map::value_type	Intersection_map_entry
typedef Intersection_map::iterator	Intersection_map_iterator
Public Member Functions
Constrcution methods.
	_Conic_x_monotone_arc_2 ()
	_Conic_x_monotone_arc_2 (const Self &arc)
	_Conic_x_monotone_arc_2 (const Base &arc)
	_Conic_x_monotone_arc_2 (const Base &arc, const Conic_id &id)
	_Conic_x_monotone_arc_2 (const Base &arc, const Point_2 &source, const Point_2 &target, const Conic_id &id)
	_Conic_x_monotone_arc_2 (const Point_2 &source, const Point_2 &target)
	_Conic_x_monotone_arc_2 (const Algebraic &a, const Algebraic &b, const Algebraic &c, const Point_2 &source, const Point_2 &target)
const Self &	operator= (const Self &arc)
Accessing the arc properties.
const Integer &	r () const
const Integer &	s () const
const Integer &	t () const
const Integer &	u () const
const Integer &	v () const
const Integer &	w () const
const Conic_point_2 &	source () const
const Conic_point_2 &	target () const
Orientation	orientation () const
const Conic_point_2 &	left () const
const Conic_point_2 &	right () const
bool	is_directed_right () const
Bbox_2	bbox () const
Predicates.
bool	is_vertical () const
bool	contains_point (const Conic_point_2 &p) const
Constructing points on the arc.
Point_2	point_at_x (const Point_2 &p) const
template<class OutputIterator >
OutputIterator	polyline_approximation (size_t n, OutputIterator oi) const
Comparison_result	compare_to_right (const Self &arc, const Conic_point_2 &p) const
Comparison_result	compare_to_left (const Self &arc, const Conic_point_2 &p) const
template<class OutputIterator >
OutputIterator	intersect (const Self &arc, Intersection_map &inter_map, OutputIterator oi) const
Constructing x-monotone arcs.
void	split (const Conic_point_2 &p, Self &c1, Self &c2) const
Self	flip () const
Self	trim (const Conic_point_2 &ps, const Conic_point_2 &pt) const
bool	equals (const Self &arc) const
bool	can_merge_with (const Self &arc) const
void	merge (const Self &arc)
bool	is_upper () const
bool	is_lower () const
Protected Types
enum	{ IS_VERTICAL_SEGMENT = 4, IS_DIRECTED_RIGHT = 8, DEGREE_1 = 16, DEGREE_2 = 32, DEGREE_MASK = 16 + 32, PLUS_SQRT_DISC_ROOT = 64, FACING_UP = 128, FACING_DOWN = 256, FACING_MASK = 128 + 256, IS_SPECIAL_SEGMENT = 512 }
typedef Conic_arc_2	Base
typedef Conic_arc_2::Integer	Integer
typedef Conic_arc_2::Nt_traits	Nt_traits
typedef Conic_arc_2::Rat_kernel	Rat_kernel
Protected Attributes
Algebraic	alg_r
Algebraic	alg_s
Algebraic	alg_t
Algebraic	alg_u
Algebraic	alg_v
Algebraic	alg_w
Conic_id	_id

Detailed Description

template<class Conic_arc_>
class _Conic_x_monotone_arc_2< Conic_arc_ >

Representation of an x-monotone conic arc. The class is templated by a representation of a general bounded conic arc.

Member Typedef Documentation

template<class Conic_arc_>

typedef Conic_arc_2::Alg_kernel _Conic_x_monotone_arc_2< Conic_arc_ >::Alg_kernel

template<class Conic_arc_>

typedef Conic_arc_2::Algebraic _Conic_x_monotone_arc_2< Conic_arc_ >::Algebraic

template<class Conic_arc_>

typedef Conic_arc_2 _Conic_x_monotone_arc_2< Conic_arc_ >::Base [protected]

template<class Conic_arc_>

typedef Conic_arc_ _Conic_x_monotone_arc_2< Conic_arc_ >::Conic_arc_2

template<class Conic_arc_>

typedef Conic_point_2::Conic_id _Conic_x_monotone_arc_2< Conic_arc_ >::Conic_id

template<class Conic_arc_>

typedef std::pair<Conic_id, Conic_id> _Conic_x_monotone_arc_2< Conic_arc_ >::Conic_pair

template<class Conic_arc_>

typedef Conic_arc_2::Conic_point_2 _Conic_x_monotone_arc_2< Conic_arc_ >::Conic_point_2

template<class Conic_arc_>

typedef Conic_arc_2::Integer _Conic_x_monotone_arc_2< Conic_arc_ >::Integer [protected]

template<class Conic_arc_>

typedef std::list<Intersection_point_2> _Conic_x_monotone_arc_2< Conic_arc_ >::Intersection_list

