#include <DGtal/shapes/parametric/StarShaped3D.h>

Inheritance diagram for DGtal::StarShaped3D< TSpace >:

Public Types
typedef TSpace	Space

typedef Space::RealPoint	RealPoint

typedef std::pair< double, double >	AngularCoordinates

Public Member Functions
	StarShaped3D ()=default

StarShaped3D &	operator= (const StarShaped3D &other)=delete

virtual	~StarShaped3D ()=default

virtual RealPoint	interiorPoint () const

virtual RealPoint	getLowerBound () const =0

virtual RealPoint	getUpperBound () const =0

virtual RealPoint	center () const =0

virtual void	moveTo (const RealPoint &newCenter)=0

virtual AngularCoordinates	parameter (const RealPoint &p) const =0

virtual RealPoint	x (const AngularCoordinates &t) const =0

virtual RealPoint	gradient (const AngularCoordinates &t) const =0

virtual RealPoint	rt (const AngularCoordinates &t) const =0

virtual RealPoint	rp (const AngularCoordinates &t) const =0

virtual RealPoint	rtt (const AngularCoordinates &t) const =0

virtual RealPoint	rpp (const AngularCoordinates &t) const =0

virtual RealPoint	rtp (const AngularCoordinates &t) const =0

virtual Orientation	orientation (const RealPoint &p) const

virtual RealPoint	normal (const AngularCoordinates &t) const

virtual double	gaussianCurvature (const AngularCoordinates &t) const

virtual double	meanCurvature (const AngularCoordinates &t) const

virtual double	arclength (const AngularCoordinates &t1, AngularCoordinates t2, unsigned int nb) const

virtual double	surfacelength (const AngularCoordinates &t1, AngularCoordinates t2, unsigned int nb) const

void	selfDisplay (std::ostream &out) const

bool	isValid () const

Private Member Functions
template<typename T >
bool	isAlmostEqual (T x, T y) const

Detailed Description

template<typename TSpace>
class DGtal::StarShaped3D< TSpace >

Description of template class 'StarShaped3D'

Aim: Abstract class that represents any star-shaped object in dimension 3. Such a shape as a center and any segment from this center to the shape boundary is included in the shape. These shapes can thus be parameterized by a couple of angles 'Teta,Phi' turning around the center.

StarShaped3D and its derived classes are models of CEuclideanBoundedShape and CEuclideanOrientedShape.

NB: A backport from ImaGene.

Template Parameters

TSpace space in which the shape is defined.

Definition at line 71 of file StarShaped3D.h.

Member Typedef Documentation

◆ AngularCoordinates

template<typename TSpace >

typedef std::pair<double,double> DGtal::StarShaped3D< TSpace >::AngularCoordinates

Definition at line 77 of file StarShaped3D.h.

◆ RealPoint

template<typename TSpace >

typedef Space::RealPoint DGtal::StarShaped3D< TSpace >::RealPoint

Definition at line 76 of file StarShaped3D.h.

◆ Space

template<typename TSpace >

typedef TSpace DGtal::StarShaped3D< TSpace >::Space

Definition at line 75 of file StarShaped3D.h.

Constructor & Destructor Documentation

◆ StarShaped3D()

template<typename TSpace >

DGtal::StarShaped3D< TSpace >::StarShaped3D ( )

default

Constructor.

◆ ~StarShaped3D()

template<typename TSpace >

virtual DGtal::StarShaped3D< TSpace >::~StarShaped3D ( )

virtualdefault

Destructor.

Member Function Documentation

◆ arclength()

template<typename TSpace >

virtual double DGtal::StarShaped3D< TSpace >::arclength	(	const AngularCoordinates &	t1,
		AngularCoordinates	t2,
		unsigned int	nb ) const

virtual

Parameters

t1	is a couple of Teta && Phi wich are 2 angles respectivly between [0,2PI] and [0,Pi].
t2	is a couple of Teta && Phi wich are 2 angles respectivly between [0,2PI] and [0,Pi]. further from [t1].
nb	the number of points used to estimate the arclength between x(Teta1,Phi1) and x(Teta2,Phi2).

Returns: the estimated arclength.

◆ center()

template<typename TSpace >

virtual RealPoint DGtal::StarShaped3D< TSpace >::center ( ) const

pure virtual

Returns: the center of the star-shaped object.

Implemented in DGtal::Ball3D< TSpace >.

Referenced by DGtal::StarShaped3D< TSpace >::interiorPoint().

