DGtal  0.9.4beta
Public Types | Public Member Functions | Static Public Attributes | Private Attributes
DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer > Class Template Reference

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

Collaboration diagram for DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >:
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Public Types

typedef TPoint Point
 
typedef std::array< Point, 2 > PointArray
 
typedef PointArray::size_type SizeArray
 
typedef TDetComputer DetComputer
 
typedef DetComputer::ArgumentInteger Integer
 
typedef DetComputer::ResultInteger Value
 
typedef Simple2x2DetComputer< IntegerAreaFunctor
 

Public Member Functions

 BOOST_CONCEPT_ASSERT ((C2x2DetComputer< DetComputer >))
 
 InGeneralizedDiskOfGivenRadius (bool isPositive=true, const Integer &aNum2=NumberTraits< Integer >::ONE, const Integer &aDen2=NumberTraits< Integer >::ZERO)
 
 InGeneralizedDiskOfGivenRadius (const InGeneralizedDiskOfGivenRadius &other)
 
InGeneralizedDiskOfGivenRadiusoperator= (const InGeneralizedDiskOfGivenRadius &other)
 
void init (const Point &aP, const Point &aQ)
 
void init (const PointArray &aA)
 
Value operator() (const Point &aR) const
 
void selfDisplay (std::ostream &out) const
 
bool lengthIsValid (const Integer &aL2) const
 
bool isValid () const
 
void finalizeComputation () const
 

Static Public Attributes

static const SizeArray size = 2
 

Private Attributes

Integer myNum2
 
Integer myDen2
 
bool myIsPositive
 
DetComputer myDetComputer
 
Point myP
 
Point myQ
 
Point myR
 
Integer myComputedNum2
 
Integer myComputedDen2
 
Integer myPQ0
 
Integer myPQ1
 
Integer myPQnorm
 
Integer myQR0
 
Integer myQR1
 
Integer myQRnorm
 
Integer myRP0
 
Integer myRP1
 
Integer myRPnorm
 
Integer myArea
 
AreaFunctor myAreaFunctor
 

Detailed Description

template<typename TPoint, typename TDetComputer>
class DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >

Aim: This class implements an orientation functor that provides a way to determine the position of a given point with respect to the unique circle passing by the same two given points and whose radius and orientation is given.

This class is useful for some geometric algorithm involving disks of given radius, such as alpha-hull and alpha-shape computations.

The radius is given at construction. It is described by a pair of integers myNum2 and myDen2 that stands for the numerator and denominator of the squared radius. The orientation is also given at construction. It is described by a boolean equal to 'true' (resp. 'false') if the center C of the circle of squared radius myNum2 / myDen2 and passing by myP and myQ is located on the left side (resp. right side) of the oriented line myP myQ, ie. if myP , myQ , C are counter-clockwise oriented (resp. clockwise oriented).

The test is done in two steps. After an initialization step that memorizes the two points that uniquely defines the circle whose radius and orientation is given, we can test the position of a third point myR with respect to this circle. Note that the distance between myP and myR is assumed to be greater than the distance between myP and myQ and between myQ and myR.

The test is reduced to the computation of the determinant of a 2x2 matrix of integral entries, the implementation of which is delegated to a determinant computer. The reduction involves many multiplications and additions so that temporary integers must be coded with at least \( 6b + 9 \) bits for point coordinates coded with \( b \) bits. That's why it is a best practice to use BigInteger to avoid any overflows. You can use however 64 bits integers together with a smart determinant computer, like AvnaimEtAl2x2DetSignComputer, for small domains where point coordinates range within ]-2^9; 2^9[.

Basic usage:

...
typedef Z2i::Point Point;
typedef Simple2x2DetComputer<Z2i::BigInteger> DeterminantComputer;
typedef InGeneralizedDiskOfGivenRadius<Point, DeterminantComputer> Functor;
Functor functor(true, 25, 1); //circles of radius 5, directly oriented
functor.init( Point(5,0), Point(0,5) );
return functor( Point(-4,1) );
//a strictly positive value is returned because (-4,1) lies in the interior
//of the circle of center (0,0) and radius 5.

