#include <FrechetShortcut.h>

Inheritance diagram for DGtal::FrechetShortcut< TIterator, TInteger >:

Collaboration diagram for DGtal::FrechetShortcut< TIterator, TInteger >:

Data Structures
class	Backpath
class	Cone
struct	Tools

Public Types
typedef TInteger	Integer
typedef TIterator	ConstIterator
typedef FrechetShortcut < ConstIterator, Integer >	Self
typedef FrechetShortcut < std::reverse_iterator < ConstIterator >, Integer >	Reverse
typedef IteratorCirculatorTraits < ConstIterator >::Value	Point
typedef IteratorCirculatorTraits < ConstIterator >::Value	Vector
typedef Vector::Coordinate	Coordinate

Public Member Functions
	BOOST_CONCEPT_ASSERT ((CInteger< TInteger >))
	FrechetShortcut ()
	FrechetShortcut (double error)
void	init (const ConstIterator &it)
FrechetShortcut	getSelf ()
	FrechetShortcut (const Self &other)
FrechetShortcut &	operator= (const Self &other)
Reverse	getReverse () const
bool	operator== (const Self &other) const
bool	operator!= (const Self &other) const
	~FrechetShortcut ()
bool	isExtendableForward ()
bool	extendForward ()
ConstIterator	begin () const
ConstIterator	end () const
std::string	className () const
bool	isValid () const
bool	updateBackpath ()
bool	testUpdateBackpath ()
bool	isBackpathOk ()
void	resetBackpath ()
void	resetCone ()
bool	testUpdateWidth ()
Cone	computeNewCone ()
bool	updateWidth ()
void	selfDisplay (std::ostream &out) const

Protected Attributes
double	myError
std::vector< Backpath >	myBackpath
Cone	myCone
ConstIterator	myBegin
ConstIterator	myEnd

Detailed Description

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>
class DGtal::FrechetShortcut< TIterator, TInteger >

Aim: On-line computation Computation of the longest shortcut according to the Fréchet distance for a given error. See related article: Sivignon, I., (2011). A Near-Linear Time Guaranteed Algorithm for Digital Curve Simplification under the Fréchet Distance. DGCI 2011. Retrieved from http://link.springer.com/chapter/10.1007/978-3-642-19867-0_28.

Description of class 'FrechetShortcut' <p>

The algorithm we propose uses an approximation of the Fréchet distance, but a guarantee over the quality of the simplification is proved. Moreover, even if the theoretical complexity of the algorithm is in $ O(n log(n)) $, experiments show a linear behaviour in practice.

We denote by $ error(i,j) $ the Fréchet distance between the segment $[p_ip_j]$ and the part of the curve between the points $p_i$ and $p_j$. The approximation of the Fréchet distance is based on the fact that $ error(i,j) $ can be upper and lower bounded by a function of two values, namely $ w(i,j)$ $ and $ b(i,j) $, where $ w(i,j)$ $ is the width of the points between $p_i$ and $p_j$ in the direction $ p_ip_j $ and $ b(i,j) $ is the length of the longest backpath in this direction.

Then, the algorithm consists in greedily reading the points of the curves from a first point given by myBegin, while updating the values $ w(i,j) $ and $ b(i,j) $ on the fly.

This class is a model of the concept CForwardSegmentComputer

It should be used with the Curve object (defined in StdDefs.h) and

*its PointsRange as follows:

  Curve::PointsRange r = c.getPointsRange(); 
  
  typedef FrechetShortcut<Curve::PointsRange::ConstIterator,int> Shortcut;
  
  // Computation of one shortcut
  Shortcut s(error);
  
  s.init( r.begin() );
  while ( ( s.end() != r.end() )
          &&( s.extendForward() ) ) {}
  
  // Computation of a greedy segmentation
  
  typedef GreedySegmentation<Shortcut> Segmentation;
  
  Segmentation theSegmentation( r.begin(), r.end(), Shortcut(error) );
  
