Aim: This class represents a naive (resp. standard) digital straight line (DSL), ie. the set of digital points \( (x,y) \in \mathbb{Z}^2 \) such that \( \mu \leq ax - by < \mu + \omega \) with \( a,b,\mu,\omega \in \mathbb{Z} \), \( \gcd(a,b) = 1 \) and \( \omega = \max(|a|,|b|) \) (resp. \( \omega = |a| + |b| \)). Note that any DSL such that \( \omega = \max(|a|,|b|) \) (resp. \( \omega = |a| + |b| \)) is simply 8-connected (resp. 4-connected). More...

#include <DGtal/geometry/curves/ArithmeticalDSL.h>

Inheritance diagram for DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >:

[legend]

Data Structures
class	ConstIterator
	Aim: This class aims at representing an iterator that provides a way to scan the points of a DSL. It is both a model of readable iterator and of bidirectional iterator. More...

Public Types
typedef TCoordinate	Coordinate

typedef TInteger	Integer

typedef ArithmeticalDSLKernel< Coordinate, adjacency >::Space	Space

typedef Space::Point	Point

typedef Space::Vector	Vector

typedef std::pair< Vector, Vector >	Steps

typedef Coordinate	Position

typedef std::pair< unsigned char, unsigned char >	Octant

typedef DGtal::ReverseIterator< ConstIterator >	ConstReverseIterator

Public Member Functions
	BOOST_CONCEPT_ASSERT ((concepts::CInteger< Coordinate >))

	BOOST_CONCEPT_ASSERT ((concepts::CInteger< Integer >))

	ArithmeticalDSL (const Coordinate &aA, const Coordinate &aB, const Integer &aLowerIntercept, const Integer &aUpperIntercept, const Steps &aSteps, const Vector &aShift)

	ArithmeticalDSL (const Coordinate &aA, const Coordinate &aB, const Integer &aMu)

	ArithmeticalDSL (const ArithmeticalDSL &aOther)

ArithmeticalDSL &	operator= (const ArithmeticalDSL &aOther)

ArithmeticalDSL	negate () const

bool	equalsTo (const ArithmeticalDSL &aOther) const

bool	operator== (const ArithmeticalDSL &aOther) const

bool	operator!= (const ArithmeticalDSL &aOther) const

bool	sameOctant (const ArithmeticalDSL &aOther, typename Octant::first_type *theOctant) const

bool	isUpperLeaningPoint (const Point &aPoint) const

bool	isLowerLeaningPoint (const Point &aPoint) const

Octant	octant () const

	~ArithmeticalDSL ()

void	selfDisplay (std::ostream &out) const

bool	checkShiftAndSteps () const

bool	isValid () const

Coordinate	a () const

Coordinate	b () const

Integer	mu () const

Integer	omega () const

Position	patternLength () const

Vector	shift () const

Steps	steps () const

Integer	remainder (const Point &aPoint) const

Integer	orthogonalPosition (const Point &aPoint) const

Position	position (const Point &aPoint) const

Point	getPoint () const

Point	getPoint (const Position &aPosition) const

bool	before (const Point &aP1, const Point &aP2) const

bool	beforeOrEqual (const Point &aP1, const Point &aP2) const

bool	isInDSL (const Point &aPoint) const

bool	operator() (const Point &aPoint) const

ConstIterator	begin (const Point &aPoint) const

ConstIterator	end (const Point &aPoint) const

ConstReverseIterator	rbegin (const Point &aPoint) const

ConstReverseIterator	rend (const Point &aPoint) const

Static Public Member Functions
static Integer	remainder (const Coordinate &aA, const Coordinate &aB, const Point &aPoint)

static Coordinate	toCoordinate (const Integer &aI)

Static Public Attributes
static const unsigned short	foregroundAdjacency = adjacency

Protected Attributes
Steps	mySteps

Vector	myShift

Coordinate	myA

Coordinate	myB

Integer	myLowerBound

Integer	myUpperBound

Friends
class	ArithmeticalDSS< TCoordinate, TInteger, adjacency >

Detailed Description

template<typename TCoordinate, typename TInteger = TCoordinate, unsigned short adjacency = 8>
class DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >

Aim: This class represents a naive (resp. standard) digital straight line (DSL), ie. the set of digital points \( (x,y) \in \mathbb{Z}^2 \) such that \( \mu \leq ax - by < \mu + \omega \) with \( a,b,\mu,\omega \in \mathbb{Z} \), \( \gcd(a,b) = 1 \) and \( \omega = \max(|a|,|b|) \) (resp. \( \omega = |a| + |b| \)). Note that any DSL such that \( \omega = \max(|a|,|b|) \) (resp. \( \omega = |a| + |b| \)) is simply 8-connected (resp. 4-connected).

