#include <DGtal/shapes/parametric/StarShaped2D.h>

Inheritance diagram for DGtal::StarShaped2D< TSpace >:

Public Types
typedef TSpace	Space

typedef Space::RealPoint	RealPoint

Public Member Functions
	StarShaped2D ()=default

	StarShaped2D (const StarShaped2D &other)=delete

StarShaped2D &	operator= (const StarShaped2D &other)=delete

virtual	~StarShaped2D ()=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 double	parameter (const RealPoint &p) const =0

virtual RealPoint	x (const double t) const =0

virtual RealPoint	xp (const double t) const =0

virtual RealPoint	xpp (const double t) const =0

Orientation	orientation (const RealPoint &p) const

RealPoint	tangent (const double t) const

RealPoint	normal (const double t) const

double	curvature (const double t) const

double	arclength (const double t1, double t2, const unsigned int nb) const

RealPoint	findIntersection (const RealPoint &inner, const RealPoint &outer, const double epsilon) const

RealPoint	closestPointWithWitnesses (const RealPoint &p, const RealPoint &left, const RealPoint &right, const int step) 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::StarShaped2D< TSpace >

Description of template class 'StarShaped2D'

Aim: Abstract class that represents any star-shaped object in dimension 2. 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 an angle 't' turning around the center.

StarShaped2D 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 74 of file StarShaped2D.h.

Member Typedef Documentation

◆ RealPoint

template<typename TSpace >

typedef Space::RealPoint DGtal::StarShaped2D< TSpace >::RealPoint

Definition at line 79 of file StarShaped2D.h.

◆ Space

template<typename TSpace >

typedef TSpace DGtal::StarShaped2D< TSpace >::Space

Definition at line 78 of file StarShaped2D.h.

Constructor & Destructor Documentation

◆ StarShaped2D() [1/2]

template<typename TSpace >

DGtal::StarShaped2D< TSpace >::StarShaped2D ( )

default

Constructor.

◆ StarShaped2D() [2/2]

template<typename TSpace >

DGtal::StarShaped2D< TSpace >::StarShaped2D ( const StarShaped2D< TSpace > & other )

delete

Copy constructor.

Parameters

other the object to clone. Forbidden by default.

◆ ~StarShaped2D()

template<typename TSpace >

virtual DGtal::StarShaped2D< TSpace >::~StarShaped2D ( )

virtualdefault

Destructor.

Member Function Documentation

◆ arclength()

template<typename TSpace >

double DGtal::StarShaped2D< TSpace >::arclength	(	const double	t1,
		double	t2,
		const unsigned int	nb
	)		const

Parameters

t1	any angle between 0 and 2*Pi.
t2	any angle between 0 and 2*Pi, further from [t1].
nb	the number of points used to estimate the arclength between x(t1) and x(t2).

Returns: the estimated arclength.

◆ center()

template<typename TSpace >

virtual RealPoint DGtal::StarShaped2D< TSpace >::center ( ) const

pure virtual

Returns: the center of the star-shaped object.

Implemented in DGtal::AccFlower2D< TSpace >, DGtal::Astroid2D< TSpace >, DGtal::Astroid2D< Space >, DGtal::Ball2D< TSpace >, DGtal::Ellipse2D< TSpace >, DGtal::Flower2D< TSpace >, DGtal::Lemniscate2D< TSpace >, and DGtal::NGon2D< TSpace >.

Referenced by DGtal::StarShaped2D< TSpace >::interiorPoint().

◆ closestPointWithWitnesses()

template<typename TSpace >

RealPoint DGtal::StarShaped2D< TSpace >::closestPointWithWitnesses	(	const RealPoint &	p,
		const RealPoint &	left,
		const RealPoint &	right,
		const int	step
	)		const

Return a point that lies between the projection of left and right and that is the closest regarding the \(L_2\) norm

Parameters

p	the point to be projected
left	a point that is supposed to be projected left of p (regarding the angle)
right	a point that is supposed to be projected right of p (regarding the angle)
step	precision of the approximation

Returns: a point.