  // the segmentation is computed here
  Segmentation::SegmentComputerIterator it = theSegmentation.begin();
  Segmentation::SegmentComputerIterator itEnd = theSegmentation.end();
  for ( ; it != itEnd; ++it) {
    s=Shortcut(*it);
    trace.info() << s << std::endl;
    board << s; 
  }
  
  board.saveEPS("FrechetShortcutExample.eps", Board2D::BoundingBox, 5000 ); 

Template Parameters:

TIterator Iterator type on 2D digital points, TInteger type *of integer

See also:: exampleFrechetShortcut.cpp testFrechetShortcut.cpp

Definition at line 107 of file FrechetShortcut.h.

Member Typedef Documentation

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

typedef TIterator DGtal::FrechetShortcut< TIterator, TInteger >::ConstIterator

Definition at line 120 of file FrechetShortcut.h.

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

typedef Vector::Coordinate DGtal::FrechetShortcut< TIterator, TInteger >::Coordinate

Definition at line 127 of file FrechetShortcut.h.

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

typedef TInteger DGtal::FrechetShortcut< TIterator, TInteger >::Integer

Definition at line 115 of file FrechetShortcut.h.

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

typedef IteratorCirculatorTraits<ConstIterator>::Value DGtal::FrechetShortcut< TIterator, TInteger >::Point

Definition at line 125 of file FrechetShortcut.h.

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

typedef FrechetShortcut<std::reverse_iterator<ConstIterator>,Integer> DGtal::FrechetShortcut< TIterator, TInteger >::Reverse

Definition at line 122 of file FrechetShortcut.h.

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

typedef FrechetShortcut<ConstIterator,Integer> DGtal::FrechetShortcut< TIterator, TInteger >::Self

Definition at line 121 of file FrechetShortcut.h.

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

typedef IteratorCirculatorTraits<ConstIterator>::Value DGtal::FrechetShortcut< TIterator, TInteger >::Vector

Definition at line 126 of file FrechetShortcut.h.

Constructor & Destructor Documentation

template<typename TIterator , typename TInteger >

DGtal::FrechetShortcut< TIterator, TInteger >::FrechetShortcut ( )

inline

Default constructor. not valid

FrechetShortcut class

Definition at line 534 of file FrechetShortcut.ih.

References DGtal::FrechetShortcut< TIterator, TInteger >::myBackpath, DGtal::FrechetShortcut< TIterator, TInteger >::myCone, and DGtal::FrechetShortcut< TIterator, TInteger >::myError.

Referenced by DGtal::FrechetShortcut< TIterator, TInteger >::getSelf().

{
  myError = 0;
  myCone = Cone();
  
  for(int i=0;i<8;i++)
    {
      //backpath b(i,0);
      Backpath b(this,i);
      myBackpath.push_back(b);
    }
}

template<typename TIterator , typename TInteger >

DGtal::FrechetShortcut< TIterator, TInteger >::FrechetShortcut ( double error )

inline

Constructor with initialisation

Parameters:

it	an iterator on 2D points

Definition at line 551 of file FrechetShortcut.ih.

References DGtal::FrechetShortcut< TIterator, TInteger >::myBackpath, DGtal::FrechetShortcut< TIterator, TInteger >::myCone, and DGtal::FrechetShortcut< TIterator, TInteger >::myError.

{
  myError = error;
  myCone = Cone();
  
  for(int i=0;i<8;i++)
    {
      //backpath  b(i,error);
       Backpath b(this,i);
       myBackpath.push_back(b);
    }
}

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

DGtal::FrechetShortcut< TIterator, TInteger >::FrechetShortcut ( const Self & other )

Copy constructor.

Parameters:

other the object to clone.

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

DGtal::FrechetShortcut< TIterator, TInteger >::~FrechetShortcut ( )

inline

Destructor.

Definition at line 743 of file FrechetShortcut.h.

