DGtal::StarShaped3D< TSpace > Class Template Reference

#include <StarShaped3D.h>

Inheritance diagram for DGtal::StarShaped3D< TSpace >:

Public Types
typedef TSpace	Space
typedef Space::RealPoint	RealPoint
typedef pair< double, double >	AngularCoordinates

Public Member Functions
	StarShaped3D ()
	~StarShaped3D ()
virtual RealPoint	interiorPoint () const
virtual RealPoint	getLowerBound () const =0
virtual RealPoint	getUpperBound () const =0
virtual RealPoint	center () const =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 bool	isInside (const RealPoint &p) const
virtual Orientation	orientation (const RealPoint &p) const
virtual RealPoint	normal (AngularCoordinates t) const
virtual double	gaussianCurvature (AngularCoordinates t) const
virtual double	meanCurvature (AngularCoordinates t) const
virtual double	arclength (AngularCoordinates t1, AngularCoordinates t2, unsigned int nb) const
virtual double	surfacelength (AngularCoordinates t1, AngularCoordinates t2, unsigned int nb) const
void	selfDisplay (std::ostream &out) const
bool	isValid () const

Private Member Functions
StarShaped3D &	operator= (const StarShaped3D &other)

---

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

template<typename TSpace>

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

Reimplemented in DGtal::Ball3D< TSpace >.

Definition at line 77 of file StarShaped3D.h.

template<typename TSpace>

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

Reimplemented in DGtal::Ball3D< TSpace >.

Definition at line 76 of file StarShaped3D.h.

template<typename TSpace>

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

Reimplemented in DGtal::Ball3D< TSpace >.

Definition at line 75 of file StarShaped3D.h.

---

Constructor & Destructor Documentation

template<typename TSpace>

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

inline

Constructor.

Definition at line 82 of file StarShaped3D.h.

    {}

template<typename T >

DGtal::StarShaped3D< T >::~StarShaped3D ( )

inline

Destructor.

Definition at line 291 of file StarShaped3D.ih.

{
}

---

Member Function Documentation

template<typename TSpace >

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

inlinevirtual

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.

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.

Definition at line 218 of file StarShaped3D.ih.

References M_PI.

{
  while ( t2.first < t1.first ) t2.first += 2.0*M_PI;
  while ( t2.second < t1.second ) t2.second += 2.0*M_PI;

  RealPoint x0( x( t1 ) );
  double l = 0.0;
  for ( unsigned int i = 1; i <= nb; ++i )
    {
      AngularCoordinates t;
      t.first = ( ( t2.first - t1.first ) * i ) / nb;
      t.second = ( ( t2.second - t1.second ) * i ) / nb;
      AngularCoordinates h;
      h.first=t1.first + t.first;
      h.second=t1.second + t.second;
      RealPoint x1( x( h ) );
      l += sqrt( ( x1[0] - x0[0] )*( x1[0] - x0[0] )
                 + ( x1[1] - x0[1] )*( x1[1] - x0[1] ) + ( x1[2] - x0[2] )*( x1[2] - x0[2] ) );
      x0 = x1;
    }
  return l;
}

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().

template<typename TSpace >

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

inlinevirtual

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.

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),z(t)), positive is convex, negative is concave when shape is to the left and the shape boundary is followed counterclockwise.

Definition at line 178 of file StarShaped3D.ih.

{
  
  typedef typename Space::RealPoint RealPoint;
  
  RealPoint art = rt(t);
  RealPoint arp = rp(t);
  RealPoint artt = rtt(t);
  RealPoint arpp = rpp(t);
  RealPoint artp = rtp(t);


