Aim: A parallel strip in the space is the intersection of two parallel half-planes such that each half-plane includes the other. More...

#include <DGtal/geometry/surfaces/ParallelStrip.h>

Public Types
typedef TSpace	Space

typedef ParallelStrip< Space, muIncluded, muPlusNuIncluded >	Self

typedef Space::Point	Point

typedef Space::RealPoint	RealPoint

typedef Space::Vector	Vector

typedef Space::RealVector	RealVector

typedef RealPoint::Coordinate	Coordinate

typedef RealVector::Component	Component

typedef Component	Scalar

Public Member Functions
	~ParallelStrip ()

	ParallelStrip ()

	ParallelStrip (Scalar mu, const RealVector &N, Scalar nu)

	ParallelStrip (const ParallelStrip &other)

ParallelStrip &	operator= (const ParallelStrip &other)

const RealVector &	normal () const

Scalar	mu () const

Scalar	nu () const

Scalar	width () const

Scalar	axisWidth () const

Dimension	mainAxis () const

Scalar	diagonalWidth () const

Dimension	mainDiagonal () const

void	getBounds (Scalar &mu, Scalar &mu_plus_nu) const

bool	operator() (const Point &p) const

bool	operator() (const RealPoint &p) const

void	selfDisplay (std::ostream &out) const

bool	isValid () const

Protected Attributes
Scalar	myMu
	The minimal scalar value \(\mu\) of the strip.

RealVector	myN
	The unit normal vector N to the strip.

Scalar	myNu
	The width \(\nu\) of the strip.

Private Member Functions
	BOOST_CONCEPT_ASSERT ((concepts::CSpace< TSpace >))

Detailed Description

template<typename TSpace, bool muIncluded = true, bool muPlusNuIncluded = true>
class DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >

Aim: A parallel strip in the space is the intersection of two parallel half-planes such that each half-plane includes the other.

Description of template class 'ParallelStrip'

If N is the unit normal to one of the half-plane, the set of point X that is included in the strip satisfies some: \( \mu \le N \cdot X \le \mu + \nu \), where inequalities can be large or strict.

The normal to the strip is the vector N. The width of the strip is the scalar \(\nu\). The axis width of the strip is the quantity \(|\nu / N_i|\) where \(|N_i|\) is the greatest component.

Models: A ParallelStrip is a model of concepts::CPointPredicate.

Note: Parallel strips of axis width smaller than 1 are not naive digital planes since their parameters are floating-point values. However, they approach naive digital planes.; Parallel strips of diagonal width smaller than \(\sqrt{3}\) are not standard digital planes since their parameters are floating-point values. However, they approach standard digital planes.

Template Parameters

TSpace	any digital space, i.e., a model of CSpace.
muIncluded	when 'true', the first inequality is large, i.e. \( \mu \le N \cdot X \), otherwise it is strict, i.e. \( \mu < N \cdot X \)
muPlusNuIncluded	when 'true', the second inequality is large, i.e. \( N \cdot X \le \mu + \nu\), otherwise it is strict, i.e. \( N \cdot X < \mu + \nu\)

Definition at line 90 of file ParallelStrip.h.

Member Typedef Documentation

◆ Component

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

typedef RealVector::Component DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::Component

Definition at line 103 of file ParallelStrip.h.

◆ Coordinate

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

typedef RealPoint::Coordinate DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::Coordinate

Definition at line 102 of file ParallelStrip.h.

◆ Point

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

typedef Space::Point DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::Point

Definition at line 98 of file ParallelStrip.h.

◆ RealPoint

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

typedef Space::RealPoint DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::RealPoint

Definition at line 99 of file ParallelStrip.h.

◆ RealVector

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

typedef Space::RealVector DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::RealVector

Definition at line 101 of file ParallelStrip.h.

◆ Scalar

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

typedef Component DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::Scalar

Definition at line 104 of file ParallelStrip.h.

◆ Self

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

typedef ParallelStrip<Space,muIncluded,muPlusNuIncluded> DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::Self

Definition at line 97 of file ParallelStrip.h.

◆ Space

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

typedef TSpace DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::Space

Definition at line 96 of file ParallelStrip.h.

◆ Vector

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

typedef Space::Vector DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::Vector

Definition at line 100 of file ParallelStrip.h.

Constructor & Destructor Documentation

◆ ~ParallelStrip()

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::~ParallelStrip ( )

Destructor.

◆ ParallelStrip() [1/3]

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::ParallelStrip ( )

Constructor. The object is invalid.

◆ ParallelStrip() [2/3]

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::ParallelStrip	(	Scalar	mu,
		const RealVector &	N,
		Scalar	nu )

Constructor from parameters.

Parameters

mu	the minimal value of N.X
N	the normal to the plane
nu	the width of the strip.

Note that the equation is normalized so that the normal is a unit vector.

