Aim: This class represents a naive (resp. standard) digital straight segment (DSS), ie. the sequence of simply 8- (resp. 4-)connected digital points contained in a naive (resp. standard) digital straight line (DSL) between two points of it. More...

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

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

[legend]

Public Types
typedef TCoordinate	Coordinate

typedef TInteger	Integer

typedef ArithmeticalDSL< Coordinate, Integer, adjacency >	DSL

typedef DSL::Space	Space

typedef DSL::Point	Point

typedef DSL::Vector	Vector

typedef DSL::Steps	Steps

typedef Coordinate	Position

typedef DSL::ConstIterator	ConstIterator

typedef DSL::ConstReverseIterator	ConstReverseIterator

typedef DGtal::PointVector< 2, double >	PointD

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

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

	ArithmeticalDSS (const Point &aPoint)

	ArithmeticalDSS (const Coordinate &aA, const Coordinate &aB, const Integer &aLowerBound, const Integer &aUpperBound, const Point &aF, const Point &aL, const Point &aUf, const Point &aUl, const Point &aLf, const Point &aLl, const Steps &aSteps, const Vector &aShift)

	ArithmeticalDSS (const DSL &aDSL, const Point &aF, const Point &aL, const Point &aUf, const Point &aUl, const Point &aLf, const Point &aLl)

	ArithmeticalDSS (const Coordinate &aA, const Coordinate &aB, const Point &aF, const Point &aL, const Point &aUf, const Point &aUl, const Point &aLf, const Point &aLl)

	ArithmeticalDSS (const Point &aF, const Point &aL, const bool &areOnTheUpperLine=true)

	ArithmeticalDSS (const DSL &aDSL, const Point &aF, const Point &aL)

	ArithmeticalDSS (const ArithmeticalDSS &aDSS, const Point &aF, const Point &aL)

template<typename Iterator >
	ArithmeticalDSS (const Iterator &aItb, const Iterator &aIte)

	ArithmeticalDSS (const ArithmeticalDSS &aOther)

ArithmeticalDSS &	operator= (const ArithmeticalDSS &aOther)

ArithmeticalDSS	negate () const

bool	equalsTo (const ArithmeticalDSS &aOther) const

bool	operator== (const ArithmeticalDSS &aOther) const

bool	operator!= (const ArithmeticalDSS &aOther) const

	~ArithmeticalDSS ()

void	selfDisplay (std::ostream &out) const

bool	isValid () const

const DSL &	dsl () const

Coordinate	a () const

Coordinate	b () const

Integer	mu () const

Integer	omega () const

Vector	shift () const

Steps	steps () const

Point	back () const

Point	front () const

Point	Uf () const

Point	Ul () const

Point	Lf () const

Point	Ll () const

Integer	remainder (const Point &aPoint) const

Integer	orthogonalPosition (const Point &aPoint) const

Position	position (const Point &aPoint) 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	isInDSS (const Point &aPoint) const

bool	operator() (const Point &aPoint) const

bool	isInDSL (const DSL &aDSL) const

bool	isInDSL (const DSL &aDSL, std::vector< Point > &Ulp, std::vector< Point > &Llp, Point &outP) const

ArithmeticalDSS	computeUnion (const ArithmeticalDSS &aOther) const

ConstIterator	begin () const

ConstIterator	end () const

ConstReverseIterator	rbegin () const

ConstReverseIterator	rend () const

unsigned short int	isExtendableFront (const Point &aNewPoint) const

unsigned short int	isExtendableBack (const Point &aNewPoint) const

bool	extendFront (const Point &aNewPoint)

bool	extendBack (const Point &aNewPoint)

bool	retractFront ()

bool	retractBack ()

PointD	project (const Point &aM, double aR) const

PointD	project (const Point &aM, const Point &aP) const

std::string	className () const

Static Public Attributes
static const unsigned short	foregroundAdjacency = adjacency

Protected Member Functions
bool	retractUpdateLeaningPoints (const Vector &aDirection, const Point &aFirst, const Point &aLast, const Point &aBezout, const Point &aFirstAtOppositeSide, Point &aLastAtOppositeSide, Point &aFirstAtRemovalSide, const Point &aLastAtRemovalSide)

void	retractUpdateParameters (const Vector &aNewDirection)

Protected Attributes
Point	myF

Point	myL

Point	myUf

Point	myUl

Point	myLf

Point	myLl

DSL	myDSL

Friends
class	ArithmeticalDSSFactory< TCoordinate, TInteger, adjacency >

Detailed Description

template<typename TCoordinate, typename TInteger, unsigned short adjacency>
class DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >

Aim: This class represents a naive (resp. standard) digital straight segment (DSS), ie. the sequence of simply 8- (resp. 4-)connected digital points contained in a naive (resp. standard) digital straight line (DSL) between two points of it.

