Aim: implements separable l_p metrics with approximated predicates. More...

#include <DGtal/geometry/volumes/distance/InexactPredicateLpSeparableMetric.h>

Public Types
typedef TSpace	Space
	Copy the space type.

typedef Space::Point	Point
	Type for points.

typedef Point::Coordinate	Abscissa
	Type for points.

typedef Space::Vector	Vector
	Type for vectors.

typedef TValue	Value
	Type for distance values.

typedef TValue	RawValue
	Type for raw distance values.

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

	BOOST_CONCEPT_ASSERT ((concepts::CEuclideanRing< TValue >))

	InexactPredicateLpSeparableMetric (const double anExponent)

	~InexactPredicateLpSeparableMetric ()

	InexactPredicateLpSeparableMetric (const InexactPredicateLpSeparableMetric &other)

InexactPredicateLpSeparableMetric &	operator= (const InexactPredicateLpSeparableMetric &other)

Value	operator() (const Point &aP, const Point &aQ) const

RawValue	rawDistance (const Point &aP, const Point &aQ) const

Closest	closest (const Point &origin, const Point &first, const Point &second) const

bool	hiddenBy (const Point &u, const Point &v, const Point &w, const Point &startingPoint, const Point &endPoint, const typename Point::UnsignedComponent dim) const

void	selfDisplay (std::ostream &out) const

bool	isValid () const

Private Member Functions
Value	distanceLp (const Point &aP, const Point &aQ) const

Abscissa	binarySearchHidden (const Abscissa &udim, const Abscissa &vdim, const Value &nu, const Value &nv, const Abscissa &lower, const Abscissa &upper) const

Private Attributes
Value	myExponent
	Exponent value.

Detailed Description

template<typename TSpace, typename TValue = double>
class DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >

Aim: implements separable l_p metrics with approximated predicates.

Description of template class 'InexactPredicateLpSeparableMetric'

Given a parameter p, the class implement classical l_p metric as a model of CSeparableMetric. Hence, given two points \( x=(x_0...x_{n-1})\), \( y=(y_0...y_{n-1})\) in the given digital space (see below), we define a metric such that:

\( distance(x,y)= \left( \sum_{i=0}^{n-1} |x_i-y_i|^p\right)^{1/p}\)

This class is said to be inexact in the sense that the power p a real number (of type TValue, e.g. double or float) and the power is given by std::pow on double numbers. As a consequence, hiddenBy and closest methods may be inexact (numerical issues).

The exponent p is specifed at the constructor.

Template Parameters

TSpace	the model of CSpace on which the metric is defined.
TValue	value type of the distance computation (e.g. float or double –defaut–). Model of CEuclideanRing.

Definition at line 81 of file InexactPredicateLpSeparableMetric.h.

Member Typedef Documentation

◆ Abscissa

template<typename TSpace , typename TValue = double>

typedef Point::Coordinate DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >::Abscissa

Type for points.

Definition at line 95 of file InexactPredicateLpSeparableMetric.h.

◆ Point

template<typename TSpace , typename TValue = double>

typedef Space::Point DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >::Point

Type for points.

Definition at line 93 of file InexactPredicateLpSeparableMetric.h.

◆ RawValue

template<typename TSpace , typename TValue = double>

typedef TValue DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >::RawValue

Type for raw distance values.

Definition at line 101 of file InexactPredicateLpSeparableMetric.h.

◆ Space

template<typename TSpace , typename TValue = double>

typedef TSpace DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >::Space

Copy the space type.

Definition at line 87 of file InexactPredicateLpSeparableMetric.h.

◆ Value

template<typename TSpace , typename TValue = double>

typedef TValue DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >::Value

Type for distance values.

Definition at line 99 of file InexactPredicateLpSeparableMetric.h.

◆ Vector

template<typename TSpace , typename TValue = double>

typedef Space::Vector DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >::Vector

Type for vectors.

Definition at line 97 of file InexactPredicateLpSeparableMetric.h.

Constructor & Destructor Documentation

◆ InexactPredicateLpSeparableMetric() [1/2]

template<typename TSpace , typename TValue = double>

DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >::InexactPredicateLpSeparableMetric ( const double anExponent )

Constructor.

◆ ~InexactPredicateLpSeparableMetric()

template<typename TSpace , typename TValue = double>

DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >::~InexactPredicateLpSeparableMetric ( )

Destructor.

◆ InexactPredicateLpSeparableMetric() [2/2]

template<typename TSpace , typename TValue = double>

DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >::InexactPredicateLpSeparableMetric ( const InexactPredicateLpSeparableMetric< TSpace, TValue > & other )

inline

Copy constructor.

Parameters

other the object to clone.

Definition at line 118 of file InexactPredicateLpSeparableMetric.h.

    {
      myExponent = other.myExponent;
    }

References DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >::myExponent.

Member Function Documentation

◆ binarySearchHidden()

template<typename TSpace , typename TValue = double>

Abscissa DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >::binarySearchHidden	(	const Abscissa &	udim,
		const Abscissa &	vdim,
		const Value &	nu,
		const Value &	nv,
		const Abscissa &	lower,
		const Abscissa &	upper ) const

private

Perform a binary search on the interval [lower,upper] to detect the mid-point between u and v according to the l_p distance. It returns the abscissa q such that q belongs to the power cell of u (strictly) but not q-1.