Referenced by test_shape().

◆ curvature()

template<typename TSpace >

double DGtal::StarShaped2D< TSpace >::curvature ( const double t ) const

Parameters

t	any angle between 0 and 2*Pi.

Returns: the algebraic 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.

◆ findIntersection()

template<typename TSpace >

RealPoint DGtal::StarShaped2D< TSpace >::findIntersection	(	const RealPoint &	inner,
		const RealPoint &	outer,
		const double	epsilon
	)		const

Return a point on the segment [inner;outer] that is at most \(\epsilon\) from the shape in \(L_2\) norm.

Parameters

inner	a point that is inside the shape
outer	a point that is outside the shape
epsilon	error parameter

Returns: the intersected point.

Referenced by test_shape().

◆ getLowerBound()

template<typename TSpace >

virtual RealPoint DGtal::StarShaped2D< TSpace >::getLowerBound ( ) const

pure virtual

Returns: the lower bound of the shape bounding box.

Implemented in DGtal::AccFlower2D< TSpace >, DGtal::Astroid2D< TSpace >, DGtal::Astroid2D< Space >, DGtal::Ball2D< TSpace >, DGtal::Ellipse2D< TSpace >, DGtal::Flower2D< TSpace >, DGtal::Lemniscate2D< TSpace >, and DGtal::NGon2D< TSpace >.

◆ getUpperBound()

template<typename TSpace >

virtual RealPoint DGtal::StarShaped2D< TSpace >::getUpperBound ( ) const

pure virtual

Returns: the upper bound of the shape bounding box.

Implemented in DGtal::AccFlower2D< TSpace >, DGtal::Astroid2D< TSpace >, DGtal::Astroid2D< Space >, DGtal::Ball2D< TSpace >, DGtal::Ellipse2D< TSpace >, DGtal::Flower2D< TSpace >, DGtal::Lemniscate2D< TSpace >, and DGtal::NGon2D< TSpace >.

◆ interiorPoint()

template<typename TSpace >

virtual RealPoint DGtal::StarShaped2D< TSpace >::interiorPoint ( ) const

inlinevirtual

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

Definition at line 111 of file StarShaped2D.h.

    {
      return center();
    }

References DGtal::StarShaped2D< TSpace >::center().

◆ isAlmostEqual()

template<typename TSpace >

template<typename T >

bool DGtal::StarShaped2D< TSpace >::isAlmostEqual	(	T	x,
		T	y
	)		const

inlineprivate

Equality test using relative tolerance.

Definition at line 267 of file StarShaped2D.h.

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

◆ isValid()

template<typename TSpace >

bool DGtal::StarShaped2D< TSpace >::isValid ( ) const

Checks the validity/consistency of the object.

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

◆ moveTo()

template<typename TSpace >

virtual void DGtal::StarShaped2D< 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::AccFlower2D< TSpace >, DGtal::Astroid2D< TSpace >, DGtal::Astroid2D< Space >, DGtal::Ball2D< TSpace >, DGtal::Ellipse2D< TSpace >, DGtal::Flower2D< TSpace >, DGtal::Lemniscate2D< TSpace >, and DGtal::NGon2D< TSpace >.

◆ normal()

template<typename TSpace >

RealPoint DGtal::StarShaped2D< TSpace >::normal ( const double t ) const

Parameters

t	any angle between 0 and 2*Pi.

Returns: the vector (x''(t),y''(t)) made unitary which is the unit normal to the shape boundary looking inside the shape.

◆ operator=()

template<typename TSpace >

StarShaped2D & DGtal::StarShaped2D< TSpace >::operator= ( const StarShaped2D< TSpace > & other )

delete

Assignment.

Parameters

other the object to copy.

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

◆ orientation()

template<typename TSpace >

Orientation DGtal::StarShaped2D< TSpace >::orientation ( const RealPoint & p ) const

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

Parameters

p	input point

Returns: the orientation of the point (INSIDE ON or OUTSIDE).