Obviously, a given DSS belongs to infinitely many DSLs, but one of them has minimal parameters, ie has a minimal \( \omega \). ArithmeticalDSS uses this minimal bounding DSL to represent its slope and its intercept.
ArithmeticalDSS stores as data members not only this minimal bounding DSL, but also its ending points as well as the first and last lower and upper leaning points, due to the role that these points play in the update algorithms. Indeed, ArithmeticalDSS provides some methods to update its internal representation:

ArithmeticalDSS::extendFront and ArithmeticalDSS::extendBack based on the incremental recognition algorithm of [Debled and Reveilles, 1995 : [46]].
ArithmeticalDSS::retractFront and ArithmeticalDSS::retractBack based on [Lachaud et. al., 2007, Th. 5 : [72]].

See Digital straight lines and segments for further details. See also NaiveDSS8 and StandardDSS4, which are aliases of this class.

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.

This class is a model of CPointFunctor and of CConstBidirectionalRange.

See also: ArithmeticalDSL NaiveDSL StandardDSL; exampleArithmeticalDSL.cpp exampleArithmeticalDSS.cpp

Definition at line 55 of file ArithmeticalDSSFactory.h.

Member Typedef Documentation

◆ ConstIterator

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

typedef DSL::ConstIterator DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::ConstIterator

Type of iterator.

Definition at line 148 of file ArithmeticalDSS.h.

◆ ConstReverseIterator

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

typedef DSL::ConstReverseIterator DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::ConstReverseIterator

Type of reverse iterator.

Definition at line 152 of file ArithmeticalDSS.h.

◆ Coordinate

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

typedef TCoordinate DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::Coordinate

Type used for the points coordinates and the slope parameters.

Definition at line 113 of file ArithmeticalDSS.h.

◆ DSL

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

typedef ArithmeticalDSL<Coordinate, Integer, adjacency> DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::DSL

Type of the bounding DSL.

Definition at line 124 of file ArithmeticalDSS.h.

◆ Integer

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

typedef TInteger DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::Integer

Type used for the intercepts and the remainders.

Definition at line 118 of file ArithmeticalDSS.h.

◆ Point

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

typedef DSL::Point DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::Point

Type of point.

Definition at line 132 of file ArithmeticalDSS.h.

◆ PointD

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

typedef DGtal::PointVector<2, double> DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::PointD

Type of embedded points

See also: project

Definition at line 158 of file ArithmeticalDSS.h.

◆ Position

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

typedef Coordinate DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::Position

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

Definition at line 144 of file ArithmeticalDSS.h.

◆ Space

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

typedef DSL::Space DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::Space

Type of digital space.

Definition at line 128 of file ArithmeticalDSS.h.

◆ Steps

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

typedef DSL::Steps DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::Steps

Type of steps (defined as a STL pair of vectors).

Definition at line 140 of file ArithmeticalDSS.h.

◆ Vector

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

typedef DSL::Vector DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::Vector

Type of vector.

Definition at line 136 of file ArithmeticalDSS.h.

Constructor & Destructor Documentation

◆ ArithmeticalDSS() [1/9]

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

DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::ArithmeticalDSS ( const Point & aPoint )

Simple constructor. All members of the bounding DSL are set to zero and all point members are set to aPoint

◆ ArithmeticalDSS() [2/9]

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

DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::ArithmeticalDSS	(	const Coordinate &	aA,
		const Coordinate &	aB,
		const Integer &	aLowerBound,
		const Integer &	aUpperBound,
		const Point &	aF,
		const Point &	aL,
		const Point &	aUf,
		const Point &	aUl,
		const Point &	aLf,
		const Point &	aLl,
		const Steps &	aSteps,
		const Vector &	aShift )

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

See also: isValid

Parameters

aA	y-component of the direction vector
aB	x-component of the direction vector
aLowerBound	lower intercept
aUpperBound	upper intercept
aF	the first point
aL	the last point
aUf	the first upper point
aUl	the last upper point
aLf	the first lower point
aLl	the last lower point
aSteps	pair of steps used to iterate over the DSS points
aShift	shift vector

◆ ArithmeticalDSS() [3/9]

