Aim: Class that implements a binary point predicate, which is able to compare the position of two given points \( P, Q \) around a pole \( O \). More precisely, it compares the oriented angles lying between the horizontal line passing by \( O \) and the rays \( [OP) \) and \( [OQ) \) (in a counter-clockwise orientation). More...

#include <DGtal/geometry/tools/PolarPointComparatorBy2x2DetComputer.h>

Public Types
typedef TPoint	Point

typedef Point::Coordinate	Coordinate

typedef Point	Vector

typedef TDetComputer	DetComputer

typedef DetComputer::ResultInteger	ResultInteger

typedef functors::Thresholder< ResultInteger, false, false >	CustomThresholder

Public Member Functions
	BOOST_CONCEPT_ASSERT ((C2x2DetComputer< DetComputer >))

	PolarPointComparatorBy2x2DetComputer ()

	PolarPointComparatorBy2x2DetComputer (const Point &aPoint)

	PolarPointComparatorBy2x2DetComputer (const PolarPointComparatorBy2x2DetComputer &other)

PolarPointComparatorBy2x2DetComputer &	operator= (const PolarPointComparatorBy2x2DetComputer &other)

void	selfDisplay (std::ostream &out) const

bool	isValid () const

void	setPole (const Point &aPole)

bool	operator() (const Point &aPoint1, const Point &aPoint2) const

Private Member Functions
bool	isBefore (const Point &aU, const Point &aV) const

Private Attributes
Point	myPole

DetComputer	myDetComputer

CustomThresholder	myThresholder

Detailed Description

template<typename TPoint, typename TDetComputer = Simple2x2DetComputer<typename TPoint::Coordinate, DGtal::int64_t >>
class DGtal::functors::PolarPointComparatorBy2x2DetComputer< TPoint, TDetComputer >

Aim: Class that implements a binary point predicate, which is able to compare the position of two given points \( P, Q \) around a pole \( O \). More precisely, it compares the oriented angles lying between the horizontal line passing by \( O \) and the rays \( [OP) \) and \( [OQ) \) (in a counter-clockwise orientation).

See PolarPointComparatorBy2x2DetComputer::operator() and PolarPointComparatorBy2x2DetComputer::isBefore for more details about the comparison (especially in degenerate cases).

Note: We do not use any approximating function like atan, but only exact computations involving the evaluation of determinants of 2x2 matrices. With the default template parameters, the result is guaranteed to be exact for integral point coordinates lying whithin the range ]-2^30,2^30[.

Template Parameters

TPoint	type of points to compare
TDetComputer	a model of C2x2DetComputer. By default, Simple2x2DetComputer is chosen.

Examples: geometry/tools/exampleConvexHull2D.cpp.

Definition at line 79 of file PolarPointComparatorBy2x2DetComputer.h.

Member Typedef Documentation

◆ Coordinate

template<typename TPoint , typename TDetComputer = Simple2x2DetComputer<typename TPoint::Coordinate, DGtal::int64_t >>

typedef Point::Coordinate DGtal::functors::PolarPointComparatorBy2x2DetComputer< TPoint, TDetComputer >::Coordinate

Type of point coordinates

Definition at line 91 of file PolarPointComparatorBy2x2DetComputer.h.

◆ CustomThresholder

template<typename TPoint , typename TDetComputer = Simple2x2DetComputer<typename TPoint::Coordinate, DGtal::int64_t >>

typedef functors::Thresholder<ResultInteger, false, false> DGtal::functors::PolarPointComparatorBy2x2DetComputer< TPoint, TDetComputer >::CustomThresholder

Type of the object that returns a bool from the determinant returned by myDetComputer.

Definition at line 113 of file PolarPointComparatorBy2x2DetComputer.h.

◆ DetComputer

template<typename TPoint , typename TDetComputer = Simple2x2DetComputer<typename TPoint::Coordinate, DGtal::int64_t >>

typedef TDetComputer DGtal::functors::PolarPointComparatorBy2x2DetComputer< TPoint, TDetComputer >::DetComputer

Type of the object that computes the determinant of 2x2 matrix in order to determine the orientation of three points or compare the norm of two vectors.

Definition at line 101 of file PolarPointComparatorBy2x2DetComputer.h.