Precondition: udim < vdim

Parameters

udim	coordinate of u along dimension dim
vdim	coordinate of v along dimension dim
nu	partial distance of u (sum of \|xj-x_i\|^p) discarding the term along the dimension dim
nv	partial distance of v (sum of \|xj-x_i\|^p) discarding the term along the dimension dim
lower	interval lower bound
upper	interval upper bound

Returns: the u Voronoi cell greatest point coordinates along dimension dim.

◆ BOOST_CONCEPT_ASSERT() [1/2]

template<typename TSpace , typename TValue = double>

DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >::BOOST_CONCEPT_ASSERT ( (concepts::CEuclideanRing< TValue >) )

◆ BOOST_CONCEPT_ASSERT() [2/2]

template<typename TSpace , typename TValue = double>

DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >::BOOST_CONCEPT_ASSERT ( (concepts::CSpace< TSpace >) )

◆ closest()

template<typename TSpace , typename TValue = double>

Closest DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >::closest	(	const Point &	origin,
		const Point &	first,
		const Point &	second ) const

Given an origin and two points, this method decides which one is closest to the origin. This method should be faster than comparing distance values.

Parameters

origin	the origin
first	the first point
second	the second point

Returns: a Closest enum: FIRST, SECOND or BOTH.

◆ distanceLp()

template<typename TSpace , typename TValue = double>

Value DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >::distanceLp	(	const Point &	aP,
		const Point &	aQ ) const

private

Compute the Lp distance without the computation of the power 1/p. I.e. only \( \sum |p_i- q_i|^p\) is given.

Parameters

aP	a first point
aQ	a second point

Returns: the power p of the l_p distance between aP and aQ.

◆ hiddenBy()

template<typename TSpace , typename TValue = double>

bool DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >::hiddenBy	(	const Point &	u,
		const Point &	v,
		const Point &	w,
		const Point &	startingPoint,
		const Point &	endPoint,
		const typename Point::UnsignedComponent	dim ) const

Given three sites (u,v,w) and a straight segment [startingPoint,endPoint] along dimension dim, we detect if the voronoi cells of u and w strictly hide the voronoi cell of v on the straight line.

This method is in \( O(log(n))\) if n is the size of the straight segment.

Precondition: u,v and w must be such that u[dim] < v[dim] < w[dim]

Parameters

u	a site
v	a site
w	a site
startingPoint	starting point of the segment
endPoint	end point of the segment
dim	direction of the straight line

Returns: true if (u,w) hides v (strictly).

Referenced by testInexactMetrics().

◆ isValid()

template<typename TSpace , typename TValue = double>

bool DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >::isValid ( ) const

Checks the validity/consistency of the object.

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

◆ operator()()

template<typename TSpace , typename TValue = double>

Value DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >::operator()	(	const Point &	aP,
		const Point &	aQ ) const

Compute the distance between aP and aQ.

Parameters

aP	a first point.
aQ	a second point.

Returns: the distance between aP and aQ.

◆ operator=()

template<typename TSpace , typename TValue = double>

InexactPredicateLpSeparableMetric & DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >::operator= ( const InexactPredicateLpSeparableMetric< TSpace, TValue > & other )

inline

Assignment.

Parameters

other the object to copy.

Returns: a reference on 'this'.

Definition at line 128 of file InexactPredicateLpSeparableMetric.h.

    {
      myExponent = other.myExponent;
      return *this;
    }

References DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >::myExponent.

◆ rawDistance()

template<typename TSpace , typename TValue = double>

RawValue DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >::rawDistance	(	const Point &	aP,
		const Point &	aQ ) const

Compute the raw distance between aP and aQ.

Parameters

aP	a first point.
aQ	a second point.

Returns: the distance between aP and aQ.

◆ selfDisplay()

template<typename TSpace , typename TValue = double>

void DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >::selfDisplay ( std::ostream & out ) const

Writes/Displays the object on an output stream.

Parameters

out	the output stream where the object is written.

Field Documentation

◆ myExponent

template<typename TSpace , typename TValue = double>

Value DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >::myExponent

private

Exponent value.

Definition at line 260 of file InexactPredicateLpSeparableMetric.h.

Referenced by DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >::InexactPredicateLpSeparableMetric(), and DGtal::InexactPredicateLpSeparableMetric< TSpace, TValue >::operator=().

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

InexactPredicateLpSeparableMetric.h

Public Types

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ Abscissa

◆ Point

◆ RawValue

◆ Space

◆ Value

◆ Vector

Constructor & Destructor Documentation

◆ InexactPredicateLpSeparableMetric() [1/2]

◆ ~InexactPredicateLpSeparableMetric()

◆ InexactPredicateLpSeparableMetric() [2/2]

Member Function Documentation

◆ binarySearchHidden()

◆ BOOST_CONCEPT_ASSERT() [1/2]

◆ BOOST_CONCEPT_ASSERT() [2/2]

◆ closest()

◆ distanceLp()

◆ hiddenBy()

◆ isValid()

◆ operator()()

◆ operator=()

◆ rawDistance()

◆ selfDisplay()

Field Documentation

◆ myExponent