Aim: implements l_p metrics. More...

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

Public Types
typedef TSpace	Space
	Copy the space type.

typedef Space::RealPoint	Point
	Type for points (RealPoint for this class)

typedef double	Value
	Type for distance values.

typedef double	RawValue
	Type for raw distance values.

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

	LpMetric (const double anExponent)

	~LpMetric ()

	LpMetric (const LpMetric &other)

LpMetric &	operator= (const LpMetric &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

void	selfDisplay (std::ostream &out) const

bool	isValid () const

Private Attributes
Value	myExponent
	Exponent value.

Detailed Description

template<typename TSpace>
class DGtal::LpMetric< TSpace >

Aim: implements l_p metrics.

Description of template class 'LpMetric'

Given a parameter p, the class implements classical l_p metric as a model of CMetricSpace. Hence, given two points \( x=(x_0...x_{n-1})\), \( y=(y_0...y_{n-1})\), we define a metric as:

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

This class performs all computations on C++ double converting the digital points to Space::RealPoint

The exponent p is specifed at the constructor.

Template Parameters

TSpace the model of CSpace on which the metric is defined.

Examples: graph/volDistanceTraversal.cpp.

Definition at line 74 of file LpMetric.h.

Member Typedef Documentation

◆ Point

template<typename TSpace >

typedef Space::RealPoint DGtal::LpMetric< TSpace >::Point

Type for points (RealPoint for this class)

Definition at line 84 of file LpMetric.h.

◆ RawValue

template<typename TSpace >

typedef double DGtal::LpMetric< TSpace >::RawValue

Type for raw distance values.

Definition at line 88 of file LpMetric.h.

◆ Space

template<typename TSpace >

typedef TSpace DGtal::LpMetric< TSpace >::Space

Copy the space type.

Definition at line 80 of file LpMetric.h.

◆ Value

template<typename TSpace >

typedef double DGtal::LpMetric< TSpace >::Value

Type for distance values.

Definition at line 86 of file LpMetric.h.

Constructor & Destructor Documentation

◆ LpMetric() [1/2]

template<typename TSpace >

DGtal::LpMetric< TSpace >::LpMetric ( const double anExponent )

inline

Constructor.

Parameters

anExponent the exponent (p) of the lp metric.

Definition at line 95 of file LpMetric.h.

95 : myExponent(anExponent)

96 {}

DGtal::LpMetric::myExponent

Value myExponent

Exponent value.

Definition LpMetric.h:207

◆ ~LpMetric()

template<typename TSpace >

DGtal::LpMetric< TSpace >::~LpMetric ( )

inline

Destructor.

Definition at line 102 of file LpMetric.h.

103 {}

◆ LpMetric() [2/2]

template<typename TSpace >

DGtal::LpMetric< TSpace >::LpMetric ( const LpMetric< TSpace > & other )

inline

Copy constructor.

Parameters

other the object to clone.

Definition at line 109 of file LpMetric.h.

    {
      myExponent = other.myExponent;
    }

References DGtal::LpMetric< TSpace >::myExponent.

Member Function Documentation

◆ BOOST_CONCEPT_ASSERT()

template<typename TSpace >

DGtal::LpMetric< TSpace >::BOOST_CONCEPT_ASSERT ( (concepts::CSpace< TSpace >) )

◆ closest()

template<typename TSpace >

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

inline

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.

Definition at line 170 of file LpMetric.h.

    {
      auto dfirst = rawDistance(origin,first);
      auto dsecond = rawDistance(origin,second);
      if (dfirst < dsecond)
        return ClosestFIRST;
      else
        if (dfirst > dsecond)
          return ClosestSECOND;
      
      return ClosestBOTH;
    }

References DGtal::ClosestBOTH, DGtal::ClosestFIRST, DGtal::ClosestSECOND, and DGtal::LpMetric< TSpace >::rawDistance().

Referenced by TEST_CASE().

◆ isValid()

template<typename TSpace >

bool DGtal::LpMetric< TSpace >::isValid ( ) const

inline

Checks the validity/consistency of the object.

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

Definition at line 198 of file LpMetric.h.

    {
      return true;
    }

◆ operator()()

template<typename TSpace >

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

inline

Compute the distance between aP and aQ.

Parameters

aP	a first point.
aQ	a second point.

Returns: the distance between aP and aQ.

Definition at line 137 of file LpMetric.h.

    {
      return std::pow( rawDistance(aP,aQ), 1.0/myExponent);
    }

References DGtal::LpMetric< TSpace >::myExponent, and DGtal::LpMetric< TSpace >::rawDistance().

◆ operator=()

template<typename TSpace >

LpMetric & DGtal::LpMetric< TSpace >::operator= ( const LpMetric< TSpace > & other )

inline

Assignment.

Parameters

other the object to copy.

Returns: a reference on 'this'.

Definition at line 119 of file LpMetric.h.

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

References DGtal::LpMetric< TSpace >::myExponent.

◆ rawDistance()

template<typename TSpace >

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

inline

Compute the raw distance between aP and aQ.

Parameters

aP	a first point.
aQ	a second point.

Returns: the distance between aP and aQ.

Definition at line 150 of file LpMetric.h.

    {
      RawValue tmp=0.0;
      for(typename Point::Dimension i = 0; i < aP.size(); ++i)
        tmp += static_cast<RawValue>(std::pow(NumberTraits<typename Point::Coordinate>::castToDouble(std::abs(aP[i] - aQ[i])),
                                              myExponent));
      return tmp;
    }

References DGtal::LpMetric< TSpace >::myExponent, and DGtal::PointVector< dim, TEuclideanRing, TContainer >::size().

Referenced by DGtal::LpMetric< TSpace >::closest(), DGtal::LpMetric< TSpace >::operator()(), and TEST_CASE().

◆ selfDisplay()

template<typename TSpace >

void DGtal::LpMetric< TSpace >::selfDisplay ( std::ostream & out ) const

inline

Writes/Displays the object on an output stream.

Parameters

out	the output stream where the object is written.

Definition at line 189 of file LpMetric.h.

    {
      out << "[LpMetric] Lp Metric exponent=" << myExponent ;
    }

References DGtal::LpMetric< TSpace >::myExponent.

Field Documentation

◆ myExponent

template<typename TSpace >

Value DGtal::LpMetric< TSpace >::myExponent

private

Exponent value.

Definition at line 207 of file LpMetric.h.

Referenced by DGtal::LpMetric< TSpace >::LpMetric(), DGtal::LpMetric< TSpace >::operator()(), DGtal::LpMetric< TSpace >::operator=(), DGtal::LpMetric< TSpace >::rawDistance(), and DGtal::LpMetric< TSpace >::selfDisplay().

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

LpMetric.h

Public Types

Public Member Functions

Private Attributes

Detailed Description

Member Typedef Documentation

◆ Point

◆ RawValue

◆ Space

◆ Value

Constructor & Destructor Documentation

◆ LpMetric() [1/2]

◆ ~LpMetric()

◆ LpMetric() [2/2]

Member Function Documentation

◆ BOOST_CONCEPT_ASSERT()

◆ closest()

◆ isValid()

◆ operator()()

◆ operator=()

◆ rawDistance()

◆ selfDisplay()

Field Documentation

◆ myExponent