◆ gaussianCurvature()

template<typename TSpace >

virtual double DGtal::StarShaped3D< TSpace >::gaussianCurvature ( const AngularCoordinates & t ) const

virtual

Parameters

t	is a couple of Teta && Phi wich are 2 angles respectivly between [0,2PI] and [0,Pi].

Returns: the gaussian curvature at point (x(t),y(t)), positive is convex, negative is concave when shape is to the left and the shape boundary is followed counterclockwise.

◆ getLowerBound()

template<typename TSpace >

virtual RealPoint DGtal::StarShaped3D< TSpace >::getLowerBound ( ) const

pure virtual

Returns: the lower bound of the shape bounding box.

Implemented in DGtal::Ball3D< TSpace >.

◆ getUpperBound()

template<typename TSpace >

virtual RealPoint DGtal::StarShaped3D< TSpace >::getUpperBound ( ) const

pure virtual

Returns: the upper bound of the shape bounding box.

Implemented in DGtal::Ball3D< TSpace >.

◆ gradient()

template<typename TSpace >

virtual RealPoint DGtal::StarShaped3D< TSpace >::gradient ( const AngularCoordinates & t ) const

pure virtual

Parameters

t	is a couple of Teta && Phi wich are 2 angles respectivly between [0,2PI] and [0,Pi].

Returns: the vector (gradf(M).

Implemented in DGtal::Ball3D< TSpace >.

◆ interiorPoint()

template<typename TSpace >

virtual RealPoint DGtal::StarShaped3D< TSpace >::interiorPoint ( ) const

inlinevirtual

Returns: a point p such that 'isInside(p)' returns 'true'.

Definition at line 102 of file StarShaped3D.h.

    {
      return center();
    }

References DGtal::StarShaped3D< TSpace >::center().

◆ isAlmostEqual()

template<typename TSpace >

template<typename T >

bool DGtal::StarShaped3D< TSpace >::isAlmostEqual	(	T	x,
		T	y ) const

inlineprivate

Equality test using relative tolerance.

Definition at line 309 of file StarShaped3D.h.

    {
      return std::abs(x - y) <= std::numeric_limits<T>::epsilon();
    }

◆ isValid()

template<typename TSpace >

bool DGtal::StarShaped3D< TSpace >::isValid ( ) const

Checks the validity/consistency of the object.

Returns: 'true' if the object is valid, 'false' otherwise.

◆ meanCurvature()

template<typename TSpace >

virtual double DGtal::StarShaped3D< TSpace >::meanCurvature ( const AngularCoordinates & t ) const

virtual

Parameters

t	is a couple of Teta && Phi wich are 2 angles respectivly between [0,2PI] and [0,Pi]

Returns: the mean curvature at point (x(t),y(t)), positive is convex, negative is concave when shape is to the left and the shape boundary is followed counterclockwise.

◆ moveTo()

template<typename TSpace >

virtual void DGtal::StarShaped3D< TSpace >::moveTo ( const RealPoint & newCenter )

pure virtual

Move the center of the star-shaped object to a new position

Parameters

newCenter the new center position

Implemented in DGtal::Ball3D< TSpace >.

◆ normal()

template<typename TSpace >

virtual RealPoint DGtal::StarShaped3D< TSpace >::normal ( const AngularCoordinates & t ) const

virtual

Parameters

t	is a couple of Teta && Phi wich are 2 angles respectivly between [0,2PI] and [0,Pi].

Returns: the vector normal made unitary which is the unit normal to the shape boundary looking inside the shape.

◆ operator=()

template<typename TSpace >

StarShaped3D & DGtal::StarShaped3D< TSpace >::operator= ( const StarShaped3D< TSpace > & other )

delete

Assignment.

Parameters

other the object to copy.

Returns: a reference on 'this'. Forbidden by default.

◆ orientation()

template<typename TSpace >

virtual Orientation DGtal::StarShaped3D< TSpace >::orientation ( const RealPoint & p ) const

virtual

Return the orienatation of a point with respect to a shape.

Parameters

p	input point

Returns: the orientation of the point (<0 means inside, ...)

◆ parameter()

template<typename TSpace >

virtual AngularCoordinates DGtal::StarShaped3D< TSpace >::parameter ( const RealPoint & p ) const

pure virtual

Parameters

p	any point in the sapce.

Returns: the angles parameters (Teta, Phi) corresponding to this point for the shape.