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

DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::ArithmeticalDSS	(	const DSL &	aDSL,
		const Point &	aF,
		const Point &	aL,
		const Point &	aUf,
		const Point &	aUl,
		const Point &	aLf,
		const Point &	aLl )

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

See also: isValid

Parameters

aDSL	bounding DSL
aF	the first point
aL	the last point
aUf	the first upper point
aUl	the last upper point
aLf	the first lower point
aLl	the last lower point

◆ ArithmeticalDSS() [4/9]

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

DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::ArithmeticalDSS	(	const Coordinate &	aA,
		const Coordinate &	aB,
		const Point &	aF,
		const Point &	aL,
		const Point &	aUf,
		const Point &	aUl,
		const Point &	aLf,
		const Point &	aLl )

Constructor. Minimal set of parameters to build the DSS in constant time. The user should be sure that the slope is consistent with the position of the leaning points.

See also: isValid

Parameters

aA	y-component of the direction vector
aB	x-component of the direction vector
aF	the first point
aL	the last point
aUf	the first upper point
aUl	the last upper point
aLf	the first lower point
aLl	the last lower point

NB: in O(1)

◆ ArithmeticalDSS() [5/9]

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

DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::ArithmeticalDSS	(	const Point &	aF,
		const Point &	aL,
		const bool &	areOnTheUpperLine = true )

Construction of a sequence of patterns (or reversed patterns) from two end points.

Parameters

aF	the first point
aL	the last point
areOnTheUpperLine	boolean equal to 'true' if the two given end points are upper leaning points (pattern case, default), 'false' if they are lower leaning points (reversed pattern case).

NB: logarithmic-time in the greatest component of the vector starting from aF and pointing to aL

◆ ArithmeticalDSS() [6/9]

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

DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::ArithmeticalDSS	(	const DSL &	aDSL,
		const Point &	aF,
		const Point &	aL )

Construction as the subsegment of minimal parameters of a given DSL.

Parameters

aDSL	bounding DSL
aF	first point of the subsegment
aL	last point of the subsegment

NB: logarithmic-time in the greatest component of the direction vector of the subsegment. Uses smartCH algorithm (see Roussillon 2014 [105]).

See also: ArithmeticalDSSFactory

◆ ArithmeticalDSS() [7/9]

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

DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::ArithmeticalDSS	(	const ArithmeticalDSS< TCoordinate, TInteger, adjacency > &	aDSS,
		const Point &	aF,
		const Point &	aL )

Construction as the subsegment of minimal parameters of a greater DSS.

Parameters

aDSS	bounding DSS
aF	first point of the subsegment
aL	last point of the subsegment

NB: logarithmic-time in the greatest component of the direction vector of the subsegment. Uses reversedSmartCH algorithm (see Roussillon 2014 [105]).

See also: ArithmeticalDSSFactory

◆ ArithmeticalDSS() [8/9]

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

template<typename Iterator >

DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::ArithmeticalDSS	(	const Iterator &	aItb,
		const Iterator &	aIte )

Construction from a range of iterator on points.

Parameters

aItb	begin iterator
aIte	end iterator

Template Parameters

Iterator a model of forward iterator

NB: linear-time in the size of the range

◆ ArithmeticalDSS() [9/9]

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

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

Copy constructor.

Parameters

aOther the object to clone.

◆ ~ArithmeticalDSS()

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

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

Destructor.

Member Function Documentation

◆ a()

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

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

Returns: a parameter of the bounding DSL of minimal parameters

◆ b()

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

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

Returns: b parameter of the bounding DSL of minimal parameters

◆ back()

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

Point DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::back ( ) const

Returns: back point of the DSS, ie. first visited point equal to * ArithmeticalDSS::begin()

◆ before()

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

bool DGtal::ArithmeticalDSS< 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 aP2 is strictly before aP2, 'false' otherwise

See also: beforeOrEqual position

◆ beforeOrEqual()

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

bool DGtal::ArithmeticalDSS< 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 aP2 is before or equal to aP2, 'false' otherwise

See also: before position

◆ begin()

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

ConstIterator DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::begin ( ) const

Returns: begin iterator, which points to the point returned by ArithmeticalDSS::back()

Referenced by exampleConstructors(), and exampleNaiveDSS().

◆ BOOST_CONCEPT_ASSERT() [1/2]

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

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

◆ BOOST_CONCEPT_ASSERT() [2/2]

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

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

◆ className()

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

std::string DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::className ( ) const

Returns: the style name used for drawing this object.

Referenced by exampleNaiveDSS(), exampleStandardDSS(), and exampleUpdate().

