Aim: Represents a digital straight line with slope in the first quadrant (Q0: x >= 0, y >= 0 ). More...

#include <DGtal/arithmetic/StandardDSLQ0.h>

Data Structures
struct	ConstIterator

Public Types
typedef TFraction	Fraction

typedef StandardDSLQ0< TFraction >	Self

typedef Fraction::Integer	Integer

typedef Fraction::UnsignedInteger	UnsignedInteger

typedef Fraction::Quotient	Quotient

typedef IntegerComputer< Integer >	IC

typedef IC::IntegerParamType	IntegerParamType

typedef IC::Vector2I	Vector2I

typedef IC::Point2I	Point2I

typedef IC::Point2I	Point

Public Member Functions
	~StandardDSLQ0 ()

	StandardDSLQ0 ()

	StandardDSLQ0 (const StandardDSLQ0 &other)

StandardDSLQ0 &	operator= (const StandardDSLQ0 &other)

	StandardDSLQ0 (Fraction aSlope, IntegerParamType aMu)

	StandardDSLQ0 (IntegerParamType a1, IntegerParamType b1, IntegerParamType mu1)

bool	operator() (const Point &p) const

Fraction	slope () const

const Integer &	mu () const

Integer	mup () const

Integer	a () const

Integer	b () const

Vector2I	v () const

ConstIterator	begin (Point p) const

ConstIterator	end (Point p) const

const Pattern< Fraction > &	pattern () const

Integer	r (const Point &p) const

Point	U () const

Point	L () const

Point	lowestY (IntegerParamType x) const

Point	uppermostY (IntegerParamType x) const

Point	lowestX (IntegerParamType y) const

Point	uppermostX (IntegerParamType y) const

bool	before (const Point &p1, const Point &p2) const

bool	beforeOrEqual (const Point &p1, const Point &p2) const

Self	reversedSmartDSS (const Point &A, const Point &B) const

Self	reversedSmartDSS (Point U1, Point U2, const Point &A, const Point &B) const

Self	DSSWithinTwoPatterns (Point U1, Point U2, const Point &A, const Point &B) const

Self	smartDSS (const Point &A, const Point &B) const

void	selfDisplay (std::ostream &out) const

bool	isValid () const

Protected Attributes
Pattern< Fraction >	myPattern
	the characteristic pattern of this DSL. More...

Integer	myMu
	the shift to origin. More...

Static Private Member Functions
static Fraction	deepest (Fraction f1, Fraction f2, Fraction f3)

static Fraction	deepest (Fraction f1, Fraction f2)

Private Attributes
IC	ic
	Used in some computations. More...

Detailed Description

template<typename TFraction>
class DGtal::StandardDSLQ0< TFraction >

Aim: Represents a digital straight line with slope in the first quadrant (Q0: x >= 0, y >= 0 ).

Description of template class 'StandardDSLQ0'

It is the 4-connected set of points (x,y) of Z2 satisfying:

\( mu <= ax - by < mu + a + b \)

You may move on it point by point with iterators ConstIterator. You can find upper and lower leaning points, find points on the DSL given one coordinate. You may extract subsegment with smartDSS() and reversedSmartDSS() algorithms.

Template Parameters

TFraction the type chosen to represent fractions, a model of CFraction. You may use SternBrocot::Fraction for instance.

Model of boost::CopyConstructible, boost::Assignable, concepts::CPointPredicate

See also: The documentation about Digital straight lines and subsegments

Definition at line 79 of file StandardDSLQ0.h.

Member Typedef Documentation

◆ Fraction

template<typename TFraction >

typedef TFraction DGtal::StandardDSLQ0< TFraction >::Fraction

Definition at line 83 of file StandardDSLQ0.h.

◆ IC

template<typename TFraction >

typedef IntegerComputer<Integer> DGtal::StandardDSLQ0< TFraction >::IC

Definition at line 91 of file StandardDSLQ0.h.

◆ Integer

template<typename TFraction >

typedef Fraction::Integer DGtal::StandardDSLQ0< TFraction >::Integer

Definition at line 85 of file StandardDSLQ0.h.

◆ IntegerParamType

template<typename TFraction >

typedef IC::IntegerParamType DGtal::StandardDSLQ0< TFraction >::IntegerParamType

Definition at line 92 of file StandardDSLQ0.h.