template<class Conic_arc_>

typedef std::map<Conic_pair, Intersection_list, Less_conic_pair> _Conic_x_monotone_arc_2< Conic_arc_ >::Intersection_map

template<class Conic_arc_>

typedef Intersection_map::value_type _Conic_x_monotone_arc_2< Conic_arc_ >::Intersection_map_entry

template<class Conic_arc_>

typedef Intersection_map::iterator _Conic_x_monotone_arc_2< Conic_arc_ >::Intersection_map_iterator

template<class Conic_arc_>

typedef std::pair<Conic_point_2, unsigned int> _Conic_x_monotone_arc_2< Conic_arc_ >::Intersection_point_2

template<class Conic_arc_>

typedef Conic_arc_2::Nt_traits _Conic_x_monotone_arc_2< Conic_arc_ >::Nt_traits [protected]

template<class Conic_arc_>

typedef Conic_arc_2::Point_2 _Conic_x_monotone_arc_2< Conic_arc_ >::Point_2

template<class Conic_arc_>

typedef Conic_arc_2::Rat_kernel _Conic_x_monotone_arc_2< Conic_arc_ >::Rat_kernel [protected]

template<class Conic_arc_>

typedef _Conic_x_monotone_arc_2<Conic_arc_2> _Conic_x_monotone_arc_2< Conic_arc_ >::Self

Member Enumeration Documentation

template<class Conic_arc_>

anonymous enum [protected]

Enumerator:

IS_VERTICAL_SEGMENT
IS_DIRECTED_RIGHT
DEGREE_1
DEGREE_2
DEGREE_MASK
PLUS_SQRT_DISC_ROOT
FACING_UP
FACING_DOWN
FACING_MASK
IS_SPECIAL_SEGMENT

Constructor & Destructor Documentation

template<class Conic_arc_>

_Conic_x_monotone_arc_2< Conic_arc_ >::_Conic_x_monotone_arc_2 ( ) [inline]

Default constructor.

template<class Conic_arc_>

_Conic_x_monotone_arc_2< Conic_arc_ >::_Conic_x_monotone_arc_2 ( const Self & arc ) [inline]

Copy constructor.

Parameters:

arc	The copied arc.

template<class Conic_arc_>

_Conic_x_monotone_arc_2< Conic_arc_ >::_Conic_x_monotone_arc_2 ( const Base & arc ) [inline]

Construct an x-monotone arc from a conic arc.

Parameters:

arc	The given (base) arc.

Precondition:: The given arc is x-monotone.

template<class Conic_arc_>

_Conic_x_monotone_arc_2< Conic_arc_ >::_Conic_x_monotone_arc_2	(	const Base &	arc,
		const Conic_id &	id
	)		`[inline]`

Construct an x-monotone arc from a conic arc.

Parameters:

arc	The given (base) arc.
id	The ID of the base arc.

template<class Conic_arc_>

_Conic_x_monotone_arc_2< Conic_arc_ >::_Conic_x_monotone_arc_2	(	const Base &	arc,
		const Point_2 &	source,
		const Point_2 &	target,
		const Conic_id &	id
	)		`[inline]`

Construct an x-monotone sub-arc from a conic arc.

Parameters:

arc	The given (base) arc.
source	The source point.
target	The target point.
id	The ID of the base arc.

Here is the call graph for this function:

template<class Conic_arc_>

_Conic_x_monotone_arc_2< Conic_arc_ >::_Conic_x_monotone_arc_2	(	const Point_2 &	source,
		const Point_2 &	target
	)		`[inline]`

Construct a special segment connecting to given endpoints (for the usage of the landmarks point-location strategy).

Parameters:

source	The source point.
target	The target point.

Here is the call graph for this function:

template<class Conic_arc_>

_Conic_x_monotone_arc_2< Conic_arc_ >::_Conic_x_monotone_arc_2	(	const Algebraic &	a,
		const Algebraic &	b,
		const Algebraic &	c,
		const Point_2 &	source,
		const Point_2 &	target
	)		`[inline]`

Construct a special segment of a given line connecting to given endpoints.

Parameters:

a,b,c	The coefficients of the supporting line (ax + by + c = 0).
source	The source point.
target	The target point.

Here is the call graph for this function:

Member Function Documentation

template<class Conic_arc_>

Bbox_2 _Conic_x_monotone_arc_2< Conic_arc_ >::bbox ( ) const [inline]

Get a bounding box for the conic arc.

Returns:: The bounding box.

template<class Conic_arc_>

bool _Conic_x_monotone_arc_2< Conic_arc_ >::can_merge_with ( const Self & arc ) const [inline]

Check whether it is possible to merge the arc with the given arc.

Parameters:

arc	The query arc.

Returns:: (true) if it is possible to merge the two arcs; (false) otherwise.