◆ computeUnion()

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

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

Compute the union of two DSSs. If the union belongs to a DSL, returns the DSS of minimal characteristics that includes the two DSSs. Otherwise, returns the void DSS (DSS(Point(0,0)). See Sivignon 2014 [114]).

Parameters

aOther a DSS

Returns: a DSS

nb: runs in O(1) when: 1) the union of the two DSSs is not part of a DSL, 2) the two DSSs are connected, 3) the last point of the first DSS and the first point of the second DSS have the same ordinate (or abscissa). Otherwise, runs in O(log(n)) where n is the total length of the union.

◆ dsl()

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

const DSL & DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::dsl ( ) const

Returns: the bounding DSL of minimal parameters NB: since we return a const reference, you must copy the result, if you want to keep it beyond the object's existence.

◆ end()

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

ConstIterator DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::end ( ) const

Returns: end iterator, which points after the point returned by ArithmeticalDSS::front()

Referenced by exampleConstructors(), and exampleNaiveDSS().

◆ equalsTo()

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

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

Equality.

Parameters

aOther the object to compare with.

Returns: 'true' if all the members of the two objects are equal, 'false' otherwise

Referenced by exampleUpdate().

◆ extendBack()

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

bool DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::extendBack ( const Point & aNewPoint )

Tests whether the union between a point, which is located at the back of the DSS, and the DSS is still a DSS. Computes the parameters of the new DSS with the adding point if true.

Parameters

aNewPoint the point to add

Returns: 'true' if the union is a DSS, 'false' otherwise.

See also: isExtendableBack extendFront

◆ extendFront()

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

bool DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::extendFront ( const Point & aNewPoint )

Tests whether the union between a point, which is located at the front of the DSS, and the DSS is still a DSS. Computes the parameters of the new DSS with the adding point if true.

Parameters

aNewPoint the point to add

Returns: 'true' if the union is a DSS, 'false' otherwise.

See also: isExtendableFront extendBack

Referenced by exampleUpdate().

◆ front()

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

Point DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::front ( ) const

Returns: front point of the DSS, ie. last visited point equal to * - - ArithmeticalDSS::end()

◆ isExtendableBack()

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

unsigned short int DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::isExtendableBack ( const Point & aNewPoint ) const

Tests whether the union between a new point, which is located at the back of the DSS, and the DSS is still a DSS.

Parameters

aNewPoint the point to test

Returns: an integer equal to 0 if the union between aNewPoint and the segment is not a DSS, but strictly greater than 0 otherwise. The value gives the way of updating the members of the DSS: 1: initialization of the first step 2: repetition of the first step 3: initialization of the second step on the left 4: initialization of the second step on the right 5: weakly interior on the left 6: weakly interior on the right 7: weakly exterior on the left 8: weakly exterior on the right 9: strongly interior, nothing to update

See also: extend isExtendableFront

◆ isExtendableFront()

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

unsigned short int DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::isExtendableFront ( const Point & aNewPoint ) const

Tests whether the union between a new point, which is located at the front of the DSS, and the DSS is still a DSS.

Parameters

aNewPoint a point to test

Returns: an integer equal to 0 if the union between aNewPoint and the segment is not a DSS, but strictly greater than 0 otherwise. The value gives the way of updating the members of the DSS: 1: initialization of the first step 2: repetition of the first step 3: initialization of the second step on the left 4: initialization of the second step on the right 5: weakly interior on the left 6: weakly interior on the right 7: weakly exterior on the left 8: weakly exterior on the right 9: strongly interior, nothing to update

See also: extend isExtendableBack

◆ isInDSL() [1/3]

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

bool DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::isInDSL ( const DSL & aDSL ) const

Returns a boolean equal to true if 'this' belongs to the DSL aDSL, false otherwise.

Returns: 'true' if 'this' belongs to the DSL aDSL. 'false' otherwise.

Parameters

aDSL any DSL

◆ isInDSL() [2/3]

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

bool DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::isInDSL	(	const DSL &	aDSL,
		std::vector< Point > &	Ulp,
		std::vector< Point > &	Llp,
		Point &	outP ) const

Returns a boolean equal to true if 'this' belongs to the DSL aDSL, false otherwise. Also returns extra information about the leaning points included in 'this' or a point outside aDSL.

Parameters

[in]	aDSL	any DSL
[in,out]	Ulp	the list of aDSL upper leaning points on 'this', if any
[in,out]	Llp	the list of aDSL lower leaning points on 'this', if any
[in,out]	outP	a point of 'this' that does not belong to aDSL, if any

Returns: 'true' if 'this' belongs to the DSL aDSL. 'false' otherwise.