Implemented in DGtal::Ball3D< TSpace >.

◆ rp()

template<typename TSpace >

virtual RealPoint DGtal::StarShaped3D< TSpace >::rp ( const AngularCoordinates & t ) const

pure virtual

Parameters

t	is a couple of Teta && Phi wich are 2 angles respectivly between [0,2PI] and [0,Pi].

Returns: the vector (rp(M)) wich is the first partial derivative with respect to Phi.

Implemented in DGtal::Ball3D< TSpace >.

◆ rpp()

template<typename TSpace >

virtual RealPoint DGtal::StarShaped3D< TSpace >::rpp ( const AngularCoordinates & t ) const

pure virtual

Parameters

t	is a couple of Teta && Phi wich are 2 angles respectivly between [0,2PI] and [0,Pi].

Returns: the vector (rpp(M)) wich is second the partial derivative with respect to Phi.

Implemented in DGtal::Ball3D< TSpace >.

◆ rt()

template<typename TSpace >

virtual RealPoint DGtal::StarShaped3D< TSpace >::rt ( const AngularCoordinates & t ) const

pure virtual

Parameters

t	is a couple of Teta && Phi wich are 2 angles respectivly between [0,2PI] and [0,Pi].

Returns: the vector (rt(M)) wich is the partial derivative with respect to Teta.

Implemented in DGtal::Ball3D< TSpace >.

◆ rtp()

template<typename TSpace >

virtual RealPoint DGtal::StarShaped3D< TSpace >::rtp ( const AngularCoordinates & t ) const

pure virtual

Parameters

t	is a couple of Teta && Phi wich are 2 angles respectivly between [0,2PI] and [0,Pi].

Returns: the vector (rpp(M)) wich is second the partial derivative with respect to Teta then Phi.

Implemented in DGtal::Ball3D< TSpace >.

◆ rtt()

template<typename TSpace >

virtual RealPoint DGtal::StarShaped3D< TSpace >::rtt ( const AngularCoordinates & t ) const

pure virtual

Parameters

t	is a couple of Teta && Phi wich are 2 angles respectivly between [0,2PI] and [0,Pi].

Returns: the vector (rtt(M)) wich is second the partial derivative with respect to Teta(twice).

Implemented in DGtal::Ball3D< TSpace >.

◆ selfDisplay()

template<typename TSpace >

void DGtal::StarShaped3D< TSpace >::selfDisplay ( std::ostream & out ) const

Writes/Displays the object on an output stream.

Parameters

out	the output stream where the object is written.

◆ surfacelength()

template<typename TSpace >

virtual double DGtal::StarShaped3D< TSpace >::surfacelength	(	const AngularCoordinates &	t1,
		AngularCoordinates	t2,
		unsigned int	nb ) const

virtual

Parameters

t1	is a couple of Teta && Phi wich are 2 angles respectivly between [0,2PI] and [0,Pi].
t2	is a couple of Teta && Phi wich are 2 angles respectivly between [0,2PI] and [0,Pi]. further from [t1].
nb	the number of points used to estimate the surface between x(Teta1,Phi1) and x(Teta2,Phi2).

Returns: the estimated surfacelength.

◆ x()

template<typename TSpace >

virtual RealPoint DGtal::StarShaped3D< TSpace >::x ( const AngularCoordinates & t ) const

pure virtual

Parameters

t	is a couple of Theta && Phi wich are 2 angles respectivly between [0,2PI] and [0,Pi].

Returns: the vector (x(t),y(t),z(t)) which is the position on the shape boundary.

Implemented in DGtal::Ball3D< TSpace >.

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

StarShaped3D.h

Public Types

Public Member Functions

Private Member Functions

Detailed Description

Member Typedef Documentation

◆ AngularCoordinates

◆ RealPoint

◆ Space

Constructor & Destructor Documentation

◆ StarShaped3D()

◆ ~StarShaped3D()

Member Function Documentation

◆ arclength()

◆ center()

◆ gaussianCurvature()

◆ getLowerBound()

◆ getUpperBound()

◆ gradient()

◆ interiorPoint()

◆ isAlmostEqual()

◆ isValid()

◆ meanCurvature()

◆ moveTo()

◆ normal()

◆ operator=()

◆ orientation()

◆ parameter()

◆ rp()

◆ rpp()

◆ rt()

◆ rtp()

◆ rtt()

◆ selfDisplay()

◆ surfacelength()

◆ x()