DGtal::concepts::COrientationFunctor< T > Struct Template Reference

Aim: This concept gathers models implementing an orientation test of \( k+1 \) points in a space of dimension \( n \). More...

#include <DGtal/geometry/tools/determinant/COrientationFunctor.h>

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

Public Types
typedef T::PointArray	PointArray
typedef T::SizeArray	SizeArray
Public Types inherited from DGtal::concepts::CPointFunctor< T >
typedef T::Point	Point
typedef T::Value	Value

Public Member Functions
	BOOST_CONCEPT_ASSERT ((concepts::CSignedNumber< typename T::Value >))
	BOOST_CONCEPT_USAGE (COrientationFunctor)
Public Member Functions inherited from DGtal::concepts::CUnaryFunctor< T, T::Point, T::Value >
	BOOST_CONCEPT_USAGE (CUnaryFunctor)

Private Attributes
T	myX
PointArray	myA
SizeArray	myS

Detailed Description

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

Aim: This concept gathers models implementing an orientation test of \( k+1 \) points in a space of dimension \( n \).

Description of concept 'COrientationFunctor'

The orientation of \( k+1 \) points \( (p_1, \ldots, p_{k+1}) \) is given by the sign of the algebraic distance between \( p_{k+1} \) and an algebraic variety, chosen such that it is uniquely defined by the first \( k \) points \( (p_1, \ldots, p_{k}) \).

These \( k+1 \) points are provided in two steps so that this concept is a refinement of CPointFunctor:

• First, we set the first \( k \) points by a method 'init'.
• Then, we look at the position of the \( k+1 \) -th point with respect to the first \( k \) ones: the parenthesis operator takes an input point and returns a signed value.
  

The returned value, which is a model of CSignedNumber, is guaranteed to be:

• zero if the \( k+1 \) points belong to the same algebraic variety.
• strictly negative if \( k+1 \) -th point belongs to the interior of the algebraic variety defined by the first \( k \) points.
  
• strictly positive if \( k+1 \) -th point belongs to the exterior of the algebraic variety defined by the first \( k \) points.
  

Refinement of CPointFunctor

Associated types

As a refinement of CPointFunctor, it has the following nested types:

• Point type of input points
• Value type of the result, at least a model of CSignedNumbe

In addition it has the following inner types:

• PointArray a model of static array of k points
• Size type used for representing the size of the array

Notation

• X : A type that is a model of COrientationFunctor
• x : object of type X
• a : object of type PointArray

Definitions

Valid expressions and semantics

Name	Expression	Type requirements	Return type	Precondition	Semantics	Post condition	Complexity
array dimension	X::size		SizeArray		size of the array, equal to k
initialization	x.init(a)	a is of type PointArray	void		implicitely set the algebraic curve		model-dependent

Models

InHalfPlaneBy2x2DetComputer InHalfPlaneBySimpleMatrix InGeneralizedDiskOfGivenRadius

Template Parameters

T	the type that should be a model of COrientationFunctor.

Definition at line 113 of file COrientationFunctor.h.

Member Typedef Documentation

PointArray

template<typename T >

typedef T::PointArray DGtal::concepts::COrientationFunctor< T >::PointArray

Definition at line 120 of file COrientationFunctor.h.

SizeArray

template<typename T >

typedef T::SizeArray DGtal::concepts::COrientationFunctor< T >::SizeArray

Definition at line 121 of file COrientationFunctor.h.

Member Function Documentation

BOOST_CONCEPT_ASSERT()

template<typename T >

DGtal::concepts::COrientationFunctor< T >::BOOST_CONCEPT_ASSERT

(

(concepts::CSignedNumber< typename T::Value >)

)

BOOST_CONCEPT_USAGE()

template<typename T >

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

inline

Definition at line 123 of file COrientationFunctor.h.

    {
      concepts::ConceptUtils::sameType( myS, T::size ); 
      myX.init( myA );
    }

References DGtal::concepts::COrientationFunctor< T >::myA, DGtal::concepts::COrientationFunctor< T >::myS, DGtal::concepts::COrientationFunctor< T >::myX, and DGtal::concepts::ConceptUtils::sameType().

Field Documentation

myA

template<typename T >

PointArray DGtal::concepts::COrientationFunctor< T >::myA

private

Definition at line 131 of file COrientationFunctor.h.

Referenced by DGtal::concepts::COrientationFunctor< T >::BOOST_CONCEPT_USAGE().

myS

template<typename T >

SizeArray DGtal::concepts::COrientationFunctor< T >::myS

private

Definition at line 132 of file COrientationFunctor.h.

Referenced by DGtal::concepts::COrientationFunctor< T >::BOOST_CONCEPT_USAGE().

myX

template<typename T >

T DGtal::concepts::COrientationFunctor< T >::myX

private

Definition at line 130 of file COrientationFunctor.h.

Referenced by DGtal::concepts::COrientationFunctor< T >::BOOST_CONCEPT_USAGE().

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

• COrientationFunctor.h