[Reveilles, 1991 : [102]].

A naive DSL can be declared and constructed as follows:

#include "DGtal/arithmetic/geometry/curves/ArithmeticalDSL.h"
...
ArithmeticalDSL<DGtal::int32_t, DGtal::int64_t, 8> line( 17711, 28657, 1607895256 );
// equivalent to ArithmeticalDSL<DGtal::int32_t, DGtal::int64_t> line( 17711, 28657, 1607895256 );

See Digital straight lines and segments for further details.

This class is a model of CPointFunctor and of CConstBidirectionalRange.

In the standard case, it is enough to replace 8 by 4.

Template Parameters

TCoordinate	a model of integer for the DGtal point coordinates and the slope parameters.
TInteger	a model of integer for the intercepts and the remainders that represents a larger range of integers than TCoordinate.
adjacency	an unsigned integer equal to 8 (default) for naive DSL, and 4 for standard DSL.

See also: ArithmeticalDSL NaiveDSL StandardDSL; exampleArithmeticalDSL.cpp

Definition at line 106 of file ArithmeticalDSL.h.

Member Typedef Documentation

◆ ConstReverseIterator

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

DGtal::ReverseIterator<ConstIterator> DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::ConstReverseIterator

Type of const reverse iterator, adapted from ConstIterator.

Definition at line 297 of file ArithmeticalDSL.h.

◆ Coordinate

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

TCoordinate DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::Coordinate

Type used for the points coordinates and the slope parameters.

Definition at line 127 of file ArithmeticalDSL.h.

◆ Integer

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

TInteger DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::Integer

Type used for the intercepts and the remainders.

Definition at line 132 of file ArithmeticalDSL.h.

◆ Octant

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

std::pair<unsigned char, unsigned char> DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::Octant

Type of the octant values, defined as a STL pair of int

Definition at line 158 of file ArithmeticalDSL.h.

◆ Point

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

Space::Point DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::Point

Type of point.

Definition at line 141 of file ArithmeticalDSL.h.

◆ Position

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

Coordinate DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::Position

Type used for the position of a point in the DSL.

Definition at line 153 of file ArithmeticalDSL.h.

◆ Space

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

ArithmeticalDSLKernel<Coordinate,adjacency>::Space DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::Space

Type of digital plane.

Definition at line 137 of file ArithmeticalDSL.h.

◆ Steps

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

std::pair<Vector,Vector> DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::Steps

Type of step vectors, defined as STL pair of vectors.

Definition at line 149 of file ArithmeticalDSL.h.

◆ Vector

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

Space::Vector DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::Vector

Type of vector.

Definition at line 145 of file ArithmeticalDSL.h.

Constructor & Destructor Documentation

◆ ArithmeticalDSL() [1/3]

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::ArithmeticalDSL	(	const Coordinate &	aA,
		const Coordinate &	aB,
		const Integer &	aLowerIntercept,
		const Integer &	aUpperIntercept,
		const Steps &	aSteps,
		const Vector &	aShift )

Constructor. The user gives all the (redondant) parameters and should be sure that the resulting DSL is valid.

See also: isValid

Parameters

aA	y-component of the direction vector
aB	x-component of the direction vector
aLowerIntercept	lower intercept
aUpperIntercept	upper intercept
aSteps	pair of steps used to iterate over the DSL points
aShift	shift vector

◆ ArithmeticalDSL() [2/3]

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::ArithmeticalDSL	(	const Coordinate &	aA,
		const Coordinate &	aB,
		const Integer &	aMu )

Constructor with the minimal set of parameters.

Parameters

aA	y-component of the direction vector
aB	x-component of the direction vector
aMu	intercept

◆ ArithmeticalDSL() [3/3]

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::ArithmeticalDSL ( const ArithmeticalDSL< TCoordinate, TInteger, adjacency > & aOther )

Copy constructor.

Parameters

aOther the object to clone.