◆ Point

template<typename TFraction >

typedef IC::Point2I DGtal::StandardDSLQ0< TFraction >::Point

Definition at line 97 of file StandardDSLQ0.h.

◆ Point2I

template<typename TFraction >

typedef IC::Point2I DGtal::StandardDSLQ0< TFraction >::Point2I

Definition at line 94 of file StandardDSLQ0.h.

◆ Quotient

template<typename TFraction >

typedef Fraction::Quotient DGtal::StandardDSLQ0< TFraction >::Quotient

Definition at line 87 of file StandardDSLQ0.h.

◆ Self

template<typename TFraction >

typedef StandardDSLQ0<TFraction> DGtal::StandardDSLQ0< TFraction >::Self

Definition at line 84 of file StandardDSLQ0.h.

◆ UnsignedInteger

template<typename TFraction >

typedef Fraction::UnsignedInteger DGtal::StandardDSLQ0< TFraction >::UnsignedInteger

Definition at line 86 of file StandardDSLQ0.h.

◆ Vector2I

template<typename TFraction >

typedef IC::Vector2I DGtal::StandardDSLQ0< TFraction >::Vector2I

Definition at line 93 of file StandardDSLQ0.h.

Constructor & Destructor Documentation

◆ ~StandardDSLQ0()

template<typename TFraction >

DGtal::StandardDSLQ0< TFraction >::~StandardDSLQ0 ( )

Destructor.

◆ StandardDSLQ0() [1/4]

template<typename TFraction >

DGtal::StandardDSLQ0< TFraction >::StandardDSLQ0 ( )

Constructor. Null DSL.

◆ StandardDSLQ0() [2/4]

template<typename TFraction >

DGtal::StandardDSLQ0< TFraction >::StandardDSLQ0 ( const StandardDSLQ0< TFraction > & other )

Copy constructor.

Parameters

other the object to clone.

◆ StandardDSLQ0() [3/4]

template<typename TFraction >

DGtal::StandardDSLQ0< TFraction >::StandardDSLQ0	(	Fraction	aSlope,
		IntegerParamType	aMu
	)

Creates the DSL(a,b,mu).

Parameters

aSlope	the slope a/b, where gcd(a,b)=1
aMu	the shift to origin.

◆ StandardDSLQ0() [4/4]

template<typename TFraction >

DGtal::StandardDSLQ0< TFraction >::StandardDSLQ0	(	IntegerParamType	a1,
		IntegerParamType	b1,
		IntegerParamType	mu1
	)

Creates the DSL(a/g,b/g,mu), where g = gcd( a, b).

Parameters

a1	any integer
b1	any integer
mu1	the shift to origin.

Member Function Documentation

◆ a()

template<typename TFraction >

Integer DGtal::StandardDSLQ0< TFraction >::a ( ) const

Returns: a the numerator of the slope.

◆ b()

template<typename TFraction >

Integer DGtal::StandardDSLQ0< TFraction >::b ( ) const

Returns: b the denominator of the slope.

◆ before()

template<typename TFraction >

bool DGtal::StandardDSLQ0< TFraction >::before	(	const Point &	p1,
		const Point &	p2
	)		const

Returns: true if p1 is before p2 in the DSL.

◆ beforeOrEqual()

template<typename TFraction >

bool DGtal::StandardDSLQ0< TFraction >::beforeOrEqual	(	const Point &	p1,
		const Point &	p2
	)		const

Returns: true if p1 is before or equal to p2 in the DSL.

◆ begin()

template<typename TFraction >

ConstIterator DGtal::StandardDSLQ0< TFraction >::begin ( Point p ) const

Parameters

p	a point in the DSL.

Returns: an iterator on the DSL pointing on p.

◆ deepest() [1/2]

template<typename TFraction >

static Fraction DGtal::StandardDSLQ0< TFraction >::deepest	(	Fraction	f1,
		Fraction	f2
	)

staticprivate

◆ deepest() [2/2]

template<typename TFraction >

static Fraction DGtal::StandardDSLQ0< TFraction >::deepest	(	Fraction	f1,
		Fraction	f2,
		Fraction	f3
	)

staticprivate

◆ DSSWithinTwoPatterns()

template<typename TFraction >

Self DGtal::StandardDSLQ0< TFraction >::DSSWithinTwoPatterns	(	Point	U1,
		Point	U2,
		const Point &	A,
		const Point &	B
	)		const

Used by reversedSmartDSS. Computes the exact characteristics of the subsegment [A,B] of this DSL. Note that |U2-U1| = 2 * length().

