Aim: Small class that contains the code that depends on the arithmetical thickness (either naive or standard) of a digital straight line (DSL). It provides mainly two static methods: More...

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

Public Types
typedef SpaceND< 2, TCoordinate >	Space

typedef Space::Vector	Vector

typedef std::pair< Vector, Vector >	Steps

Public Member Functions
	BOOST_STATIC_CONSTANT (unsigned short, ForegroundAdjacency=8)

	BOOST_STATIC_CONSTANT (unsigned short, BackgroundAdjacency=4)

Static Public Member Functions
template<typename TInteger >
static Vector	shift (const TInteger &a, const TInteger &b)

template<typename TInteger >
static Steps	steps (const TInteger &a, const TInteger &b)

template<typename TInteger >
static TInteger	norm (const TInteger &a, const TInteger &b)

Detailed Description

template<typename TCoordinate, unsigned short adjacency = 8>
struct DGtal::ArithmeticalDSLKernel< TCoordinate, adjacency >

Aim: Small class that contains the code that depends on the arithmetical thickness (either naive or standard) of a digital straight line (DSL). It provides mainly two static methods:

ArithmeticalDSLKernel::shift that returns the shift vector of a DSL from its slope parameters \( a \) and \( b \). ie. the vector \( s \) translating a point of remainder \( r \) to a point of remainder \( r + \omega \)
ArithmeticalDSLKernel::steps that returns the step vectors of a DSL ie. the couple of vectors \( v \) and \( w \) used to iterate over the points of a DSL in an orientation given by the DSL parameters \( a \) and \( b \). Obviously, these two vectors are equal to 0 if \( \omega = 0 \) (not valid DSL). Moreover, the first vector ( \( v \)) is equal to the direction vector, while the second one ( \( w \)) is equal to 0, if \( \omega = 1 \), ie. if the lower leaning line and the upper leaning line are counfounded. Though, in the general case, the first vector ( \( v \)) translates any point \( p \) of remainder \( r \) to its unique neighbor point \( q \) of remainder greater than or equal to \( r \), while the second one ( \( w \)) is such that \( v - w = s \).

These methods are specialized with respect to the chosen adjacency 8 (default) or 4.

Digital straight lines and segments

Template Parameters

TCoordinate	a model of integer for the DGtal point coordinates
adjacency	integer equal to 8 (default) for naive (simply 8-connected) DSL, and 4 for standard (simply 4-connected) DSL.

See also: ArithmeticalDSL; exampleArithmeticalDSL.cpp

Definition at line 91 of file ArithmeticalDSLKernel.h.

Member Typedef Documentation

◆ Space

template<typename TCoordinate , unsigned short adjacency = 8>

typedef SpaceND<2, TCoordinate> DGtal::ArithmeticalDSLKernel< TCoordinate, adjacency >::Space

Type of the digital plane.

Definition at line 99 of file ArithmeticalDSLKernel.h.

◆ Steps

template<typename TCoordinate , unsigned short adjacency = 8>

typedef std::pair<Vector, Vector> DGtal::ArithmeticalDSLKernel< TCoordinate, adjacency >::Steps

Type of the step vectors, defined as a STL pair of Vector

Definition at line 107 of file ArithmeticalDSLKernel.h.

◆ Vector

template<typename TCoordinate , unsigned short adjacency = 8>

typedef Space::Vector DGtal::ArithmeticalDSLKernel< TCoordinate, adjacency >::Vector

Type of the shift vector.

Definition at line 103 of file ArithmeticalDSLKernel.h.

Member Function Documentation

◆ BOOST_STATIC_CONSTANT() [1/2]

template<typename TCoordinate , unsigned short adjacency = 8>

DGtal::ArithmeticalDSLKernel< TCoordinate, adjacency >::BOOST_STATIC_CONSTANT	(	unsigned short	,
		BackgroundAdjacency	= `4`
	)

Adjacency used for the complement

◆ BOOST_STATIC_CONSTANT() [2/2]

template<typename TCoordinate , unsigned short adjacency = 8>

DGtal::ArithmeticalDSLKernel< TCoordinate, adjacency >::BOOST_STATIC_CONSTANT	(	unsigned short	,
		ForegroundAdjacency	= `8`
	)

Adjacency used for the DSL

◆ norm()

template<typename TCoordinate , unsigned short adjacency = 8>

template<typename TInteger >

static TInteger DGtal::ArithmeticalDSLKernel< TCoordinate, adjacency >::norm	(	const TInteger &	a,
		const TInteger &	b
	)

static

Returns the \( L_{\infty} \) (for the 8-adjacency) or the \( L_1 \) norm (for the 4-adjacency) of two integers a and b,

Parameters

a	a-parameter
b	b-parameter

Template Parameters

TInteger a model of integer for the parameters a and b

Returns: the norm

◆ shift()

template<typename TCoordinate , unsigned short adjacency = 8>

template<typename TInteger >

static Vector DGtal::ArithmeticalDSLKernel< TCoordinate, adjacency >::shift	(	const TInteger &	a,
		const TInteger &	b
	)

static

Given parameters a and b, this method computes the shift vector translating a point of remainder \( r \) to a point of remainder \( r + \omega \)

NB: The shift vector is set to (0,0) if \( \omega = 0 \), ie. a and b are both null.

NB: If ( a , b ) lies between two octants (resp. quadrants) (eg. b > 0 and a = 0), the shift vector of the next octant (resp. quadrant) is chosen with respect to the counter-clockwise orientation.

Parameters

a	a-parameter
b	b-parameter

Template Parameters

TInteger a model of integer for the parameters a and b

Returns: the shift vector

See also: exampleArithmeticalDSL.cpp

Referenced by specialCases(), and test().

◆ steps()

template<typename TCoordinate , unsigned short adjacency = 8>

template<typename TInteger >

static Steps DGtal::ArithmeticalDSLKernel< TCoordinate, adjacency >::steps	(	const TInteger &	a,
		const TInteger &	b
	)

static

Given parameters a and b, this method returns the two step vectors, ie. the vectors that are used to iterate over the points of a DSL of slope a / b.

In the general case, the first vector \( v \) translates any point \( p \) of remainder \( r \) to its unique neighbor point \( q \) of remainder greater than or equal to \( r \), while the second one \( w \) is such that \( v - w = s \).

NB: The two vectors are set to (0,0) if \( \omega = 0 \), ie. a and b are both null.

NB: The second vector is set to (0,0) if \( \omega = 1 \), ie. if either a or b is null, if either a == b or either a == - b in the naive case.

Parameters

a	a-parameter
b	b-parameter

Template Parameters

TInteger a model of integer for the parameters a and b

Returns: the the pair of steps

See also: exampleArithmeticalDSL.cpp

Referenced by specialCases(), and test().

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

ArithmeticalDSLKernel.h

Public Types

Public Member Functions

Static Public Member Functions

Detailed Description

Member Typedef Documentation

◆ Space

◆ Steps

◆ Vector

Member Function Documentation

◆ BOOST_STATIC_CONSTANT() [1/2]

◆ BOOST_STATIC_CONSTANT() [2/2]

◆ norm()

◆ shift()

◆ steps()