Aim: Small class useful to compute, in an incremental way, the determinant of a 2x2 matrix from its four coefficients, ie. \( \begin{vmatrix} a & x \\ b & y \end{vmatrix} \). More...

#include <DGtal/geometry/tools/determinant/SimpleIncremental2x2DetComputer.h>

Public Types
typedef TArgumentInteger	ArgumentInteger

typedef ArgumentInteger	Integer

typedef ArgumentInteger	argument_type

typedef TResultInteger	ResultInteger

typedef ResultInteger	Value

typedef ResultInteger	result_type

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

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

	SimpleIncremental2x2DetComputer ()

	SimpleIncremental2x2DetComputer (const SimpleIncremental2x2DetComputer &other)

SimpleIncremental2x2DetComputer &	operator= (const SimpleIncremental2x2DetComputer &other)

	~SimpleIncremental2x2DetComputer ()

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

ResultInteger	operator() (const ArgumentInteger &aX, const ArgumentInteger &aY) 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
void	partialComputation () const

Private Attributes
ResultInteger	myA

ResultInteger	myB

ResultInteger	myAY

ResultInteger	myBX

ResultInteger	myDet

ResultInteger	myX

ResultInteger	myY

ResultInteger	myDX

ResultInteger	myDY

ResultInteger	myADY

ResultInteger	myBDX

ResultInteger	myDDet

const ResultInteger	myZero

Detailed Description

template<typename TArgumentInteger, typename TResultInteger = TArgumentInteger>
class DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >

Aim: Small class useful to compute, in an incremental way, the determinant of a 2x2 matrix from its four coefficients, ie. \( \begin{vmatrix} a & x \\ b & y \end{vmatrix} \).

This class is a model of C2x2DetComputer.

It should be used to compute the determinant \( ay - bx \), for various \( x, y \) and given \( a \) and \( b \). Let us assume that the determinant \( \delta_i = ay_i - bx_i \) is computed. The determinant \( \delta_j = ay_j - bx_j \) is then computed incrementally as follows: \( \delta_j = a(y_j - y_i) - b(x_j - x_i) \). The computation is simplified if the differences \( (x_j - x_i) \) and \( (y_j - y_i) \) are equal to 0 or 1, as it may occur in digital geometry.

In order to use SimpleIncremental2x2DetComputer

first, you must set the first column vector, ie. \( a \) and \( b \), using method SimpleIncremental2x2DetComputer::init().
then, you must call method SimpleIncremental2x2DetComputer::operator() on the second column vector, ie. \( x \) and \( y \).

Template Parameters

TArgumentInteger	a model of CEuclideanRing for the input coefficients of the 2x2 matrix
TResultInteger	a model of CEuclideanRing for the result. It must be either unbounded or twice as big as TArgumentInteger, ie. if TArgumentInteger is a type coded on b bits, TResultInteger must be coded on 2b+1 bits

Note that if you use the same type for the arguments and the result, the code may fail to provide the exact result because of a possible overflow.

See also: Simple2x2DetComputer

Definition at line 93 of file SimpleIncremental2x2DetComputer.h.

Member Typedef Documentation

◆ argument_type

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

typedef ArgumentInteger DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::argument_type

STL alias of type ArgumentInteger

Definition at line 109 of file SimpleIncremental2x2DetComputer.h.

◆ ArgumentInteger

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

typedef TArgumentInteger DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::ArgumentInteger

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

Definition at line 100 of file SimpleIncremental2x2DetComputer.h.

◆ Integer

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

typedef ArgumentInteger DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::Integer

DGtal alias of type ArgumentInteger

Definition at line 105 of file SimpleIncremental2x2DetComputer.h.

◆ result_type

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

typedef ResultInteger DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::result_type

STL alias of type ResultInteger

Definition at line 124 of file SimpleIncremental2x2DetComputer.h.

◆ ResultInteger

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

typedef TResultInteger DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::ResultInteger

Type of integer for the returned determinant

Definition at line 114 of file SimpleIncremental2x2DetComputer.h.

◆ Value

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

typedef ResultInteger DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::Value

DGtal alias type of ResultInteger

Definition at line 120 of file SimpleIncremental2x2DetComputer.h.

Constructor & Destructor Documentation

◆ SimpleIncremental2x2DetComputer() [1/2]

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::SimpleIncremental2x2DetComputer ( )

Default constructor.

◆ SimpleIncremental2x2DetComputer() [2/2]

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::SimpleIncremental2x2DetComputer ( const SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger > & other )

Copy constructor.

Parameters

other the object to clone.

◆ ~SimpleIncremental2x2DetComputer()

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::~SimpleIncremental2x2DetComputer ( )

Destructor.