Here is the call graph for this function:

Here is the caller graph for this function:

template<class Conic_arc_>

Comparison_result _Conic_x_monotone_arc_2< Conic_arc_ >::compare_to_left	(	const Self &	arc,
		const Conic_point_2 &	p
	)		const `[inline]`

Compare to arcs immediately to the leftt of their intersection point.

Parameters:

arc	The compared arc.
p	The reference intersection point.

Returns:: The relative position of the arcs to the left of p.

Precondition:: Both arcs we compare are not vertical segments.

Here is the call graph for this function:

Here is the caller graph for this function:

template<class Conic_arc_>

Comparison_result _Conic_x_monotone_arc_2< Conic_arc_ >::compare_to_right	(	const Self &	arc,
		const Conic_point_2 &	p
	)		const `[inline]`

Compare to arcs immediately to the right of their intersection point.

Parameters:

arc	The compared arc.
p	The reference intersection point.

Returns:: The relative position of the arcs to the right of p.

Precondition:: Both arcs we compare are not vertical segments.

Here is the call graph for this function:

Here is the caller graph for this function:

template<class Conic_arc_>

bool _Conic_x_monotone_arc_2< Conic_arc_ >::contains_point ( const Conic_point_2 & p ) const [inline]

Check whether the given point lies on the arc.

Parameters:

p	The qury point.
(true)	if p lies on the arc; (false) otherwise.

Here is the caller graph for this function:

template<class Conic_arc_>

bool _Conic_x_monotone_arc_2< Conic_arc_ >::equals ( const Self & arc ) const [inline]

Check whether the two arcs are equal (have the same graph).

Parameters:

arc	The compared arc.

Returns:: (true) if the two arcs have the same graph; (false) otherwise.

Here is the caller graph for this function:

template<class Conic_arc_>

Self _Conic_x_monotone_arc_2< Conic_arc_ >::flip ( ) const [inline]

Flip the arc.

Returns:: An arc with swapped source and target and a reverse orienation.

Here is the caller graph for this function:

template<class Conic_arc_>

template<class OutputIterator >

OutputIterator _Conic_x_monotone_arc_2< Conic_arc_ >::intersect	(	const Self &	arc,
		Intersection_map &	inter_map,
		OutputIterator	oi
	)		const `[inline]`

Compute the intersections with the given arc.

Parameters:

arc	The given intersecting arc.
inter_map	Maps conic pairs to lists of their intersection points.
oi	The output iterator.

Returns:: The past-the-end iterator.

Here is the call graph for this function:

Here is the caller graph for this function:

template<class Conic_arc_>

bool _Conic_x_monotone_arc_2< Conic_arc_ >::is_directed_right ( ) const [inline]

Return true iff the conic arc is directed right iexicographically.

Here is the caller graph for this function:

template<class Conic_arc_>

bool _Conic_x_monotone_arc_2< Conic_arc_ >::is_lower ( ) const [inline]

template<class Conic_arc_>

bool _Conic_x_monotone_arc_2< Conic_arc_ >::is_upper ( ) const [inline]

template<class Conic_arc_>

bool _Conic_x_monotone_arc_2< Conic_arc_ >::is_vertical ( ) const [inline]

Check if the conic arc is a vertical segment.

Here is the caller graph for this function:

template<class Conic_arc_>

const Conic_point_2& _Conic_x_monotone_arc_2< Conic_arc_ >::left ( ) const [inline]

Get the left endpoint of the arc.

Here is the caller graph for this function:

template<class Conic_arc_>

void _Conic_x_monotone_arc_2< Conic_arc_ >::merge ( const Self & arc ) [inline]

Merge the current arc with the given arc.

Parameters:

arc	The arc to merge with.

Precondition:: The two arcs are mergeable.

Here is the call graph for this function:

Here is the caller graph for this function:

template<class Conic_arc_>

const Self& _Conic_x_monotone_arc_2< Conic_arc_ >::operator= ( const Self & arc ) [inline]

Assignment operator.

Parameters:

arc	The copied arc.

template<class Conic_arc_>

Orientation _Conic_x_monotone_arc_2< Conic_arc_ >::orientation ( ) const [inline]

Get the orientation of the arc.

Returns:: The orientation.

Here is the caller graph for this function:

template<class Conic_arc_>

Point_2 _Conic_x_monotone_arc_2< Conic_arc_ >::point_at_x ( const Point_2 & p ) const [inline]

Compute a point on the arc with the same x-coordiante as the given point.

Parameters:

p	The given point.

Precondition:: The arc is not vertical and p is in the x-range of the arc.

Returns:: A point on the arc with the same x-coordiante as p.

