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 DGtal::concepts::CSeparableMetric< T >::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) );
     }