{};

Member Function Documentation

template<typename TIterator , typename TInteger >

TIterator DGtal::FrechetShortcut< TIterator, TInteger >::begin ( ) const

inline

Returns:: begin iterator of the FrechetShortcut range.

Definition at line 866 of file FrechetShortcut.ih.

Referenced by DGtal::Display2DFactory::draw().

                                                      {
  return myBegin;
}

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

DGtal::FrechetShortcut< TIterator, TInteger >::BOOST_CONCEPT_ASSERT ( (CInteger< TInteger >) )

template<typename TIterator , typename TInteger >

std::string DGtal::FrechetShortcut< TIterator, TInteger >::className ( ) const

inline

Returns:: the name of the class.

Definition at line 883 of file FrechetShortcut.ih.

{
  return "FrechetShortcut";
}

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

FrechetShortcut< TIterator, TInteger >::Cone FrechetShortcut::computeNewCone ( )

inline

Computes the cone defined by the point *myBegin and the new point *myEnd + 1 and intersect it with myCone (unchanged)

Returns:: the new cone

Definition at line 665 of file FrechetShortcut.ih.

References DGtal::FrechetShortcut< TIterator, TInteger >::Cone::intersectCones(), M_PI, and M_PI_2.

{
  double x0, y0,x1,y1;
  Point firstP = Point(*myBegin);
  Point newP = Point(*(myEnd+1));
  
  Cone newCone=myCone;
  
  // compute the tangent points defined by the first point and the
  // circle C(newP,error)
  bool intersect = Tools::circleTangentPoints(firstP[0],firstP[1], newP[0], newP[1], myError/(sqrt(2.0F)), &x0, &y0,
                                       &x1, &y1);
  
  if(intersect)
    {
      // define a cone according to the new tangent points
      Cone c;
      // case where there is one single tangent point
      if(fabs(x0-x1) < 0.00001 && fabs(y0-y1) < 0.00001)
        {
          double angle = Tools::computeAngle(firstP[0],firstP[1],newP[0],newP[1]);
          assert(angle != -1);
          double angle0 = angle - M_PI_2;
          if(angle0<0)
            angle0 = angle0+2*M_PI;
          double angle1 = angle + M_PI_2;
          if(angle1>2*M_PI)
            angle1 = angle1-2*M_PI;
          c = Cone(angle0,angle1);
        }
      else
        c = Cone(firstP[0],firstP[1],x0,y0,x1,y1);
      
      newCone.intersectCones(c); 
    }
  
  return newCone;
}

template<typename TIterator , typename TInteger >

TIterator DGtal::FrechetShortcut< TIterator, TInteger >::end ( ) const

inline

Returns:: end iterator of the FrechetShortcut range.

Definition at line 873 of file FrechetShortcut.ih.

Referenced by DGtal::Display2DFactory::draw().

                                                    {
  ConstIterator i(myEnd); ++i;
  return i;
}

template<typename TIterator , typename TInteger >

bool DGtal::FrechetShortcut< TIterator, TInteger >::extendForward ( )

inline

Tests whether the FrechetShortcut can be extended at the front. Extend the FrechetShortcut if yes.

Returns:: 'true' if yes, 'false' otherwise.

Definition at line 642 of file FrechetShortcut.ih.

{
  bool flag = (updateWidth() && updateBackpath());
  
  if(flag)
    ++myEnd;
  
  return flag;
}

template<typename TIterator , typename TInteger >

DGtal::FrechetShortcut< std::reverse_iterator< TIterator >, TInteger > DGtal::FrechetShortcut< TIterator, TInteger >::getReverse ( ) const

inline

Returns:: a reverse version of '*this'.

Definition at line 615 of file FrechetShortcut.ih.

{
  return Reverse(myError);
}

template<typename TIterator , typename TInteger >

DGtal::FrechetShortcut< TIterator, TInteger > DGtal::FrechetShortcut< TIterator, TInteger >::getSelf ( )

inline

Definition at line 580 of file FrechetShortcut.ih.