Here is the call graph for this function:

Here is the caller graph for this function:

template<class Conic_arc_>

template<class OutputIterator >

OutputIterator _Conic_x_monotone_arc_2< Conic_arc_ >::polyline_approximation	(	size_t	n,
		OutputIterator	oi
	)		const `[inline]`

Get a polyline approximating the conic arc.

Parameters:

n	The maximal number of sample points.
oi	An output iterator, whose value-type is pair<double,double> (representing an approximated point). In case the arc is a line segment, there are 2 output points, otherwise the arc is approximated by the polyline defined by (p_0, p_1, ..., p_n), where p_0 and p_n are the left and right endpoints of the arc, respectively.

Here is the call graph for this function:

Here is the caller graph for this function:

template<class Conic_arc_>

const Integer& _Conic_x_monotone_arc_2< Conic_arc_ >::r ( ) const [inline]

Get the coefficients of the underlying conic.

Here is the caller graph for this function:

template<class Conic_arc_>

const Conic_point_2& _Conic_x_monotone_arc_2< Conic_arc_ >::right ( ) const [inline]

Get the right endpoint of the arc.

Here is the caller graph for this function:

template<class Conic_arc_>

const Integer& _Conic_x_monotone_arc_2< Conic_arc_ >::s ( ) const [inline]

Here is the caller graph for this function:

template<class Conic_arc_>

const Conic_point_2& _Conic_x_monotone_arc_2< Conic_arc_ >::source ( ) const [inline]

Get the arc's source.

Returns:: The source point.

Here is the caller graph for this function:

template<class Conic_arc_>

void _Conic_x_monotone_arc_2< Conic_arc_ >::split	(	const Conic_point_2 &	p,
		Self &	c1,
		Self &	c2
	)		const `[inline]`

Split the arc into two at a given split point.

Parameters:

p	The split point.
c1	Output: The first resulting arc, lying to the left of p.
c2	Output: The first resulting arc, lying to the right of p.

Precondition:: p lies in the interior of the arc (not one of its endpoints).

Here is the call graph for this function:

Here is the caller graph for this function:

template<class Conic_arc_>

const Integer& _Conic_x_monotone_arc_2< Conic_arc_ >::t ( ) const [inline]

Here is the caller graph for this function:

template<class Conic_arc_>

const Conic_point_2& _Conic_x_monotone_arc_2< Conic_arc_ >::target ( ) const [inline]

Get the arc's target.

Returns:: The target point.

Here is the caller graph for this function:

template<class Conic_arc_>

Self _Conic_x_monotone_arc_2< Conic_arc_ >::trim	(	const Conic_point_2 &	ps,
		const Conic_point_2 &	pt
	)		const `[inline]`

Trim the arc given its new endpoints.

Parameters:

ps	The new source point.
pt	The new target point.

Returns:: The new trimmed arc.

Precondition:: Both ps and pt lies on the arc and must conform with the current direction of the arc.

Here is the call graph for this function:

template<class Conic_arc_>

const Integer& _Conic_x_monotone_arc_2< Conic_arc_ >::u ( ) const [inline]

Here is the caller graph for this function:

template<class Conic_arc_>

const Integer& _Conic_x_monotone_arc_2< Conic_arc_ >::v ( ) const [inline]

Here is the caller graph for this function:

template<class Conic_arc_>

const Integer& _Conic_x_monotone_arc_2< Conic_arc_ >::w ( ) const [inline]

Here is the caller graph for this function:

Member Data Documentation

template<class Conic_arc_>

Conic_id _Conic_x_monotone_arc_2< Conic_arc_ >::_id [protected]

template<class Conic_arc_>

Algebraic _Conic_x_monotone_arc_2< Conic_arc_ >::alg_r [protected]

template<class Conic_arc_>

Algebraic _Conic_x_monotone_arc_2< Conic_arc_ >::alg_s [protected]

template<class Conic_arc_>

Algebraic _Conic_x_monotone_arc_2< Conic_arc_ >::alg_t [protected]

template<class Conic_arc_>

Algebraic _Conic_x_monotone_arc_2< Conic_arc_ >::alg_u [protected]

template<class Conic_arc_>

Algebraic _Conic_x_monotone_arc_2< Conic_arc_ >::alg_v [protected]

template<class Conic_arc_>

Algebraic _Conic_x_monotone_arc_2< Conic_arc_ >::alg_w [protected]

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

SPAR/AIModule/BWTA/vendors/CGAL/CGAL/Arr_geometry_traits/Conic_x_monotone_arc_2.h

Classes

Public Types

Public Member Functions

Protected Types

Protected Attributes

Detailed Description

template<class Conic_arc_> class _Conic_x_monotone_arc_2< Conic_arc_ >

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<class Conic_arc_>
class _Conic_x_monotone_arc_2< Conic_arc_ >