Aim: Class that provides a way of computing the sign of the determinant of a 2x2 matrix from its four coefficients, ie. More...

#include <DGtal/geometry/tools/determinant/AvnaimEtAl2x2DetSignComputer.h>

Public Types
typedef TInteger	ArgumentInteger

typedef ArgumentInteger	Integer

typedef ArgumentInteger	argument_type

typedef Integer	ResultInteger

typedef ResultInteger	Value

typedef ResultInteger	result_type

Public Member Functions
	BOOST_CONCEPT_ASSERT ((concepts::CEuclideanRing< ArgumentInteger >))

	BOOST_CONCEPT_ASSERT ((concepts::CBoundedNumber< ArgumentInteger >))

	BOOST_STATIC_CONSTANT (unsigned int, base=std::numeric_limits< Integer >::radix)

	BOOST_STATIC_CONSTANT (unsigned int, exponent=std::numeric_limits< Integer >::digits)

	AvnaimEtAl2x2DetSignComputer ()

void	init (const ArgumentInteger &aA, const ArgumentInteger &aB)

ResultInteger	operator() (const ArgumentInteger &aU, const ArgumentInteger &aV) const

ResultInteger	operator() (const ArgumentInteger &aA, const ArgumentInteger &aB, const ArgumentInteger &aX, const ArgumentInteger &aY)

void	selfDisplay (std::ostream &out) const

bool	isValid () const

Private Member Functions
int	quadrant (const Integer &aX, const Integer &aY) const

Integer	computation (const Integer &aA, const Integer &aB, const Integer &aX, const Integer &aY) const

Integer	recursiveComputation (const Integer &aA, const Integer &aB, const Integer &aX, const Integer &aY) const

Private Attributes
Integer	myA

Integer	myB

Integer	myMax

Detailed Description

template<typename TInteger>
class DGtal::AvnaimEtAl2x2DetSignComputer< TInteger >

Aim: Class that provides a way of computing the sign of the determinant of a 2x2 matrix from its four coefficients, ie.

\( \begin{vmatrix} a & x \\ b & y \end{vmatrix} \)

It returns:

1 if \( ay - bx > 0\),
-1 if \( ay - bx < 0 \),
0 if \( ay - bx = 0 \).

If the coefficients are coded with b bits, the computation only uses numbers coded with b bits too without any overflows [Avnaim et.al., 1997 : [8]].

This class is a model of C2x2DetComputer.

Template Parameters

TInteger both a model of CEuclideanRing (it has the usual arithmetic operators) and a model of CBoundedNumber. It can be DGtal::int8_t, DGtal::int16_t, DGtal::int32_t, DGtal::int64_t as well as float and double.

See also: Simple2x2DetComputer

Examples: geometry/tools/determinant/exampleInHalfPlane.cpp, and geometry/tools/exampleAlphaShape.cpp.

Definition at line 144 of file AvnaimEtAl2x2DetSignComputer.h.

Member Typedef Documentation

◆ argument_type

template<typename TInteger >

typedef ArgumentInteger DGtal::AvnaimEtAl2x2DetSignComputer< TInteger >::argument_type

STL alias of type ArgumentInteger

Definition at line 162 of file AvnaimEtAl2x2DetSignComputer.h.

◆ ArgumentInteger

template<typename TInteger >

typedef TInteger DGtal::AvnaimEtAl2x2DetSignComputer< TInteger >::ArgumentInteger

Type of integer for the input coefficients of the 2x2 matrix

Definition at line 151 of file AvnaimEtAl2x2DetSignComputer.h.

◆ Integer

template<typename TInteger >

typedef ArgumentInteger DGtal::AvnaimEtAl2x2DetSignComputer< TInteger >::Integer

DGtal alias of type ArgumentInteger

Definition at line 158 of file AvnaimEtAl2x2DetSignComputer.h.

◆ result_type

template<typename TInteger >

typedef ResultInteger DGtal::AvnaimEtAl2x2DetSignComputer< TInteger >::result_type

STL alias of type ResultInteger

Definition at line 176 of file AvnaimEtAl2x2DetSignComputer.h.