Parameters

A	any point belonging to this DSL, A < B.
B	any point belonging to this DSL, A < B.
U1	the first upper leaning point such that U1 <= A.
U2	the second upper leaning point such that B <= U2.

Returns: the minimal DSL containing [A,B].

◆ end()

template<typename TFraction >

ConstIterator DGtal::StandardDSLQ0< TFraction >::end ( Point p ) const

Parameters

p	a point in the DSL.

Returns: an iterator on the DSL pointing after p.

◆ isValid()

template<typename TFraction >

bool DGtal::StandardDSLQ0< TFraction >::isValid ( ) const

Checks the validity/consistency of the object.

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

◆ L()

template<typename TFraction >

Point DGtal::StandardDSLQ0< TFraction >::L ( ) const

Returns: the first lower leaning point of the DSL with greater x than U().

◆ lowestX()

template<typename TFraction >

Point DGtal::StandardDSLQ0< TFraction >::lowestX ( IntegerParamType y ) const

Returns: the point on this DSL with this y coordinate and lowest x coordinate.

◆ lowestY()

template<typename TFraction >

Point DGtal::StandardDSLQ0< TFraction >::lowestY ( IntegerParamType x ) const

Returns: the point on this DSL with this x coordinate and lowest y coordinate.

◆ mu()

template<typename TFraction >

const Integer& DGtal::StandardDSLQ0< TFraction >::mu ( ) const

Returns: the shift to origin, which is also the lower diopantine constraint.

◆ mup()

template<typename TFraction >

Integer DGtal::StandardDSLQ0< TFraction >::mup ( ) const

Returns: the upper diopantine constraint, ie. mu + a + b - 1

◆ operator()()

template<typename TFraction >

bool DGtal::StandardDSLQ0< TFraction >::operator() ( const Point & p ) const

Parameters

p	any point in Z2.

Returns: 'true' iff the point p belongs to this.

◆ operator=()

template<typename TFraction >

StandardDSLQ0& DGtal::StandardDSLQ0< TFraction >::operator= ( const StandardDSLQ0< TFraction > & other )

Assignment.

Parameters

other the object to copy.

Returns: a reference on 'this'.

◆ pattern()

template<typename TFraction >

const Pattern<Fraction>& DGtal::StandardDSLQ0< TFraction >::pattern ( ) const

Returns: the pattern of this DSL

◆ r()

template<typename TFraction >

Integer DGtal::StandardDSLQ0< TFraction >::r ( const Point & p ) const

Remainder a p.x - b p.y of point p in this DSL.

Parameters

p	any point in Z2

Returns: a p.x - b p.y

◆ reversedSmartDSS() [1/2]

template<typename TFraction >

Self DGtal::StandardDSLQ0< TFraction >::reversedSmartDSS	(	const Point &	A,
		const Point &	B
	)		const

Algorithm ReversedSmartDSS. See M. Said and J.-O. Lachaud, DGCI2010.

Computes the exact characteristics of the subsegment [A,B] of this DSL in time O(log(|B-A|)). An even better bound in the output is achieved.

Parameters

A	any point belonging to this DSL, A < B.
B	any point belonging to this DSL, A < B.

Returns: the minimal DSL containing [A,B].

◆ reversedSmartDSS() [2/2]

template<typename TFraction >

Self DGtal::StandardDSLQ0< TFraction >::reversedSmartDSS	(	Point	U1,
		Point	U2,
		const Point &	A,
		const Point &	B
	)		const

Algorithm ReversedSmartDSS. See M. Said and J.-O. Lachaud, DGCI2010.

Computes the exact characteristics of the subsegment [A,B] of this DSL in time O(log(|B-A|)). An even better bound in the output is achieved.

Parameters

A	any point belonging to this DSL, A < B.
B	any point belonging to this DSL, A < B.
U1	the first upper leaning point such that U1 <= A.
U2	the second upper leaning point such that B <= U2.