◆ isInDSL() [3/3]

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

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

Returns: 'true' if aPoint is in the DSL of minimal parameters containing this segment, 'false' otherwise.

Parameters

aPoint any point

◆ isInDSS()

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

bool DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::isInDSS ( const Point & aPoint ) const

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

Parameters

aPoint any point

◆ isValid()

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

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

Checks the validity/consistency of the object.

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

NB: in O( log( max( |myA |,| myB | ) ) )

Referenced by exampleConstructors(), and exampleUpdate().

◆ Lf()

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

Point DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::Lf ( ) const

Returns: first lower leaning point of the DSS

◆ Ll()

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

Point DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::Ll ( ) const

Returns: last lower leaning point of the DSS

◆ mu()

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

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

Returns: mu parameter, the intercept of the bounding DSL of minimal parameters

◆ negate()

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

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

Returns a copy of '*this' with a reverse orientation, ie. with parameters -myA , -myB , -myUpperBound , -myLowerBound and swapped leaning points.

Returns: the negation of '*this'.

◆ omega()

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

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

Returns: omega parameter, the thickness of the bounding DSL of minimal parameters

◆ operator!=()

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

bool DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::operator!= ( const ArithmeticalDSS< 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 , unsigned short adjacency>

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

◆ operator=()

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

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

Assignment.

Parameters

aOther the object to copy.

Returns: a reference on 'this'.

◆ operator==()

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

bool DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::operator== ( const ArithmeticalDSS< 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

◆ orthogonalPosition()

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

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

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

Parameters

aPoint the point whose position is returned

Returns: the position

◆ position()

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

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

Returns the position of aPoint (which does not necessarily belong to the DSS) computed along the direction given by myShift

Parameters

aPoint the point whose position is returned

Returns: the position

Referenced by exampleNaiveDSS().

◆ project() [1/2]

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

PointD DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::project	(	const Point &	aM,
		const Point &	aP ) const

Projects the point aM onto the straight line going through point aP.

Parameters

aM	any point (may not be part of the DSS).
aP	any point (may not be part of the DSS).

Returns: the projected point.

◆ project() [2/2]

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

PointD DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::project	(	const Point &	aM,
		double	aR ) const

Projects the point aM onto the straight line whose points have remainder aR.

Parameters

aM	any point (may not be part of the DSS).
aR	the remainder (may not be an integer).

Returns: the projected point.

◆ rbegin()

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

ConstReverseIterator DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::rbegin ( ) const

Returns: begin reverse iterator, which points to the point returned by ArithmeticalDSS::front()

◆ remainder()

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

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

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

Returns: remainder of aPoint

Parameters

aPoint any point

Referenced by exampleNaiveDSS().

◆ rend()

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

ConstReverseIterator DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::rend ( ) const

Returns: end iterator, which points before the point returned by ArithmeticalDSS::back()

◆ retractBack()

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

bool DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::retractBack ( )

Removes the back point of the DSS if it remains strictly more than one point

Returns: 'true' if the retraction has been done, 'false' otherwise

See also: retract

◆ retractFront()

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

bool DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::retractFront ( )

Removes the front point of the DSS if it remains strictly more than one point

Returns: 'true' if the retraction has been done, 'false' otherwise

See also: retract

Referenced by exampleUpdate().

◆ retractUpdateLeaningPoints()

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

bool DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::retractUpdateLeaningPoints	(	const Vector &	aDirection,
		const Point &	aFirst,
		const Point &	aLast,
		const Point &	aBezout,
		const Point &	aFirstAtOppositeSide,
		Point &	aLastAtOppositeSide,
		Point &	aFirstAtRemovalSide,
		const Point &	aLastAtRemovalSide )

protected

Updates the leaning points of the DSS if the end point is a leaning point that has to be removed from the DSS.

Parameters

aDirection	direction vector
aFirst	new end of the DSS
aLast	opposite end of the DSS
aBezout	weakly exterior point used to compute the new slope and to update the leaning points
aFirstAtOppositeSide	first leaning point located at the side that is not affected by the removal
aLastAtOppositeSide	last leaning point located at the side that is not affected by the removal but that has to be updated
aFirstAtRemovalSide	first leaning point that is removed and has to be updated.
aLastAtRemovalSide	last leaning point located on the same side than aFirstAtRemovalSide

Returns: 'true' is the slope has to be updated, 'false' otherwise

See also: retractFront retractBack

◆ retractUpdateParameters()

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

void DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::retractUpdateParameters ( const Vector & aNewDirection )

protected

Updates the parameters of the bounding DSL after the retraction.

