Estimates the parameters of a circle from a set of 2D points lying on the circle. More...

#include <FitCircle.hpp>

Inheritance diagram for TRTK::FitCircle< T >:

Collaboration diagram for TRTK::FitCircle< T >:

Public Types
typedef super::Vector2T	Vector2T
	2D column vector with value type T.
typedef super::Vector3T	Vector3T
	3D column vector with value type T.
typedef super::VectorXT	VectorXT
	Column vector of arbitrary size with value type T.
typedef super::MatrixXT	MatrixXT
	Matrix of arbitrary size with value type T.
typedef super::Matrix2T	Matrix2T
	2 x 2 matrix with value type T.
enum	Error { DATA_POINTS_TOO_SIMILAR, INFINITY_NOT_AVAILABLE, NAN_NOT_AVAILABLE, NOT_ENOUGH_POINTS, UNKNOWN_ERROR, WRONG_POINT_SIZE }
typedef Eigen::Array< T, Eigen::Dynamic, 1 >	ArrayXT
	General-purpose array of arbitrary size with value type T.
typedef Eigen::Matrix< T, 4, 1 >	Vector4T
	4D column vector with value type T.
typedef Eigen::Matrix< T, 3, 3 >	Matrix3T
	3 x 3 matrix with value type T.
Public Member Functions
	FitCircle ()
	Constructs an empty FitCircle object.
	FitCircle (const std::vector< Coordinate< T > > &points)
	Constructs a FitCircle object.
	FitCircle (const std::vector< Vector2T, Eigen::aligned_allocator< Vector2T > > &points)
	Constructs a FitCircle object.
	FitCircle (const std::vector< Vector3T > &points)
	Constructs a FitCircle object.
virtual	~FitCircle ()
	Destructs the FitCircle object.
void	compute ()
	Estimates the parameters of the circle.
unsigned	getNumberPointsRequired () const
	Returns the minimum number of data points required to compute a model.
const Coordinate< T > &	getCenterPoint () const
	Returns the center point of the plane.
T	getDistanceTo (const Coordinate< T > &point) const
	Returns the shortest distance from the circle to the given point.
T	getRadius () const
	Returns the radius of the circle.
T	getRMS () const
	Returns the root mean square error.
void	setPoints (const std::vector< Coordinate< T > > &)
	Sets the point set.
void	setPoints (const std::vector< Vector2T, Eigen::aligned_allocator< Vector2T > > &)
	Sets the point set.
void	setPoints (const std::vector< Vector3T > &)
	Sets the point set.
Public Attributes
EIGEN_MAKE_ALIGNED_OPERATOR_NEW typedef T	value_type
	Internally used value type (should be a floating point type).
Protected Attributes
MatrixXT	m_points

Detailed Description

template<class T>
class TRTK::FitCircle< T >

Estimates the parameters of a circle from a set of 2D points lying on the circle.

Template Parameters:

T	scalar type of the coordinates

This class allows estimating the center point and the radius of a circle from known points on the circle. The points may be erroneous since a least square fitting is done. If \( (x_i, y_i)^T \) are the data points, \( (x_0, y_0)^T \) the center point, and \( r \) the radius, then FitCircle tries to minimize the sum of the squared residuals as shown below:

\[ (x_0, y_0, r) := \arg\min_{(x_0, y_0, r)} \sum_{i=1}^N \left[(x_i - x_0)^2 + (y_i - y_0)^2 - r^2 \right]^2 \]

Here is a more elaborate example to see how to use the class:

 #include <cstdlib>
 #include <iostream>

 #include <TRTK/FitCircle.hpp>
 #include <TRTK/Tools.hpp>

 using namespace TRTK;

 int main()
 {
     double pi = 3.1415926535;

     std::vector<Coordinate<double> > circlePoints;

     // Construct some points lying on a circle.

     double radius = 7;
     Coordinate<double> centerPoint = Coordinate<double>(4, 2);

     for (double phi = 0.0; phi < 2.0 * pi; phi += pi/10)
     {
         using std::sin;
         using std::cos;
         using Tools::randn;

         double x = radius * cos(phi) + randn(0.0, 0.1);
         double y = radius * sin(phi) + randn(0.0, 0.1);

         Coordinate<double> point = centerPoint + Coordinate<double>(x, y);

         circlePoints.push_back(point);
     }

     // Estimate the circle parameters.

     FitCircle<double> fitCircle(circlePoints);

     fitCircle.compute();

     std::cout << "Center point: " << fitCircle.getCenterPoint() << std::endl;
     std::cout << "Radius: " << fitCircle.getRadius() << std::endl;

     return 0;
 }

Output:

 Center point: (4.03589, 1.97525)
 Radius: 7.03509

Author:: Fabian Killus, Christoph Haenisch

Version:: 0.2.0

Date:: last changed on 2012-03-20

Definition at line 118 of file FitCircle.hpp.