  RealPoint n(art[1]*arp[2]-art[2]*arp[1],art[2]*arp[0]-art[0]*arp[2],art[0]*arp[1]-art[1]*arp[0]);
  double norme= sqrt(n[0]*n[0]+n[1]*n[1]+n[2]*n[2]);
  n[0]=n[0]/norme;
  n[1]=n[1]/norme;
  n[2]=n[2]/norme;
  double E = art[0] * art[0]+ art[1] * art[1]+ art[2] * art[2];
  double F= art[0] * arp[0]+ art[1] * arp[1]+ art[2] * arp[2];
  double G = arp[0] * arp[0]+ arp[1] * arp[1]+ arp[2] * arp[2];
  double L = artt[0] * n[0]+ artt[1] * n[1]+ artt[2] * n[2];
  double M = artp[0] * n[0]+ artp[1] * n[1]+ artp[2] * n[2];
  double N = arpp[0] * n[0]+ arpp[1] * n[1]+ arpp[2] * n[2];

  double K = (L*N-M*M)/(E*G-F*F);

  return K;
}

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 >.

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 >.

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 >.

template<typename TSpace>

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

inlinevirtual

Returns:

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

Definition at line 95 of file StarShaped3D.h.

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

    {
      return center();
    }

template<typename TSpace >

bool DGtal::StarShaped3D< TSpace >::isInside ( const RealPoint &  p ) const

inlinevirtual

Parameters:

p	any point in the plane.

Returns:

'true' if the point is inside the shape, 'false' if it is strictly outside.

Parameters:

p	any point in the plane.

Returns:

'true' if the point is inside or on the shape, 'false' if it is strictly outside.

Definition at line 58 of file StarShaped3D.ih.

{
  AngularCoordinates t = parameter( p );
  RealPoint x_rel = x( t );
  x_rel -= center();
  double d_x = x_rel[0]*x_rel[0] + x_rel[1]*x_rel[1] + x_rel[2]*x_rel[2];
  RealPoint p_rel( p );
  p_rel -= center();
  double d_p = p_rel[0]*p_rel[0] + p_rel[1]*p_rel[1]+ p_rel[2]*p_rel[2];
  
  return d_p <= d_x;
}

template<typename T >

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

inline

Checks the validity/consistency of the object.

Returns:

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

Reimplemented in DGtal::Ball3D< TSpace >.

Definition at line 317 of file StarShaped3D.ih.

{
  return true;
}

template<typename TSpace >

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

inlinevirtual

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.

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),z(t)), positive is convex, negative is concave when shape is to the left and the shape boundary is followed counterclockwise.

Definition at line 137 of file StarShaped3D.ih.

{
  typedef typename Space::RealPoint RealPoint;
  

  RealPoint art = rt(t);
  RealPoint arp = rp(t);
  RealPoint artt = rtt(t);
  RealPoint arpp = rpp(t);
  RealPoint artp = rtp(t);

  RealPoint n(art[1]*arp[2]-art[2]*arp[1],art[2]*arp[0]-art[0]*arp[2],art[0]*arp[1]-art[1]*arp[0]);
  double norme= sqrt(n[0]*n[0]+n[1]*n[1]+n[2]*n[2]);
  n[0]=n[0]/norme;
  n[1]=n[1]/norme;
  n[2]=n[2]/norme;
  double E = art[0] * art[0]+ art[1] * art[1]+ art[2] * art[2];
  double F= art[0] * arp[0]+ art[1] * arp[1]+ art[2] * arp[2];
  double G = arp[0] * arp[0]+ arp[1] * arp[1]+ arp[2] * arp[2];
  double L = artt[0] * n[0]+ artt[1] * n[1]+ artt[2] * n[2];
  double M = artp[0] * n[0]+ artp[1] * n[1]+ artp[2] * n[2];
  double N = arpp[0] * n[0]+ arpp[1] * n[1]+ arpp[2] * n[2];
  double H = (E*N-2.0f*F*M+G*L)/(2.0f*(E*G-F*F));
    

  return H;
}

template<typename TSpace >

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

inlinevirtual

Parameters:

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

Returns:

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

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.

Parameters:

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

Returns:

the vector (gradient(f(x,y,z))) made unitary which is the unit normal to the shape boundary looking inside the shape.