◆ ~ArithmeticalDSL()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::~ArithmeticalDSL ( )

Destructor.

Member Function Documentation

◆ a()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

Coordinate DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::a ( ) const

Returns: a parameter (y-component of the direction vector)

Referenced by exampleNaiveDSL(), and exampleStandardDSL().

◆ b()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

Coordinate DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::b ( ) const

Returns: b parameter (x-component of the direction vector)

Referenced by exampleNaiveDSL(), and exampleStandardDSL().

◆ before()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

bool DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::before	(	const Point &	aP1,
		const Point &	aP2 ) const

Returns a boolean equal to 'true' if aP1 is located (strictly) before aP2 in the direction orthogonal to myShift, 'false' otherwise.

Parameters

aP1	any point
aP2	any point

Returns: 'true' is aP1 is strictly before aP2, 'false' otherwise

See also: beforeOrEqual position

◆ beforeOrEqual()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

bool DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::beforeOrEqual	(	const Point &	aP1,
		const Point &	aP2 ) const

Returns a boolean equal to 'true' if aP1 is located before aP2 or is equal to aP2, 'false' otherwise.

Parameters

aP1	any point
aP2	any point

Returns: 'true' is aP1 is before or equal to aP2, 'false' otherwise

See also: before position

◆ begin()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

ConstIterator DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::begin ( const Point & aPoint ) const

Parameters

aPoint any point of the DSL

Precondition: aPoint should belong to the DSL

Returns: begin iterator, which points to aPoint

Referenced by exampleNaiveDSL(), and exampleStandardDSL().

◆ BOOST_CONCEPT_ASSERT() [1/2]

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::BOOST_CONCEPT_ASSERT ( (concepts::CInteger< Coordinate >) )

◆ BOOST_CONCEPT_ASSERT() [2/2]

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::BOOST_CONCEPT_ASSERT ( (concepts::CInteger< Integer >) )

◆ checkShiftAndSteps()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

bool DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::checkShiftAndSteps ( ) const

Checks the consistency between the slope parameters, ie. myA , myB and the translating vectors myShift , mySteps

Returns: 'true' if ok, 'false' otherwise

Precondition: myA and myB must not be both null

◆ end()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

ConstIterator DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::end ( const Point & aPoint ) const

Parameters

aPoint any point of the DSL

Precondition: aPoint should belong to the DSL

Returns: end iterator, which points to the point located after aPoint

Referenced by exampleNaiveDSL(), and exampleStandardDSL().

◆ equalsTo()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

bool DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::equalsTo ( const ArithmeticalDSL< TCoordinate, TInteger, adjacency > & aOther ) const

Equality.

Parameters

aOther the object to compare with.

Returns: 'true' if the parameters of the DSL are equal (orientation matters), 'false' otherwise

◆ getPoint() [1/2]

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

Point DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::getPoint ( ) const

Returns the unique point of the DSL located at position zero in O(1).

Precondition: the arithmetical thickness is not equal to zero

Returns: the point of the DSL located at position zero

◆ getPoint() [2/2]

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

Point DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::getPoint ( const Position & aPosition ) const

Returns the unique point of the DSL located at position aPosition in O(1).

Precondition: the arithmetical thickness is not equal to zero

Parameters

aPosition position of the returned point

Returns: the point of the DSL located at position aPosition

◆ isInDSL()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

bool DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::isInDSL ( const Point & aPoint ) const

Returns: 'true' if aPoint is in the DSL 'false' otherwise.

Parameters

aPoint any point

◆ isLowerLeaningPoint()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

bool DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::isLowerLeaningPoint ( const Point & aPoint ) const

Test if a point is a lower leaning point of *this

Parameters

aPoint a point

Returns: 'true' if aPoint is a lower leaning point of *this, false otherwise

◆ isUpperLeaningPoint()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

bool DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::isUpperLeaningPoint ( const Point & aPoint ) const

Test if a point is an upper leaning point of *this

Parameters

aPoint a point

Returns: 'true' if aPoint is an upper leaning point of *this, false otherwise

◆ isValid()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

bool DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::isValid ( ) const

Checks the validity/consistency of the object.

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

NB: runs in O( log( max( |myA |,| myB | ) ) ) because it checks if myA and myB are relatively primes.

Referenced by exampleArithmeticalDSLTypes().