Member Enumeration Documentation

template<class T>

enum TRTK::Fit::Error [inherited]

Enumerator:

DATA_POINTS_TOO_SIMILAR	The data points are to similar.
INFINITY_NOT_AVAILABLE	The type T cannot represent infinity (see `std::numeric_limits<T>`).
NAN_NOT_AVAILABLE	The type T cannot represent NaN (see `std::numeric_limits<T>`).
NOT_ENOUGH_POINTS	More points are required to estimate the transformation.
UNKNOWN_ERROR	An unknown error occured.
WRONG_POINT_SIZE	One or more points have a wrong size.

Definition at line 69 of file Fit.hpp.

Constructor & Destructor Documentation

template<class T >

TRTK::FitCircle< T >::FitCircle ( )

Constructs an empty FitCircle object.

Template Parameters:

T	scalar type of the coordinates

Definition at line 164 of file FitCircle.hpp.

template<class T >

TRTK::FitCircle< T >::FitCircle ( const std::vector< Coordinate< T > > & points )

Constructs a FitCircle object.

Template Parameters:

T	scalar type of the coordinates

Parameters:

[in] points Points lying on the circle. The points can be 2D or 3D homogeneous coordinates.

Definition at line 180 of file FitCircle.hpp.

template<class T >

TRTK::FitCircle< T >::FitCircle ( const std::vector< Vector2T, Eigen::aligned_allocator< Vector2T > > & points )

Constructs a FitCircle object.

Template Parameters:

T	scalar type of the coordinates

Parameters:

[in] points Points lying on the circle.

Definition at line 196 of file FitCircle.hpp.

template<class T >

TRTK::FitCircle< T >::FitCircle ( const std::vector< Vector3T > & points )

Constructs a FitCircle object.

Template Parameters:

T	scalar type of the coordinates

Parameters:

[in] points Points lying on the circle. The points are assumed to be homogeneous coordinates, whose third coordinate entry is equal to one.

Definition at line 214 of file FitCircle.hpp.

template<class T >

TRTK::FitCircle< T >::~FitCircle ( ) [virtual]

Destructs the FitCircle object.

Template Parameters:

T	scalar type of the coordinates

Definition at line 228 of file FitCircle.hpp.

Member Function Documentation

template<class T >

void TRTK::FitCircle< T >::compute ( ) [virtual]

Estimates the parameters of the circle.

Template Parameters:

T	scalar type of the coordinates

There must be at least 3 points to perform the fitting.

Exceptions:

ErrorObj If there are not enough points to fit the circle, an error object is thrown and its error code is set to WRONG_POINT_SIZE.

See also:: setPoints(), getCenterPoint() and getRadius()

Implements TRTK::Fit2D< T >.

Definition at line 247 of file FitCircle.hpp.

template<class T >

const Coordinate< T > & TRTK::FitCircle< T >::getCenterPoint ( ) const

Returns the center point of the plane.

Template Parameters:

T	scalar type of the coordinates

Definition at line 350 of file FitCircle.hpp.

template<class T >

T TRTK::FitCircle< T >::getDistanceTo ( const Coordinate< T > & point ) const [virtual]

Returns the shortest distance from the circle to the given point.

Template Parameters:

T	scalar type of the coordinates

Parameters:

[in] point A 2D coordinate.

Implements TRTK::Fit2D< T >.

Definition at line 364 of file FitCircle.hpp.

template<class T >

T TRTK::FitCircle< T >::getRadius ( ) const

Returns the radius of the circle.

Template Parameters:

T	scalar type of the coordinates

Definition at line 414 of file FitCircle.hpp.

template<class T >

T TRTK::FitCircle< T >::getRMS ( ) const [virtual]

Returns the root mean square error.

Template Parameters:

T	scalar type of the coordinates

Implements TRTK::Fit2D< T >.

Definition at line 386 of file FitCircle.hpp.

template<class T >

void TRTK::Fit2D< T >::setPoints ( const std::vector< Vector2T, Eigen::aligned_allocator< Vector2T > > & points ) [inherited]

Sets the point set.

Template Parameters:

T	scalar type of the coordinates

Parameters:

[in] points 2D coordinates.

Definition at line 163 of file Fit2D.hpp.

template<class T >

void TRTK::Fit2D< T >::setPoints ( const std::vector< Coordinate< T > > & points ) [virtual, inherited]

Sets the point set.

Template Parameters:

T	scalar type of the coordinates

Parameters:

[in] points The points can either be plain 2D or 3D homogeneous coordinates.

Exceptions:

ErrorObj If there are any coordinates other than 2D or 3D coordinates, an error object is thrown and its error code is set to WRONG_POINT_SIZE.

Implements TRTK::Fit< T >.

Definition at line 130 of file Fit2D.hpp.

template<class T >

void TRTK::Fit2D< T >::setPoints ( const std::vector< Vector3T > & points ) [inherited]

Sets the point set.

Template Parameters:

T	scalar type of the coordinates

Parameters:

[in] points 3D homogeneous coordinates.

Definition at line 182 of file Fit2D.hpp.

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

D:/Programmierung/C/TRTK/include/TRTK/FitCircle.hpp

TRTK::FitCircle< T > Class Template Reference

Public Types

Public Member Functions

Public Attributes

Protected Attributes

Detailed Description

template<class T> class TRTK::FitCircle< T >

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

template<class T>
class TRTK::FitCircle< T >