Returns: the minimal DSL containing [A,B].

See also: reversedSmartDSS( const Point & A, const Point & B )

◆ selfDisplay()

template<typename TFraction >

void DGtal::StandardDSLQ0< TFraction >::selfDisplay ( std::ostream & out ) const

Writes/Displays the object on an output stream.

Parameters

out	the output stream where the object is written.

◆ slope()

template<typename TFraction >

Fraction DGtal::StandardDSLQ0< TFraction >::slope ( ) const

Returns: the slope of this DSL, an irreducible fraction

◆ smartDSS()

template<typename TFraction >

Self DGtal::StandardDSLQ0< TFraction >::smartDSS	(	const Point &	A,
		const Point &	B
	)		const

Algorithm SmartDSS. See M. Said and J.-O. Lachaud, DGCI2009.

Computes the exact characteristics of the subsegment [A,B] of this DSL in time O(sum_k u_k), where the continued fraction of this DSL slope a/b is [u_0; u_1, u_2, ... ]

Parameters

A	any point belonging to this DSL, A < B.
B	any point belonging to this DSL, A < B.

Returns: the minimal DSL containing [A,B].

◆ U()

template<typename TFraction >

Point DGtal::StandardDSLQ0< TFraction >::U ( ) const

Returns: the first upper leaning point of the DSL in the first quadrant (x >= 0).

◆ uppermostX()

template<typename TFraction >

Point DGtal::StandardDSLQ0< TFraction >::uppermostX ( IntegerParamType y ) const

Returns: the point on this DSL with this y coordinate and uppermost x coordinate.

◆ uppermostY()

template<typename TFraction >

Point DGtal::StandardDSLQ0< TFraction >::uppermostY ( IntegerParamType x ) const

Returns: the point on this DSL with this x coordinate and uppermost y coordinate.

◆ v()

template<typename TFraction >

Vector2I DGtal::StandardDSLQ0< TFraction >::v ( ) const

Returns: the vector for the pattern, ie ( slope().q(), slope().p() )

Field Documentation

◆ ic

template<typename TFraction >

IC DGtal::StandardDSLQ0< TFraction >::ic

private

Used in some computations.

Definition at line 386 of file StandardDSLQ0.h.

◆ myMu

template<typename TFraction >

Integer DGtal::StandardDSLQ0< TFraction >::myMu

protected

the shift to origin.

Definition at line 381 of file StandardDSLQ0.h.

◆ myPattern

template<typename TFraction >

Pattern<Fraction> DGtal::StandardDSLQ0< TFraction >::myPattern

protected

the characteristic pattern of this DSL.

Definition at line 379 of file StandardDSLQ0.h.

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

StandardDSLQ0.h

Data Structures

Public Types

Public Member Functions

Protected Attributes

Static Private Member Functions

Private Attributes

Detailed Description

template<typename TFraction> class DGtal::StandardDSLQ0< TFraction >

Member Typedef Documentation

◆ Fraction

◆ IC

◆ Integer

◆ IntegerParamType

◆ Point

◆ Point2I

◆ Quotient

◆ Self

◆ UnsignedInteger

◆ Vector2I

Constructor & Destructor Documentation

◆ ~StandardDSLQ0()

◆ StandardDSLQ0() [1/4]

◆ StandardDSLQ0() [2/4]

◆ StandardDSLQ0() [3/4]

◆ StandardDSLQ0() [4/4]

Member Function Documentation

◆ a()

◆ b()

◆ before()

◆ beforeOrEqual()

◆ begin()

◆ deepest() [1/2]

◆ deepest() [2/2]

◆ DSSWithinTwoPatterns()

◆ end()

◆ isValid()

◆ L()

◆ lowestX()

◆ lowestY()

◆ mu()

◆ mup()

◆ operator()()

◆ operator=()

◆ pattern()

◆ r()

◆ reversedSmartDSS() [1/2]

◆ reversedSmartDSS() [2/2]

◆ selfDisplay()

◆ slope()

◆ smartDSS()

◆ U()

◆ uppermostX()

◆ uppermostY()

◆ v()

Field Documentation

◆ ic

◆ myMu

◆ myPattern

template<typename TFraction>
class DGtal::StandardDSLQ0< TFraction >