References DGtal::FrechetShortcut< TIterator, TInteger >::FrechetShortcut(), and DGtal::FrechetShortcut< TIterator, TInteger >::myError.

{
  FrechetShortcut<TIterator,TInteger> other = FrechetShortcut(myError);
  return other;
}

template<typename TIterator , typename TInteger >

void DGtal::FrechetShortcut< TIterator, TInteger >::init ( const ConstIterator & it )

inline

Initialisation.

Parameters:

it	an iterator on 2D points

Definition at line 569 of file FrechetShortcut.ih.

References DGtal::FrechetShortcut< TIterator, TInteger >::myBegin, DGtal::FrechetShortcut< TIterator, TInteger >::myEnd, DGtal::FrechetShortcut< TIterator, TInteger >::resetBackpath(), and DGtal::FrechetShortcut< TIterator, TInteger >::resetCone().

{
  myBegin = it;
  myEnd = it;
  resetCone();
  resetBackpath();
}

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

bool FrechetShortcut::isBackpathOk ( )

inline

Test if there exist a backpath of length greater than the threshold

Definition at line 808 of file FrechetShortcut.ih.

{
  // compute the quadrant of the direction of P(i,j)
  
  Point firstP = Point(*myBegin);
  Point P = Point(*(myEnd+1));
  
  int q = Tools::computeQuadrant(firstP,P);
  
  
  // to handle non simple curves (a point is visited twice)
  if(firstP==P)
    return true;
  
  // compute the direction vector pipj
  Point v;
  v[0] = P[0]-firstP[0];
  v[1] = P[1]-firstP[1];
  
  // compute the angle between the direction vector and the elementary
  // direction (defined by the quadrant)
  Point dir_elem = Tools::chainCode2Vect(q);
  
  double angle = Tools::angleVectVect(v,dir_elem);
  
   boost::icl::interval_set<double> intervals = myBackpath[q].myForbiddenIntervals;
  if(contains(intervals,angle))
    return false;
  
  return true;
  
}

template<typename TIterator , typename TInteger >

bool DGtal::FrechetShortcut< TIterator, TInteger >::isExtendableForward ( )

inline

Tests whether the FrechetShortcut can be extended at the front.

Returns:: 'true' if yes, 'false' otherwise.

Definition at line 656 of file FrechetShortcut.ih.

{
  
  return (testUpdateWidth() && testUpdateBackpath());
  
}

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

bool DGtal::FrechetShortcut< TIterator, TInteger >::isValid ( ) const

Checks the validity/consistency of the object.

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

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

bool DGtal::FrechetShortcut< TIterator, TInteger >::operator!= ( const Self & other ) const

inline

Difference operator.

Parameters:

other the object to compare with.

Returns:: 'false' if equal 'true' otherwise

Definition at line 633 of file FrechetShortcut.ih.

                                                                                                                    {
  return (!(*this == other));
}

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

DGtal::FrechetShortcut< TIterator, TInteger > & DGtal::FrechetShortcut< TIterator, TInteger >::operator= ( const Self & other )

inline

Assignment.

Parameters:

other the object to copy.

Returns:: a reference on 'this'.

Definition at line 597 of file FrechetShortcut.ih.

References DGtal::FrechetShortcut< TIterator, TInteger >::myBackpath, DGtal::FrechetShortcut< TIterator, TInteger >::myBegin, DGtal::FrechetShortcut< TIterator, TInteger >::myCone, DGtal::FrechetShortcut< TIterator, TInteger >::myEnd, and DGtal::FrechetShortcut< TIterator, TInteger >::myError.

{
  
  if(this != &other)
    {
      myError = other.myError;
      myBackpath = other.myBackpath;
      myCone = other.myCone;
      myBegin = other.myBegin;
      myEnd = other.myEnd;
    }
  return *this;
}

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

bool DGtal::FrechetShortcut< TIterator, TInteger >::operator== ( const Self & other ) const

inline

Equality operator.

Parameters:

other the object to compare with.