◆ mu()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

Integer DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::mu ( ) const

Returns: mu parameter, the intercept \( \mu \)

◆ negate()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

ArithmeticalDSL DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::negate ( ) const

Returns a copy of '*this' with a reverse orientation, ie. with parameters ( -myA , -myB , -myUpperIntercept , -myLowerIntercept).

Returns: the negation of '*this'.

Referenced by exampleNaiveDSL(), and exampleStandardDSL().

◆ octant()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

Octant DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::octant ( ) const

Returns the octants of the DSL as a pair of integers. If the parameters are such that \( abs(@a myA) = abs(@a myB) \) or \( @a myA = 0 \) or \( @a myB = 0 \), it returns two octants (for instance octants 0 and 7 if \( @a myA = 0 \)).

Returns: the octants as a pair of integers

◆ omega()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

Integer DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::omega ( ) const

Returns: the arithmetical thickness \( \omega \)

See also: patternLength

◆ operator!=()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

bool DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::operator!= ( const ArithmeticalDSL< TCoordinate, TInteger, adjacency > & aOther ) const

Difference.

Parameters

aOther the object to compare with.

Returns: 'true' the two set of points that are implicitly defined are different, 'false' otherwise

◆ operator()()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

bool DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::operator() ( const Point & aPoint ) const

Returns: 'true' if aPoint is in the DSL 'false' otherwise.

Parameters

aPoint any point

See also: isInDSL

◆ operator=()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

ArithmeticalDSL & DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::operator= ( const ArithmeticalDSL< TCoordinate, TInteger, adjacency > & aOther )

Assignment.

Parameters

aOther the object to copy.

Returns: a reference on 'this'.

◆ operator==()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

bool DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::operator== ( const ArithmeticalDSL< TCoordinate, TInteger, adjacency > & aOther ) const

Equality.

Parameters

aOther the object to compare with.

Returns: 'true' the two sets of points that are implicitly defined are equal (without respect to the orientation), 'false' otherwise

See also: equalsTo

◆ orthogonalPosition()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

Integer DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::orthogonalPosition ( const Point & aPoint ) const

Returns the position of aPoint (which does not necessarily belong to the DSL) computed along the direction that is orthogonal to the direction vector

Parameters

aPoint the point whose position is returned

Returns: the position

◆ patternLength()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

Position DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::patternLength ( ) const

Returns: the pattern length (equal to \( omega \))

See also: omega

◆ position()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

Position DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::position ( const Point & aPoint ) const

Returns the position of aPoint (which does not necessarily belong to the DSL) computed along the direction orthogonal to myShift

Parameters

aPoint the point whose position is returned

Returns: the position

◆ rbegin()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

ConstReverseIterator DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::rbegin ( const Point & aPoint ) const

Parameters

aPoint any point of the DSL

Precondition: aPoint sould belongs to the DSL

Returns: begin reverse iterator, which points to aPoint

◆ remainder() [1/2]

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

static Integer DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::remainder	(	const Coordinate &	aA,
		const Coordinate &	aB,
		const Point &	aPoint )

static

Returns the remainder of aPoint with respect to the direction vector of components aA and aB

Parameters

aA	y-component of the direction vector
aB	x-component of the direction vector
aPoint	any point

Returns: remainder of aPoint

◆ remainder() [2/2]

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

Integer DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::remainder ( const Point & aPoint ) const

Returns the remainder of aPoint (which does not necessarily belong to the DSL)

Returns: remainder of aPoint

Parameters

aPoint any point

◆ rend()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

ConstReverseIterator DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::rend ( const Point & aPoint ) const

Parameters

aPoint any point of the DSL

Precondition: aPoint sould belongs to the DSL

Returns: end iterator, which points to the point located before aPoint

◆ sameOctant()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

bool DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::sameOctant	(	const ArithmeticalDSL< TCoordinate, TInteger, adjacency > &	aOther,
		typename Octant::first_type *	theOctant ) const

Test if DSLs lie in the same octant.

Parameters

	aOther	the object to compare with.
[out]	theOctant	where to store the common octant if the DSLs are in the same octant.

Returns: 'true' if the two DSLs lie in the same octant, 'false' otherwise

See also: sameOctant

◆ selfDisplay()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

void DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::selfDisplay ( std::ostream & out ) const

Writes/Displays the object on an output stream.