◆ parameter()

template<typename TSpace >

virtual double DGtal::StarShaped2D< TSpace >::parameter ( const RealPoint & p ) const

pure virtual

Parameters

p	any point in the plane.

Returns: the angle parameter between 0 and 2*Pi corresponding to this point for the shape.

Implemented in DGtal::AccFlower2D< TSpace >, DGtal::Astroid2D< TSpace >, DGtal::Astroid2D< Space >, DGtal::Ball2D< TSpace >, DGtal::Ellipse2D< TSpace >, DGtal::Flower2D< TSpace >, DGtal::Lemniscate2D< TSpace >, and DGtal::NGon2D< TSpace >.

◆ selfDisplay()

template<typename TSpace >

void DGtal::StarShaped2D< TSpace >::selfDisplay ( std::ostream & out ) const

Writes/Displays the object on an output stream.

Parameters

out	the output stream where the object is written.

◆ tangent()

template<typename TSpace >

RealPoint DGtal::StarShaped2D< TSpace >::tangent ( const double t ) const

Parameters

t	any angle between 0 and 2*Pi.

Returns: the vector (x'(t),y'(t)) made unitary which is the unit tangent to the shape boundary.

◆ x()

template<typename TSpace >

virtual RealPoint DGtal::StarShaped2D< TSpace >::x ( const double t ) const

pure virtual

Parameters

t	any angle between 0 and 2*Pi.

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

Implemented in DGtal::AccFlower2D< TSpace >, DGtal::Astroid2D< TSpace >, DGtal::Astroid2D< Space >, DGtal::Ball2D< TSpace >, DGtal::Ellipse2D< TSpace >, DGtal::Flower2D< TSpace >, DGtal::Lemniscate2D< TSpace >, and DGtal::NGon2D< TSpace >.

◆ xp()

template<typename TSpace >

virtual RealPoint DGtal::StarShaped2D< TSpace >::xp ( const double t ) const

pure virtual

Parameters

t	any angle between 0 and 2*Pi.

Returns: the vector (x'(t),y'(t)) which is the tangent to the shape boundary.

Implemented in DGtal::AccFlower2D< TSpace >, DGtal::Astroid2D< TSpace >, DGtal::Astroid2D< Space >, DGtal::Ball2D< TSpace >, DGtal::Ellipse2D< TSpace >, DGtal::Flower2D< TSpace >, DGtal::Lemniscate2D< TSpace >, and DGtal::NGon2D< TSpace >.

◆ xpp()

template<typename TSpace >

virtual RealPoint DGtal::StarShaped2D< TSpace >::xpp ( const double t ) const

pure virtual

Parameters

t	any angle between 0 and 2*Pi.

Returns: the vector (x''(t),y''(t)).

Implemented in DGtal::AccFlower2D< TSpace >, DGtal::Astroid2D< TSpace >, DGtal::Astroid2D< Space >, DGtal::Ball2D< TSpace >, DGtal::Ellipse2D< TSpace >, DGtal::Flower2D< TSpace >, DGtal::Lemniscate2D< TSpace >, and DGtal::NGon2D< TSpace >.

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

StarShaped2D.h

Public Types

Public Member Functions

Private Member Functions

Detailed Description

Member Typedef Documentation

◆ RealPoint

◆ Space

Constructor & Destructor Documentation

◆ StarShaped2D() [1/2]

◆ StarShaped2D() [2/2]

◆ ~StarShaped2D()

Member Function Documentation

◆ arclength()

◆ center()

◆ closestPointWithWitnesses()

◆ curvature()

◆ findIntersection()

◆ getLowerBound()

◆ getUpperBound()

◆ interiorPoint()

◆ isAlmostEqual()

◆ isValid()

◆ moveTo()

◆ normal()

◆ operator=()

◆ orientation()

◆ parameter()

◆ selfDisplay()

◆ tangent()

◆ x()

◆ xp()

◆ xpp()