Parameters

aNewDirection direction vector

See also: retractFront retractBack

◆ selfDisplay()

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

void DGtal::ArithmeticalDSS< 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 , unsigned short adjacency>

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

Returns: the shift vector

◆ steps()

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

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

Returns: the couple of vectors used to iterate over the DSS point.

◆ Uf()

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

Point DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::Uf ( ) const

Returns: first upper leaning point of the DSS

◆ Ul()

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

Point DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::Ul ( ) const

Returns: last upper leaning point of the DSS

Friends And Related Symbol Documentation

◆ ArithmeticalDSSFactory< TCoordinate, TInteger, adjacency >

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

friend class ArithmeticalDSSFactory< TCoordinate, TInteger, adjacency >

friend

Definition at line 793 of file ArithmeticalDSS.h.

Field Documentation

◆ foregroundAdjacency

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

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

static

Adjacency of the DSL.

Definition at line 104 of file ArithmeticalDSS.h.

◆ myDSL

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

DSL DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::myDSL

protected

Bounding DSL of minimal parameters

Definition at line 781 of file ArithmeticalDSS.h.

◆ myF

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

Point DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::myF

protected

First point

Definition at line 755 of file ArithmeticalDSS.h.

◆ myL

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

Point DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::myL

protected

Last point

Definition at line 759 of file ArithmeticalDSS.h.

◆ myLf

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

Point DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::myLf

protected

First lower leaning point ( of remainder myMu + myOmega - 1 )

Definition at line 771 of file ArithmeticalDSS.h.

◆ myLl

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

Point DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::myLl

protected

Last lower leaning point ( of remainder myMu + myOmega - 1 )

Definition at line 775 of file ArithmeticalDSS.h.

◆ myUf

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

Point DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::myUf

protected

First upper leaning point ( of remainder myMu )

Definition at line 763 of file ArithmeticalDSS.h.

◆ myUl

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

Point DGtal::ArithmeticalDSS< TCoordinate, TInteger, adjacency >::myUl

protected

Last upper leaning point ( of remainder myMu )

Definition at line 767 of file ArithmeticalDSS.h.

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

Public Types

Public Member Functions

Static Public Attributes

Protected Member Functions

Protected Attributes

Friends

Detailed Description

Member Typedef Documentation

◆ ConstIterator

◆ ConstReverseIterator

◆ Coordinate

◆ DSL

◆ Integer

◆ Point

◆ PointD

◆ Position

◆ Space

◆ Steps

◆ Vector

Constructor & Destructor Documentation

◆ ArithmeticalDSS() [1/9]

◆ ArithmeticalDSS() [2/9]

◆ ArithmeticalDSS() [3/9]

◆ ArithmeticalDSS() [4/9]

◆ ArithmeticalDSS() [5/9]

◆ ArithmeticalDSS() [6/9]

◆ ArithmeticalDSS() [7/9]

◆ ArithmeticalDSS() [8/9]

◆ ArithmeticalDSS() [9/9]

◆ ~ArithmeticalDSS()

Member Function Documentation

◆ a()

◆ b()

◆ back()

◆ before()

◆ beforeOrEqual()

◆ begin()

◆ BOOST_CONCEPT_ASSERT() [1/2]

◆ BOOST_CONCEPT_ASSERT() [2/2]

◆ className()

◆ computeUnion()

◆ dsl()

◆ end()

◆ equalsTo()

◆ extendBack()

◆ extendFront()

◆ front()

◆ isExtendableBack()

◆ isExtendableFront()

◆ isInDSL() [1/3]

◆ isInDSL() [2/3]

◆ isInDSL() [3/3]

◆ isInDSS()

◆ isValid()

◆ Lf()

◆ Ll()

◆ mu()

◆ negate()

◆ omega()

◆ operator!=()

◆ operator()()

◆ operator=()

◆ operator==()

◆ orthogonalPosition()

◆ position()

◆ project() [1/2]

◆ project() [2/2]

◆ rbegin()

◆ remainder()

◆ rend()

◆ retractBack()

◆ retractFront()

◆ retractUpdateLeaningPoints()

◆ retractUpdateParameters()

◆ selfDisplay()

◆ shift()

◆ steps()

◆ Uf()

◆ Ul()

Friends And Related Symbol Documentation