Definition at line 119 of file StarShaped3D.ih.

{
  RealPoint aNormal( gradient(t));
  double norm = sqrt(aNormal[0]*aNormal[0] + aNormal[1]*aNormal[1] +aNormal[2]*aNormal[2]);
  return (RealPoint(aNormal[0]/norm,aNormal[1]/norm,aNormal[2]/norm));
}

template<typename TSpace>

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

private

Constructor. Forbidden by default (protected to avoid g++ warnings). Assignment.

Parameters:

other

the object to copy.

Returns:

a reference on 'this'. Forbidden by default.

template<typename TSpace >

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

inlinevirtual

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

Parameters:

p	input point

Returns:

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

Parameters:

p	any point in the plane.

Returns:

'true' if the point is inside the shape, 'false' if it is strictly outside.

Definition at line 87 of file StarShaped3D.ih.

References DGtal::INSIDE, DGtal::ON, and DGtal::OUTSIDE.

{


  AngularCoordinates t = parameter( p );
  RealPoint x_rel = x( t );
  x_rel -= center();
  double d_x = x_rel[0]*x_rel[0] + x_rel[1]*x_rel[1] + x_rel[2]*x_rel[2];
  RealPoint p_rel( p );
  p_rel -= center();
  double d_p = p_rel[0]*p_rel[0] + p_rel[1]*p_rel[1] + p_rel[2]*p_rel[2];
  
  
  if ((d_p - d_x) > 0.0)
    return OUTSIDE;
  else
    if ((d_p - d_x )< 0.0)
      return INSIDE;
    else
      return ON;
}

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 >.

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 >.

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 >.

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 >.

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 >.

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 >.

template<typename T >

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

inline

Writes/Displays the object on an output stream.

Parameters:

out	the output stream where the object is written.

Reimplemented in DGtal::Ball3D< TSpace >.

Definition at line 305 of file StarShaped3D.ih.

{
  out << "[StarShaped2D]";
}

template<typename TSpace >

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

inlinevirtual

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.

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 surfacelength between x(Teta1,Phi1) and x(Teta2,Phi2).

Returns:

the estimated surfacelength.

Definition at line 251 of file StarShaped3D.ih.

References M_PI.

{
  while ( t2.first < t1.first ) t2.first += 2.0*M_PI;
  while ( t2.second < t1.second ) t2.second += 2.0*M_PI;

  double step1 = ( t2.first - t1.first )  / nb;
  double step2 = ( t2.second - t1.second )  / nb;
  AngularCoordinates t( make_pair(0.0,0.0));
  double l = 0.0;
  for ( unsigned int i = 0; i < nb; ++i )
    {
      t.first = step1 *i;
      for ( unsigned int j = 0; j < nb; ++j )
        {

          t.second = step2 * j;
          RealPoint xtp (x( make_pair( t1.first + t.first - step1 ,t1.second + t.second - step2 ) ));
          RealPoint xt1p1( x( make_pair(t1.first + t.first,t1.second + t.second) ) ); 
          RealPoint xt1p( x( make_pair(t1.first + t.first,t1.second + t.second- step2 ) ) ); 
          double D = sqrt( ( xt1p[0] - xtp[0] )*( xt1p[0] - xtp[0] ) + 
                           ( xt1p[1] - xtp[1] )*( xt1p[1] - xtp[1] ) + 
                           ( xt1p[2] - xtp[2] )*( xt1p[2] - xtp[2] ));
          double d = sqrt( ( xt1p1[0] - xt1p[0] )*( xt1p1[0] - xt1p[0] ) + 
                           ( xt1p1[1] - xt1p[1] )*( xt1p1[1] - xt1p[1] ) + 
                           ( xt1p1[2] - xt1p[2] )*( xt1p1[2] - xt1p[2] ));


          l += (d*D);
        }
    }
  return l;
}

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 files:

• StarShaped3D.h
• StarShaped3D.ih