◆ Point

template<typename TPoint , typename TDetComputer = Simple2x2DetComputer<typename TPoint::Coordinate, DGtal::int64_t >>

typedef TPoint DGtal::functors::PolarPointComparatorBy2x2DetComputer< TPoint, TDetComputer >::Point

Type of 2D points to compare

Definition at line 87 of file PolarPointComparatorBy2x2DetComputer.h.

◆ ResultInteger

template<typename TPoint , typename TDetComputer = Simple2x2DetComputer<typename TPoint::Coordinate, DGtal::int64_t >>

typedef DetComputer::ResultInteger DGtal::functors::PolarPointComparatorBy2x2DetComputer< TPoint, TDetComputer >::ResultInteger

Type of integer returned by the determinant computer

Definition at line 107 of file PolarPointComparatorBy2x2DetComputer.h.

◆ Vector

template<typename TPoint , typename TDetComputer = Simple2x2DetComputer<typename TPoint::Coordinate, DGtal::int64_t >>

typedef Point DGtal::functors::PolarPointComparatorBy2x2DetComputer< TPoint, TDetComputer >::Vector

Type of 2D vectors

Definition at line 95 of file PolarPointComparatorBy2x2DetComputer.h.

Constructor & Destructor Documentation

◆ PolarPointComparatorBy2x2DetComputer() [1/3]

template<typename TPoint , typename TDetComputer = Simple2x2DetComputer<typename TPoint::Coordinate, DGtal::int64_t >>

DGtal::functors::PolarPointComparatorBy2x2DetComputer< TPoint, TDetComputer >::PolarPointComparatorBy2x2DetComputer ( )

Default constructor. myPole is set to (0,0).

◆ PolarPointComparatorBy2x2DetComputer() [2/3]

template<typename TPoint , typename TDetComputer = Simple2x2DetComputer<typename TPoint::Coordinate, DGtal::int64_t >>

DGtal::functors::PolarPointComparatorBy2x2DetComputer< TPoint, TDetComputer >::PolarPointComparatorBy2x2DetComputer ( const Point & aPoint )

Constructor.

Parameters

aPoint pole used for the polar comparison

◆ PolarPointComparatorBy2x2DetComputer() [3/3]

template<typename TPoint , typename TDetComputer = Simple2x2DetComputer<typename TPoint::Coordinate, DGtal::int64_t >>

DGtal::functors::PolarPointComparatorBy2x2DetComputer< TPoint, TDetComputer >::PolarPointComparatorBy2x2DetComputer ( const PolarPointComparatorBy2x2DetComputer< TPoint, TDetComputer > & other )

Copy constructor.

Parameters

other the object to clone.

Member Function Documentation

◆ BOOST_CONCEPT_ASSERT()

template<typename TPoint , typename TDetComputer = Simple2x2DetComputer<typename TPoint::Coordinate, DGtal::int64_t >>

DGtal::functors::PolarPointComparatorBy2x2DetComputer< TPoint, TDetComputer >::BOOST_CONCEPT_ASSERT ( (C2x2DetComputer< DetComputer >) )

◆ isBefore()

template<typename TPoint , typename TDetComputer = Simple2x2DetComputer<typename TPoint::Coordinate, DGtal::int64_t >>

bool DGtal::functors::PolarPointComparatorBy2x2DetComputer< TPoint, TDetComputer >::isBefore	(	const Point &	aU,
		const Point &	aV
	)		const

private

Method that compares two given points both belonging to the upward (positive y-coordinates) or downward (negative y-coordinates) half-plane.

The first argument aU lies before the second one aV iff the triple myPole , aU , aV are counter-clockwise oriented.

If myPole , aU , aV are aligned aU lies before aV iff its (L2) norm is shorter.

Note that if aU or aV are equal to myPole, its norm is the shortest possible.

If aU and aV are equal, this methods returns 'false', because no point is strictly located before the other.

Parameters

aU	first point
aV	second point

Returns: 'true' if aU lies before aV, 'false' otherwise

◆ isValid()

template<typename TPoint , typename TDetComputer = Simple2x2DetComputer<typename TPoint::Coordinate, DGtal::int64_t >>

bool DGtal::functors::PolarPointComparatorBy2x2DetComputer< TPoint, TDetComputer >::isValid ( ) const

Checks the validity/consistency of the object.

Returns: 'true' if the object is valid, 'false' otherwise.