◆ ResultInteger

template<typename TInteger >

typedef Integer DGtal::AvnaimEtAl2x2DetSignComputer< TInteger >::ResultInteger

Type of integer for the returned determinant, which is an alias of type ArgumentInteger

Definition at line 168 of file AvnaimEtAl2x2DetSignComputer.h.

◆ Value

template<typename TInteger >

typedef ResultInteger DGtal::AvnaimEtAl2x2DetSignComputer< TInteger >::Value

DGtal alias type of ResultInteger

Definition at line 172 of file AvnaimEtAl2x2DetSignComputer.h.

Constructor & Destructor Documentation

◆ AvnaimEtAl2x2DetSignComputer()

template<typename TInteger >

DGtal::AvnaimEtAl2x2DetSignComputer< TInteger >::AvnaimEtAl2x2DetSignComputer ( )

Default constructor

Member Function Documentation

◆ BOOST_CONCEPT_ASSERT() [1/2]

template<typename TInteger >

DGtal::AvnaimEtAl2x2DetSignComputer< TInteger >::BOOST_CONCEPT_ASSERT ( (concepts::CBoundedNumber< ArgumentInteger >) )

◆ BOOST_CONCEPT_ASSERT() [2/2]

template<typename TInteger >

DGtal::AvnaimEtAl2x2DetSignComputer< TInteger >::BOOST_CONCEPT_ASSERT ( (concepts::CEuclideanRing< ArgumentInteger >) )

◆ BOOST_STATIC_CONSTANT() [1/2]

template<typename TInteger >

DGtal::AvnaimEtAl2x2DetSignComputer< TInteger >::BOOST_STATIC_CONSTANT	(	unsigned int	,
		base	= `std::numeric_limits< Integer >::radix`
	)

Data member storing the number of the base (radix) of the representation, 2 usually

◆ BOOST_STATIC_CONSTANT() [2/2]

template<typename TInteger >

DGtal::AvnaimEtAl2x2DetSignComputer< TInteger >::BOOST_STATIC_CONSTANT	(	unsigned int	,
		exponent	= `std::numeric_limits< Integer >::digits`
	)

Data member storing the number of non-sign bits in the representation, eg. b-1 for signed integer coded with b bits.

◆ computation()

template<typename TInteger >

Integer DGtal::AvnaimEtAl2x2DetSignComputer< TInteger >::computation	(	const Integer &	aA,
		const Integer &	aB,
		const Integer &	aX,
		const Integer &	aY
	)		const

private

Method that computes the sign of the determinant for strictly positive coefficients.

Parameters

aA	0-component of the first column vector
aB	1-component of the first column vector
aX	0-component of the second column vector
aY	1-component of the second column vector

Precondition: aA, aB, aX, aY are strictly positive.

Returns: the sign of the determinant of the 2x2 matrix, ie. 1 if aA . aY - aB . aX is strictly positive, -1 if it is strictly negative, 0 otherwise

See also: recursiveComputation

◆ init()

template<typename TInteger >

void DGtal::AvnaimEtAl2x2DetSignComputer< TInteger >::init	(	const ArgumentInteger &	aA,
		const ArgumentInteger &	aB
	)

Initialisation.

Parameters

aA	0-component of the first column vector
aB	1-component of the first column vector

See also: operator()

◆ isValid()

template<typename TInteger >

bool DGtal::AvnaimEtAl2x2DetSignComputer< TInteger >::isValid ( ) const

Checks the validity/consistency of the object.

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

◆ operator()() [1/2]

template<typename TInteger >

ResultInteger DGtal::AvnaimEtAl2x2DetSignComputer< TInteger >::operator()	(	const ArgumentInteger &	aA,
		const ArgumentInteger &	aB,
		const ArgumentInteger &	aX,
		const ArgumentInteger &	aY
	)

Operator.

