Aim: This concept gathers all models that are able to compute the (sign of the) determinant of a 2x2 matrix with integral entries. More...

#include <DGtal/geometry/tools/determinant/C2x2DetComputer.h>

Inheritance diagram for DGtal::C2x2DetComputer< T >:

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Public Types
typedef T::ArgumentInteger	ArgumentType

typedef T::ResultInteger	ResultType

Public Member Functions
	BOOST_CONCEPT_ASSERT ((concepts::CEuclideanRing< ArgumentType >))

	BOOST_CONCEPT_ASSERT ((concepts::CSignedNumber< ResultType >))

	BOOST_CONCEPT_USAGE (C2x2DetComputer)

Private Attributes
T	myX

ArgumentType	myA

ArgumentType	myB

ArgumentType	myC

ArgumentType	myD

ResultType	myR

Detailed Description

template<typename T>
struct DGtal::C2x2DetComputer< T >

Aim: This concept gathers all models that are able to compute the (sign of the) determinant of a 2x2 matrix with integral entries.

Description of concept 'C2x2DetComputer'

Invariant

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

strictly positive if the determinant is strictly positive
striclty negative if the determinant is strictly negative
zero if the determinant is null

Refinement of

boost::DefaultConstructible<T>, boost::CopyConstructible<T>, boost::Assignable<T>

Associated types

ArgumentInteger : integral type of the four entries, at least a model of CEuclideanRing
ResultInteger : integral type of the result, at least a model of CSignedNumber

Notation

X : A type that is a model of C2x2DetComputer
x : object of type X
a, b, c, d : integral entries of type ArgumentInteger
r : result to type ResultInteger

Valid expressions and semantics

Name	Expression	Return type	Semantics	Complexity
full operator()	r = x(a, b, c, d)	ResultInteger	(sign of) ad - bc	model dependent
initialization	x.init(a,b)	void	memorizes a and b	constant
partial operator()	r = x(c, d)	ResultInteger	(sign of) ad - bc	model dependent

Notes

In addition to the full operator(), this concept allows another way to compute the quantity ad - bc in two steps:

first, we set the first column vector, ie a and b.
then, we compute the quantity ad - bc from a given column vector, ie c and d with the memorized values of a and b.
This feature is a way of accepting models that incrementally computes many determinants of matrices whose first column vector, ie a and b, is constant and whose second column vector, ie c and d, slightly varies from one computation to the next one. See for instance, SimpleIncremental2x2DetComputer.

Models

Simple2x2DetComputer, SimpleIncremental2x2DetComputer, AvnaimEtAl2x2DetSignComputer, Filtered2x2DetComputer

Template Parameters

T	the type that should be a model of C2x2DetComputer.

Definition at line 107 of file C2x2DetComputer.h.

Member Typedef Documentation

◆ ArgumentType

template<typename T >

typedef T::ArgumentInteger DGtal::C2x2DetComputer< T >::ArgumentType

Definition at line 111 of file C2x2DetComputer.h.

◆ ResultType

template<typename T >

typedef T::ResultInteger DGtal::C2x2DetComputer< T >::ResultType

Definition at line 114 of file C2x2DetComputer.h.

Member Function Documentation

◆ BOOST_CONCEPT_ASSERT() [1/2]

template<typename T >

DGtal::C2x2DetComputer< T >::BOOST_CONCEPT_ASSERT ( (concepts::CEuclideanRing< ArgumentType >) )

◆ BOOST_CONCEPT_ASSERT() [2/2]

template<typename T >

DGtal::C2x2DetComputer< T >::BOOST_CONCEPT_ASSERT ( (concepts::CSignedNumber< ResultType >) )

◆ BOOST_CONCEPT_USAGE()

template<typename T >

DGtal::C2x2DetComputer< T >::BOOST_CONCEPT_USAGE ( C2x2DetComputer< T > )

inline

Definition at line 117 of file C2x2DetComputer.h.

     {
       concepts::ConceptUtils::sameType( myR, myX( myA, myB, myC, myD ) );
       myX.init(myA, myB); 
       concepts::ConceptUtils::sameType( myR, myX( myA, myB ) );
     }