◆ ParallelStrip() [3/3]

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::ParallelStrip ( const ParallelStrip< TSpace, muIncluded, muPlusNuIncluded > & other )

Copy constructor.

Parameters

other the object to clone.

Member Function Documentation

◆ axisWidth()

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

Scalar DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::axisWidth ( ) const

Returns: the axis width of the strip, i.e. its width along its main axis.

◆ BOOST_CONCEPT_ASSERT()

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::BOOST_CONCEPT_ASSERT ( (concepts::CSpace< TSpace >) )

private

◆ diagonalWidth()

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

Scalar DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::diagonalWidth ( ) const

Returns: the diagonal width of the strip (its width along its main diagonal).

◆ getBounds()

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

void DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::getBounds	(	Scalar &	mu,
		Scalar &	mu_plus_nu ) const

If N is the unit normal to the current plane, then \( \mu \le N \cdot X\) and \(N \cdot X \le \mu + \nu\) are the two half-planes defining it.

Parameters

mu	the lower bound (corresponding to the unit vector).
mu_plus_nu	the upper bound (corresponding to the unit vector).

◆ isValid()

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

bool DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::isValid ( ) const

Checks the validity/consistency of the object.

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

◆ mainAxis()

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

Dimension DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::mainAxis ( ) const

Returns: the main axis of the strip (i.e. the absolute maximal component of the normal vector).

◆ mainDiagonal()

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

Dimension DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::mainDiagonal ( ) const

Returns: the integer that specifies the main diagonal among the 2^dimension diagonals. The 1-bits of its bit representation specifies the axes that are negated.

◆ mu()

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

Scalar DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::mu ( ) const

Returns: the parameter \(\mu\) such that \( \mu \le N \cdot X\).

◆ normal()

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

const RealVector & DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::normal ( ) const

Returns: the unit normal vector to the strip.

◆ nu()

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

Scalar DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::nu ( ) const

Same as width().

Returns: the width of the strip, i.e. the parameter \(\nu\) such that \(N \cdot X \le \mu + \nu\).

◆ operator()() [1/2]

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

bool DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::operator() ( const Point & p ) const

Checks if the digital point p is in this strip. Therefore, a ParallelStrip is a model of concepts::CPointPredicate.

Parameters

p	any 3D digital point.

Returns: 'true' if it is in the strip, false otherwise.

◆ operator()() [2/2]

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

bool DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::operator() ( const RealPoint & p ) const

Checks if the (real-valued) point p is in this strip.

Parameters

p	any 3D real-valued point.

Returns: 'true' if it is in the strip, false otherwise.

◆ operator=()

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

ParallelStrip & DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::operator= ( const ParallelStrip< TSpace, muIncluded, muPlusNuIncluded > & other )

Assignment.

Parameters

other the object to copy.

Returns: a reference on 'this'.

◆ selfDisplay()

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

void DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::selfDisplay ( std::ostream & out ) const

Writes/Displays the object on an output stream.

Parameters

out	the output stream where the object is written.

◆ width()

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

Scalar DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::width ( ) const

Same as nu().

Returns: the width of the strip, i.e. the parameter \(\nu\) such that \(N \cdot X \le \mu + \nu\).

Field Documentation

◆ myMu

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

Scalar DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::myMu

protected

The minimal scalar value \(\mu\) of the strip.

Definition at line 246 of file ParallelStrip.h.

◆ myN

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

RealVector DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::myN

protected

The unit normal vector N to the strip.

Definition at line 248 of file ParallelStrip.h.

◆ myNu

template<typename TSpace , bool muIncluded = true, bool muPlusNuIncluded = true>

Scalar DGtal::ParallelStrip< TSpace, muIncluded, muPlusNuIncluded >::myNu

protected

The width \(\nu\) of the strip.

Definition at line 250 of file ParallelStrip.h.

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

ParallelStrip.h

Public Types

Public Member Functions

Protected Attributes

Private Member Functions

Detailed Description

Member Typedef Documentation

◆ Component

◆ Coordinate

◆ Point

◆ RealPoint

◆ RealVector

◆ Scalar

◆ Self

◆ Space

◆ Vector

Constructor & Destructor Documentation

◆ ~ParallelStrip()

◆ ParallelStrip() [1/3]

◆ ParallelStrip() [2/3]

◆ ParallelStrip() [3/3]

Member Function Documentation

◆ axisWidth()

◆ BOOST_CONCEPT_ASSERT()

◆ diagonalWidth()

◆ getBounds()

◆ isValid()

◆ mainAxis()

◆ mainDiagonal()

◆ mu()

◆ normal()

◆ nu()

◆ operator()() [1/2]

◆ operator()() [2/2]

◆ operator=()

◆ selfDisplay()

◆ width()

Field Documentation

◆ myMu

◆ myN

◆ myNu