Parameters

aA	0-component of the first column vector
aB	1-component of the first column vector
aX	0-component of the second column vector
aY	1-component of the second column vector

Returns: the sign of the determinant of the 2x2 matrix, ie. 1 if aA . aY - aB . aX is strictly positive, -1 if it is strictly negative, 0 otherwise

◆ operator()() [2/2]

template<typename TInteger >

ResultInteger DGtal::AvnaimEtAl2x2DetSignComputer< TInteger >::operator()	(	const ArgumentInteger &	aU,
		const ArgumentInteger &	aV
	)		const

Incremental operator.

Precondition: init must be called before

Parameters

aU	0-component of the second column vector
aV	1-component of the second column vector

Returns: the sign of the determinant of the 2x2 matrix, ie. 1 if myA . aV - myB . aU is strictly positive, -1 if it is strictly negative, 0 otherwise

◆ quadrant()

template<typename TInteger >

int DGtal::AvnaimEtAl2x2DetSignComputer< TInteger >::quadrant	(	const Integer &	aX,
		const Integer &	aY
	)		const

private

Returns the quadrant where a given vector lies

Parameters

aX	x-component of the vector
aY	y-component of the vector

Precondition: aX and aY must not be null

Returns: the quadrant where the vector of components aX , aY lies, ie. 0, 1, 2, or 3 in a counter-clockwise order with 0 if aX and aY are both positive.

◆ recursiveComputation()

template<typename TInteger >

Integer DGtal::AvnaimEtAl2x2DetSignComputer< TInteger >::recursiveComputation	(	const Integer &	aA,
		const Integer &	aB,
		const Integer &	aX,
		const Integer &	aY
	)		const

private

Method that computes the sign of the determinant for strictly positive coefficients
aA, aB, aX, aY such that aB < aY.

Parameters

aA	0-component of the first column vector
aB	1-component of the first column vector
aX	0-component of the second column vector
aY	1-component of the second column vector

Precondition: aA, aB, aX, aY are strictly positive and such that aB < aY

Returns: the sign of the determinant of the 2x2 matrix, ie. 1 if aA . aY - aB . aX is strictly positive, -1 if it is strictly negative, 0 otherwise

◆ selfDisplay()

template<typename TInteger >

void DGtal::AvnaimEtAl2x2DetSignComputer< TInteger >::selfDisplay ( std::ostream & out ) const

Writes/Displays the object on an output stream.

Parameters

out	the output stream where the object is written.

Field Documentation

◆ myA

template<typename TInteger >

Integer DGtal::AvnaimEtAl2x2DetSignComputer< TInteger >::myA

private

Data member used to store the 0-component of the first column vector, ie. a.

Definition at line 301 of file AvnaimEtAl2x2DetSignComputer.h.

◆ myB

template<typename TInteger >

Integer DGtal::AvnaimEtAl2x2DetSignComputer< TInteger >::myB

private

Data member used to store the 1-component of the first column vector, ie. b.

Definition at line 306 of file AvnaimEtAl2x2DetSignComputer.h.

◆ myMax

template<typename TInteger >

Integer DGtal::AvnaimEtAl2x2DetSignComputer< TInteger >::myMax

private

Data member storing the maximal representable integer, ie. 2 ^ b if the type of integer that is used is coded with b bits.

Definition at line 311 of file AvnaimEtAl2x2DetSignComputer.h.

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

AvnaimEtAl2x2DetSignComputer.h

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ argument_type

◆ ArgumentInteger

◆ Integer

◆ result_type

◆ ResultInteger

◆ Value

Constructor & Destructor Documentation

◆ AvnaimEtAl2x2DetSignComputer()

Member Function Documentation

◆ BOOST_CONCEPT_ASSERT() [1/2]

◆ BOOST_CONCEPT_ASSERT() [2/2]

◆ BOOST_STATIC_CONSTANT() [1/2]

◆ BOOST_STATIC_CONSTANT() [2/2]

◆ computation()

◆ init()

◆ isValid()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ quadrant()

◆ recursiveComputation()

◆ selfDisplay()

Field Documentation

◆ myA

◆ myB

◆ myMax