Returns:: 'true' if the objects are equal, false otherwise

Definition at line 623 of file FrechetShortcut.ih.

References DGtal::FrechetShortcut< TIterator, TInteger >::myBegin, DGtal::FrechetShortcut< TIterator, TInteger >::myEnd, and DGtal::FrechetShortcut< TIterator, TInteger >::myError.

                                                              {
   return ((myBegin == other.myBegin) && (myEnd == other.myEnd) && (myError == other.myError));
}

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

void FrechetShortcut::resetBackpath ( )

inline

Reset the backpaths before the computation of a new shortcut

Definition at line 845 of file FrechetShortcut.ih.

Referenced by DGtal::FrechetShortcut< TIterator, TInteger >::init().

{
  for(unsigned int i=0;i<8;i++)
    {
      myBackpath[i].reset();
    }
}

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

void FrechetShortcut::resetCone ( )

inline

Reset the cone before the computation of a new shortcut

Definition at line 855 of file FrechetShortcut.ih.

Referenced by DGtal::FrechetShortcut< TIterator, TInteger >::init().

{
  myCone.myMin = 0;
  myCone.myMax = 0;
  myCone.myInf = true;  
}

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

void FrechetShortcut::selfDisplay ( std::ostream & out ) const

inline

Writes/Displays the object on an output stream.

Parameters:

out	the output stream where the object is written.

Definition at line 898 of file FrechetShortcut.ih.

{
  
  out << "[FrechetShortcut]" <<  endl;
  out << "(Begin, End)=";
  out << "("<< Point(*myBegin) << ", " << Point(*myEnd) << ")\n";
  out << "[End FrechetShortcut]" <<  endl;
  
}

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

bool FrechetShortcut::testUpdateBackpath ( )

inline

Test if there exist a backpath of length greater than the threshold after the addition of the point pointed by *myEnd+1, but does not modify myBackpath.

Definition at line 735 of file FrechetShortcut.ih.

{
  // Save the current value of the backpath
  vector <typename FrechetShortcut<TIterator,TInteger>::Backpath> BackpathSave;
  for(unsigned int i=0;i<8;i++)
    {
      Backpath b(myBackpath[i]);
      BackpathSave.push_back(b);
    }
  // Check whether the next point could be added or not with respect to the backpath 
  bool flag = updateBackpath();
  
  // Copy back the values of backpath before the test.
  for(unsigned int i=0;i<8;i++)
    myBackpath[i] = Backpath(BackpathSave[i]);
  return flag;
}

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

bool FrechetShortcut::testUpdateWidth ( )

inline

Test if the new direction belongs to the new cone, but does not modify myCone

Definition at line 711 of file FrechetShortcut.ih.

References DGtal::FrechetShortcut< TIterator, TInteger >::Cone::isEmpty(), M_PI, DGtal::FrechetShortcut< TIterator, TInteger >::Cone::myInf, DGtal::FrechetShortcut< TIterator, TInteger >::Cone::myMax, and DGtal::FrechetShortcut< TIterator, TInteger >::Cone::myMin.

{
  Cone c = computeNewCone();
  
  Point firstP = Point(*myBegin);
  Point newP = Point(*(myEnd+1));
  if(!(c.isEmpty()))
    if(c.myInf)
      return true;
    else
      {
        double angle = Tools::computeAngle(firstP[0], firstP[1], newP[0], newP[1]);
        assert(angle != -1);
        return Tools::isBetween(angle,c.myMin,c.myMax,2*M_PI);
      }
  else
    return false;
  
}

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

bool FrechetShortcut::updateBackpath ( )

inline

Updates the backpaths (one per octant) according to the new point

Returns:: 'true' if the length of the longest backpath is lower than the threshold, false otherwise

Definition at line 791 of file FrechetShortcut.ih.