◆ operator()()

template<typename TPoint , typename TDetComputer = Simple2x2DetComputer<typename TPoint::Coordinate, DGtal::int64_t >>

bool DGtal::functors::PolarPointComparatorBy2x2DetComputer< TPoint, TDetComputer >::operator()	(	const Point &	aPoint1,
		const Point &	aPoint2
	)		const

Main operator, which compares two given points aPoint1 and aPoint2.

This method first checks whether the two points are located on the same side of the horizontal line passing by myPole or not. If so, it calls PolarPointComparatorBy2x2DetComputer::isBefore. Otherwise it concludes.

Parameters

aPoint1	first point
aPoint2	second point

Returns: 'true' if aPoint1 lies before aPoint2, 'false' otherwise

See also: PolarPointComparatorBy2x2DetComputer::isBefore

◆ operator=()

template<typename TPoint , typename TDetComputer = Simple2x2DetComputer<typename TPoint::Coordinate, DGtal::int64_t >>

PolarPointComparatorBy2x2DetComputer & DGtal::functors::PolarPointComparatorBy2x2DetComputer< TPoint, TDetComputer >::operator= ( const PolarPointComparatorBy2x2DetComputer< TPoint, TDetComputer > & other )

Assignment.

Parameters

other the object to copy.

Returns: a reference on 'this'.

◆ selfDisplay()

template<typename TPoint , typename TDetComputer = Simple2x2DetComputer<typename TPoint::Coordinate, DGtal::int64_t >>

void DGtal::functors::PolarPointComparatorBy2x2DetComputer< TPoint, TDetComputer >::selfDisplay ( std::ostream & out ) const

Writes/Displays the object on an output stream.

Parameters

out	the output stream where the object is written.

◆ setPole()

template<typename TPoint , typename TDetComputer = Simple2x2DetComputer<typename TPoint::Coordinate, DGtal::int64_t >>

void DGtal::functors::PolarPointComparatorBy2x2DetComputer< TPoint, TDetComputer >::setPole ( const Point & aPole )

Sets the pole.

Parameters

aPole new pole for the polar comparison.

Examples: geometry/tools/exampleConvexHull2D.cpp.

Referenced by convexHull(), and testSort().

Field Documentation

◆ myDetComputer

template<typename TPoint , typename TDetComputer = Simple2x2DetComputer<typename TPoint::Coordinate, DGtal::int64_t >>

DetComputer DGtal::functors::PolarPointComparatorBy2x2DetComputer< TPoint, TDetComputer >::myDetComputer

mutableprivate

Object that computes the determinant of 2x2 matrix in order to determine the orientation of three points or compare the norm of two vectors

Definition at line 222 of file PolarPointComparatorBy2x2DetComputer.h.

◆ myPole

template<typename TPoint , typename TDetComputer = Simple2x2DetComputer<typename TPoint::Coordinate, DGtal::int64_t >>

Point DGtal::functors::PolarPointComparatorBy2x2DetComputer< TPoint, TDetComputer >::myPole

private

Point used as the origin for the polar comparison of two given points

Definition at line 216 of file PolarPointComparatorBy2x2DetComputer.h.

◆ myThresholder

template<typename TPoint , typename TDetComputer = Simple2x2DetComputer<typename TPoint::Coordinate, DGtal::int64_t >>

CustomThresholder DGtal::functors::PolarPointComparatorBy2x2DetComputer< TPoint, TDetComputer >::myThresholder

private

Object that returns a bool from the determinant returned by myDetComputer

Definition at line 227 of file PolarPointComparatorBy2x2DetComputer.h.

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

PolarPointComparatorBy2x2DetComputer.h

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ Coordinate

◆ CustomThresholder

◆ DetComputer

◆ Point

◆ ResultInteger

◆ Vector

Constructor & Destructor Documentation

◆ PolarPointComparatorBy2x2DetComputer() [1/3]

◆ PolarPointComparatorBy2x2DetComputer() [2/3]

◆ PolarPointComparatorBy2x2DetComputer() [3/3]

Member Function Documentation

◆ BOOST_CONCEPT_ASSERT()

◆ isBefore()

◆ isValid()

◆ operator()()

◆ operator=()

◆ selfDisplay()

◆ setPole()

Field Documentation

◆ myDetComputer

◆ myPole

◆ myThresholder