Member Function Documentation

◆ BOOST_CONCEPT_ASSERT() [1/2]

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::BOOST_CONCEPT_ASSERT ( (concepts::CEuclideanRing< ArgumentInteger >) )

◆ BOOST_CONCEPT_ASSERT() [2/2]

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::BOOST_CONCEPT_ASSERT ( (concepts::CEuclideanRing< ArgumentInteger >) )

◆ init()

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

void DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::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 TArgumentInteger , typename TResultInteger = TArgumentInteger>

bool DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::isValid ( ) const

Checks the validity/consistency of the object.

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

◆ operator()() [1/2]

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

ResultInteger DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::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: determinant of the 2x2 matrix that consists of the two above column vectors, ie. aA . aY - aB . aX

◆ operator()() [2/2]

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

ResultInteger DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::operator()	(	const ArgumentInteger &	aX,
		const ArgumentInteger &	aY
	)		const

Incremental operator.

Precondition: init must be called before

Parameters

aX	0-component of the second column vector
aY	1-component of the second column vector

Returns: the 2x2 matrix determinant, ie. myAY . aY - myBX . aX

◆ operator=()

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

SimpleIncremental2x2DetComputer & DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::operator= ( const SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger > & other )

Assignment.

Parameters

other the object to copy.

Returns: a reference on 'this'.

◆ partialComputation()

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

void DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::partialComputation ( ) const

private

Update myDet with respect to the new value of myDY.

Precondition: myDY should be updated first

See also: operator()

◆ selfDisplay()

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

void DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::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 TArgumentInteger , typename TResultInteger = TArgumentInteger>

ResultInteger DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::myA

private

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

Definition at line 204 of file SimpleIncremental2x2DetComputer.h.

◆ myADY

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

ResultInteger DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::myADY

mutableprivate

Data member used to store the product a.dy.

Definition at line 245 of file SimpleIncremental2x2DetComputer.h.

◆ myAY

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

ResultInteger DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::myAY

mutableprivate

Data member used to store the product a.y

Definition at line 213 of file SimpleIncremental2x2DetComputer.h.

◆ myB

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

ResultInteger DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::myB

private

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

Definition at line 209 of file SimpleIncremental2x2DetComputer.h.

◆ myBDX

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

ResultInteger DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::myBDX

mutableprivate

Data member used to store the product b.dx.

Definition at line 249 of file SimpleIncremental2x2DetComputer.h.

◆ myBX

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

ResultInteger DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::myBX

mutableprivate

Data member used to store the product b.x

Definition at line 217 of file SimpleIncremental2x2DetComputer.h.

◆ myDDet

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

ResultInteger DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::myDDet

mutableprivate

Data member used to store the partial determinant, ie. a.dy - b.dx

Definition at line 253 of file SimpleIncremental2x2DetComputer.h.

◆ myDet

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

ResultInteger DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::myDet

mutableprivate

Data member used to store the determinant, ie. ay - bx

Definition at line 221 of file SimpleIncremental2x2DetComputer.h.

◆ myDX

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

ResultInteger DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::myDX

mutableprivate

Data member used to store the difference between the last 0-component of the second column vector and a new one.

Definition at line 236 of file SimpleIncremental2x2DetComputer.h.

◆ myDY

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

ResultInteger DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::myDY

mutableprivate

Data member used to store the difference between the last 1-component of the second column vector and a new one.

Definition at line 241 of file SimpleIncremental2x2DetComputer.h.

◆ myX

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

ResultInteger DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::myX

mutableprivate

Data member used to store the 0-component of the second column vector, ie. x.

Definition at line 226 of file SimpleIncremental2x2DetComputer.h.

◆ myY

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

ResultInteger DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::myY

mutableprivate

Data member used to store the 1-component of the second column vector, ie. y.

Definition at line 231 of file SimpleIncremental2x2DetComputer.h.

◆ myZero

template<typename TArgumentInteger , typename TResultInteger = TArgumentInteger>

const ResultInteger DGtal::SimpleIncremental2x2DetComputer< TArgumentInteger, TResultInteger >::myZero

private

Definition at line 255 of file SimpleIncremental2x2DetComputer.h.

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

SimpleIncremental2x2DetComputer.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

◆ SimpleIncremental2x2DetComputer() [1/2]

◆ SimpleIncremental2x2DetComputer() [2/2]

◆ ~SimpleIncremental2x2DetComputer()

Member Function Documentation

◆ BOOST_CONCEPT_ASSERT() [1/2]

◆ BOOST_CONCEPT_ASSERT() [2/2]

◆ init()

◆ isValid()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator=()

◆ partialComputation()

◆ selfDisplay()

Field Documentation

◆ myA

◆ myADY

◆ myAY

◆ myB

◆ myBDX

◆ myBX

◆ myDDet

◆ myDet

◆ myDX

◆ myDY

◆ myX

◆ myY

◆ myZero