Note that since a substantial part of the execution time comes from the allocation/desallocation of integers, we follow the same strategy used in IntegerComputer: the user instantiates once this object and performs several tests with it.

Template Parameters
TPointa model of point
TDetComputera model of C2x2DetComputer
Examples:
geometry/tools/exampleAlphaShape.cpp.

Definition at line 125 of file InGeneralizedDiskOfGivenRadius.h.

Member Typedef Documentation

template<typename TPoint , typename TDetComputer >
typedef Simple2x2DetComputer<Integer> DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::AreaFunctor

Type of functor returning the area of a parallelogram based on two vectors. Used to compute the radius of a circle passing by 3 points.

Definition at line 165 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
typedef TDetComputer DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::DetComputer

Type of determinant computer

Definition at line 150 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
typedef DetComputer::ArgumentInteger DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::Integer

Type of integers used during the computation

Definition at line 155 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
typedef TPoint DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::Point

Type of input points

Definition at line 132 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
typedef std::array<Point,2> DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::PointArray

Type of point array

Definition at line 137 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
typedef PointArray::size_type DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::SizeArray

Type used to represent the size of the array

Definition at line 141 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
typedef DetComputer::ResultInteger DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::Value

Type of returned value

Definition at line 159 of file InGeneralizedDiskOfGivenRadius.h.

Constructor & Destructor Documentation

template<typename TPoint , typename TDetComputer >
DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::InGeneralizedDiskOfGivenRadius ( bool  isPositive = true,
const Integer aNum2 = NumberTraitsInteger >::ONE,
const Integer aDen2 = NumberTraitsInteger >::ZERO 
)

Constructor of the functor from a given radius.

Parameters
isPositivebool equal to 'true' (resp. 'false') if the center C of the circle of squared radius myNum2 / myDen2 and passing by myP and myQ is located on the left side (resp. right side) of the oriented line myP myQ, ie. myP , myQ , C are counter-clockwise oriented (resp. clockwise oriented).
aNum2squared numerator of the radius (0 by default)
aDen2squared denominator of the radius (1 by default)
Precondition
aNum2 should be not zero; the object is not valid.
Warning
aNum2 and aDen2 should be both positive. If they are negative, we take their opposite. It aDen2 is zero, the radius is assumed to tend to infinite.
template<typename TPoint , typename TDetComputer >
DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::InGeneralizedDiskOfGivenRadius ( const InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer > &  other)

Copy constructor.

Parameters
otherthe object to clone.

Member Function Documentation

template<typename TPoint , typename TDetComputer >
DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::BOOST_CONCEPT_ASSERT ( (C2x2DetComputer< DetComputer >)  )
template<typename TPoint , typename TDetComputer >
void DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::finalizeComputation ( ) const

Update myComputedNum2 and myComputedDen2 from other private datas.

template<typename TPoint , typename TDetComputer >
void DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::init ( const Point aP,
const Point aQ 
)

Initialization from two points.

Parameters
aPa first point
aQa second point
Precondition
the distance between aP and aQ must be greater than the circle diameter
template<typename TPoint , typename TDetComputer >
void DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::init ( const PointArray aA)

Initialisation from two points.

Parameters
aAarray of two points
See also
InGeneralizedDiskOfGivenRadiusBy2x2DetComputer::init()
template<typename TPoint , typename TDetComputer >
bool DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::isValid ( ) const

Checks the validity/consistency of the object. More precisely, myNum2 and myDen2 must be positive, myNum2 must not be zero (only strictly positive radius are valid)

Returns
'true' if the object is valid, 'false' otherwise.
template<typename TPoint , typename TDetComputer >
bool DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::lengthIsValid ( const Integer aL2) const

Compares the length of two consecutive input points to the diameter of the circle.

Parameters
aL2any squared length between two points
Returns
'true' if either myDen2 equals zero or the given (squared) length is shorter than the (squared) diameter of the circle
template<typename TPoint , typename TDetComputer >
Value DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::operator() ( const Point aR) const

Main operator.

