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