{
  Point prevP = Point(*myEnd);
  Point P = Point(*(myEnd+1));
  
  int d = Tools::computeChainCode(prevP,P);
  
  for(unsigned int j=0;j<8;j++)
    myBackpath[j].updateBackPathFirstQuad(Tools::rot(d,j),myEnd+1);
      
  
  return isBackpathOk();
  
}

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

bool FrechetShortcut::updateWidth ( )

inline

Updates the width according to the new point

Returns:: true if the width is lower than the error, false otherwise

Definition at line 761 of file FrechetShortcut.ih.

References DGtal::FrechetShortcut< TIterator, TInteger >::Cone::isEmpty(), M_PI, DGtal::FrechetShortcut< TIterator, TInteger >::Cone::myInf, DGtal::FrechetShortcut< TIterator, TInteger >::Cone::myMax, and DGtal::FrechetShortcut< TIterator, TInteger >::Cone::myMin.

{
  Cone c = computeNewCone();
  
  myCone = c;
  
  Point firstP = Point(*myBegin);
  Point newP = Point(*(myEnd+1));
  bool flag = true;
  
  if(!(c.isEmpty()))
    if(c.myInf)
      flag = true;
    else
      {
        double angle = Tools::computeAngle
(firstP[0], firstP[1], newP[0],
                                                 newP[1]);
        assert(angle != -1);
        flag = Tools::isBetween(angle,c.myMin,c.myMax,2*M_PI);
      }
  else
    flag = false;
  
  return flag;
}

Field Documentation

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

std::vector<Backpath> DGtal::FrechetShortcut< TIterator, TInteger >::myBackpath

protected

Vector of 8 backpaths, one per octant. Stores all the information needed to update the length of the longest backpath.

Definition at line 805 of file FrechetShortcut.h.

Referenced by DGtal::FrechetShortcut< TIterator, TInteger >::FrechetShortcut(), and DGtal::FrechetShortcut< TIterator, TInteger >::operator=().

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

ConstIterator DGtal::FrechetShortcut< TIterator, TInteger >::myBegin

protected

ConstIterator pointing to the back of the shortcut

Definition at line 815 of file FrechetShortcut.h.

Referenced by DGtal::FrechetShortcut< TIterator, TInteger >::init(), DGtal::FrechetShortcut< TIterator, TInteger >::operator=(), and DGtal::FrechetShortcut< TIterator, TInteger >::operator==().

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

Cone DGtal::FrechetShortcut< TIterator, TInteger >::myCone

protected

Cone used to update the width

Definition at line 810 of file FrechetShortcut.h.

Referenced by DGtal::FrechetShortcut< TIterator, TInteger >::FrechetShortcut(), and DGtal::FrechetShortcut< TIterator, TInteger >::operator=().

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

ConstIterator DGtal::FrechetShortcut< TIterator, TInteger >::myEnd

protected

ConstIterator pointing to the front of the shortcut

Definition at line 819 of file FrechetShortcut.h.

Referenced by DGtal::FrechetShortcut< TIterator, TInteger >::init(), DGtal::FrechetShortcut< TIterator, TInteger >::operator=(), and DGtal::FrechetShortcut< TIterator, TInteger >::operator==().

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>

double DGtal::FrechetShortcut< TIterator, TInteger >::myError

protected

Error parameter used to compute the shortcut

Definition at line 799 of file FrechetShortcut.h.

Referenced by DGtal::FrechetShortcut< TIterator, TInteger >::FrechetShortcut(), DGtal::FrechetShortcut< TIterator, TInteger >::getSelf(), DGtal::FrechetShortcut< TIterator, TInteger >::operator=(), and DGtal::FrechetShortcut< TIterator, TInteger >::operator==().

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

Data Structures

Public Types

Public Member Functions

Protected Attributes

Detailed Description

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate> class DGtal::FrechetShortcut< TIterator, TInteger >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Field Documentation

template<typename TIterator, typename TInteger = typename IteratorCirculatorTraits<TIterator>::Value::Coordinate>
class DGtal::FrechetShortcut< TIterator, TInteger >