Parameters

out	the output stream where the object is written.

◆ shift()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

Vector DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::shift ( ) const

Returns: the shift vector (translating a point of remainder \( r \) to a point of remainder \( r+\omega \)).

◆ steps()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

Steps DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::steps ( ) const

Returns: the two vectors used to iterate over the DSL points.

◆ toCoordinate()

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

static Coordinate DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::toCoordinate ( const Integer & aI )

static

Friends And Related Symbol Documentation

◆ ArithmeticalDSS< TCoordinate, TInteger, adjacency >

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

friend class ArithmeticalDSS< TCoordinate, TInteger, adjacency >

friend

Definition at line 672 of file ArithmeticalDSL.h.

Field Documentation

◆ foregroundAdjacency

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

const unsigned short DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::foregroundAdjacency = adjacency

static

Adjacency of the DSL.

Definition at line 118 of file ArithmeticalDSL.h.

◆ myA

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

Coordinate DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::myA

protected

y-component of the direction vector

Definition at line 641 of file ArithmeticalDSL.h.

◆ myB

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

Coordinate DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::myB

protected

x-component of the direction vector

Definition at line 645 of file ArithmeticalDSL.h.

◆ myLowerBound

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

Integer DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::myLowerBound

protected

Lower intercept. Invariants:

for any upper leaning point U, we have remainder(U) == myLowerBound.
myLowerBound <= myUpperBound

Definition at line 651 of file ArithmeticalDSL.h.

◆ myShift

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

Vector DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::myShift

protected

Shift vector. It is computed from myA and myB in ArithmeticalDSLKernel.

See also: ArithmeticalDSLKernel::shift

Definition at line 635 of file ArithmeticalDSL.h.

◆ mySteps

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

Steps DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::mySteps

protected

Pair of steps used to iterate over the DSL points. They are computed from myA and myB in ArithmeticalDSLKernel.

See also: ArithmeticalDSLKernel::steps

Definition at line 630 of file ArithmeticalDSL.h.

◆ myUpperBound

template<typename TCoordinate , typename TInteger = TCoordinate, unsigned short adjacency = 8>

Integer DGtal::ArithmeticalDSL< TCoordinate, TInteger, adjacency >::myUpperBound

protected

Upper intercept. Invariants:

for any lower leaning point L, we have remainder(L) == myUpperBound.
if myA and myB are not both null, myUpperBound == myLowerBound + omega() - 1
myLowerBound <= myUpperBound

Definition at line 658 of file ArithmeticalDSL.h.

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

ArithmeticalDSL.h

Data Structures

Public Types

Public Member Functions

Static Public Member Functions

Static Public Attributes

Protected Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ ConstReverseIterator

◆ Coordinate

◆ Integer

◆ Octant

◆ Point

◆ Position

◆ Space

◆ Steps

◆ Vector

Constructor & Destructor Documentation

◆ ArithmeticalDSL() [1/3]

◆ ArithmeticalDSL() [2/3]

◆ ArithmeticalDSL() [3/3]

◆ ~ArithmeticalDSL()

Member Function Documentation

◆ a()

◆ b()

◆ before()

◆ beforeOrEqual()

◆ begin()

◆ BOOST_CONCEPT_ASSERT() [1/2]

◆ BOOST_CONCEPT_ASSERT() [2/2]

◆ checkShiftAndSteps()

◆ end()

◆ equalsTo()

◆ getPoint() [1/2]

◆ getPoint() [2/2]

◆ isInDSL()

◆ isLowerLeaningPoint()

◆ isUpperLeaningPoint()

◆ isValid()

◆ mu()

◆ negate()

◆ octant()

◆ omega()

◆ operator!=()

◆ operator()()

◆ operator=()

◆ operator==()

◆ orthogonalPosition()

◆ patternLength()

◆ position()

◆ rbegin()

◆ remainder() [1/2]

◆ remainder() [2/2]

◆ rend()

◆ sameOctant()

◆ selfDisplay()

◆ shift()

◆ steps()

◆ toCoordinate()

Friends And Related Symbol Documentation

◆ ArithmeticalDSS< TCoordinate, TInteger, adjacency >

Field Documentation

◆ foregroundAdjacency

◆ myA

◆ myB

◆ myLowerBound

◆ myShift

◆ mySteps

◆ myUpperBound