Warning
InGeneralizedDiskOfGivenRadiusBy2x2DetComputer::init() should be called before
Parameters
aRany point to test
Returns
orientation of the third point myR with respect to the circle of squared radius myNum2 / myDen2 and oriented by myPositive passing by myP and myQ.
  • if the third point lies on the same side of the oriented line passing by myP myQ than the circle center, the return value is:
    • zero if the third point belongs to the circle
    • strictly positive if it does not lie in the interior or on the boundary of the circle
    • strictly negative if it lies in the interior of the circle
  • otherwise, the return value is strictly negative.
Precondition
the distance between myQ and aR must be greater than the circle diameter and segment myP aR is assumed to be the longest side of the triangle myP , myQ , aR.
template<typename TPoint , typename TDetComputer >
InGeneralizedDiskOfGivenRadius& DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::operator= ( const InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer > &  other)

Assignment.

Parameters
otherthe object to copy.
Returns
a reference on 'this'.
template<typename TPoint , typename TDetComputer >
void DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::selfDisplay ( std::ostream &  out) const

Writes/Displays the object on an output stream.

Parameters
outthe output stream where the object is written.

Field Documentation

template<typename TPoint , typename TDetComputer >
Integer DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::myArea
mutableprivate

area of triangle myP myQ myR

Definition at line 362 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
AreaFunctor DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::myAreaFunctor
mutableprivate

Functor returning the area of a parallelogram based on two vectors.

Definition at line 367 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
Integer DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::myComputedDen2
mutableprivate

Denominator of the squared radius of the circle myP , myQ , myR

Definition at line 322 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
Integer DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::myComputedNum2
mutableprivate

Numerator of the squared radius of the circle myP , myQ , myR

Definition at line 318 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
Integer DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::myDen2
private

Denominator of the given squared radius

Definition at line 285 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
DetComputer DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::myDetComputer
private

Determinant computer used to compare the given (squared) radius myNum2 / myDen2 to the (squared) radius of the circle passing by myP , myQ , myR , ie. myComputedNum2 / myComputedDen2

Definition at line 301 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
bool DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::myIsPositive
private

boolean equal to 'true' (resp. 'false') if the center C of the circle of squared radius myNum2 / myDen2 and passing by myP and myQ is located on the left side (resp. right side) of the oriented line myP myQ, ie. if myP , myQ , C are counter-clockwise oriented (resp. clockwise oriented).

Definition at line 294 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
Integer DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::myNum2
private

Numerator of the given squared radius

Definition at line 281 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
Point DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::myP
mutableprivate

First point

Definition at line 306 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
Integer DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::myPQ0
mutableprivate

x-coordinate of myQ - myP

Definition at line 326 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
Integer DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::myPQ1
mutableprivate

y-coordinate of myQ - myP

Definition at line 330 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
Integer DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::myPQnorm
mutableprivate

Squared length of myQ - myP

Definition at line 334 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
Point DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::myQ
mutableprivate

Second point

Definition at line 310 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
Integer DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::myQR0
mutableprivate

x-coordinate of myR - myQ

Definition at line 338 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
Integer DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::myQR1
mutableprivate

y-coordinate of myR - myQ

Definition at line 342 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
Integer DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::myQRnorm
mutableprivate

Squared length of myR - myQ

Definition at line 346 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
Point DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::myR
mutableprivate

Third point

Definition at line 314 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
Integer DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::myRP0
mutableprivate

x-coordinate of myP - myR

Definition at line 350 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
Integer DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::myRP1
mutableprivate

y-coordinate of myP - myR

Definition at line 354 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
Integer DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::myRPnorm
mutableprivate

Squared length of myP - myR

Definition at line 358 of file InGeneralizedDiskOfGivenRadius.h.

template<typename TPoint , typename TDetComputer >
const SizeArray DGtal::InGeneralizedDiskOfGivenRadius< TPoint, TDetComputer >::size = 2
static

static size of the array, ie. 2

Definition at line 145 of file InGeneralizedDiskOfGivenRadius.h.


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