Aim: defines the concept of separable metrics. More...

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

Inheritance diagram for DGtal::concepts::CSeparableMetric< T >:

Public Types
typedef T::Point	Point
Public Types inherited from DGtal::concepts::CMetricSpace< T >
typedef T::Point	Point
typedef T::Space	Space
typedef T::Value	Value
typedef T::RawValue	RawValue

Public Member Functions
	BOOST_CONCEPT_USAGE (CSeparableMetric)
void	checkConstConstraints () const
Public Member Functions inherited from DGtal::concepts::CMetricSpace< T >
	BOOST_CONCEPT_ASSERT ((CSpace< Space >))
	BOOST_CONCEPT_ASSERT ((CQuantity< Value >))
	BOOST_CONCEPT_ASSERT ((CQuantity< RawValue >))
	BOOST_CONCEPT_USAGE (CMetricSpace)
void	checkConstConstraints () const

Private Attributes
T	myX
Point	u
Point	v
Point	w
Point	start
Point	end
bool	myBool
DGtal::Dimension	dim

Detailed Description

template<typename T>
struct DGtal::concepts::CSeparableMetric< T >

Aim: defines the concept of separable metrics.

Description of concept 'CSeparableMetric'

Separable metrics are metrics satsifying the monotonicity property. More formally, in dimension 2, consider two points \(p(x,y)\), \(q(x',y')\) with \(x<x\). Let \(r( x'',0)\) be a point on the x-axis such that \(d(p,r) = d(q,r)\) and \( s(u,0)\) be another point on the x-axis. A metric \( d\) is monotonic if

\[ u < x'' \implies d(p,s) \leq d(q,s) \]

and

\[ u > x'' \implies d(p,s) \geq d(q,s) \]

Refinement of

concepts::CMetricSpace.

Associated types

Notation

X : A type that is a model of CSeparableMetric
x, y : object of type X

Definitions

Valid expressions and semantics

Name	Expression	Type requirements	Return type	Precondition	Semantics	Post condition	Complexity
hiddenBy predicate	hiddenBy(u,v,w,startingPoint,endPoint,dim)	u,v,w,startingPoint,endPoint of type Point, dim of type DGtal::Dimension	startingPoint and endPoint only differ by their dim-th coordinate	returns true if the intersection between the segment [startingPoint,endPoint] and the Voronoi cell associated with v is empty (hidden on the segment by u and w Voronoi cells).			-

Invariants

Models

ExactPredicateLpSeparableMetric, InexactPredicateLpSeparableMetric

Notes

Template Parameters

T	the type that should be a model of concepts::CSeparableMetric.

Definition at line 101 of file CSeparableMetric.h.

Member Typedef Documentation

◆ Point

template<typename T>

typedef T::Point DGtal::concepts::CSeparableMetric< T >::Point

Definition at line 105 of file CSeparableMetric.h.

Member Function Documentation

◆ BOOST_CONCEPT_USAGE()

template<typename T>

DGtal::concepts::CSeparableMetric< T >::BOOST_CONCEPT_USAGE ( CSeparableMetric< T > )

inline

Definition at line 106 of file CSeparableMetric.h.

    {
      checkConstConstraints();
    }

References checkConstConstraints().

◆ checkConstConstraints()

template<typename T>

void DGtal::concepts::CSeparableMetric< T >::checkConstConstraints ( ) const

inline

Definition at line 110 of file CSeparableMetric.h.

    {
        // const method dummyConst should take parameter myA of type A and return
        // something of type B
      ConceptUtils::sameType( myBool, myX.hiddenBy(u,v,w,start,end,dim) );
    }