lsst::afw::geom::AffineTransform Class Reference

An affine coordinate transformation consisting of a linear transformation and an offset. More...

#include <AffineTransform.h>

Public Types
enum	Parameters {   XX =0, YX =1, XY =2, YY =3,   X =4, Y =5 }
typedef boost::shared_ptr < AffineTransform >	Ptr
typedef boost::shared_ptr < AffineTransform const >	ConstPtr
typedef Eigen::Matrix3d	Matrix
typedef Eigen::Matrix< double, 6, 1 >	ParameterVector
typedef Eigen::Matrix< double, 2, 6 >	TransformDerivativeMatrix

Public Member Functions
	AffineTransform ()
	AffineTransform (Eigen::Matrix3d const &matrix)
	AffineTransform (Eigen::Matrix2d const &linear)
	AffineTransform (Eigen::Vector2d const &translation)
	AffineTransform (Eigen::Matrix2d const &linear, Eigen::Vector2d const &translation)
	AffineTransform (LinearTransform const &linear)
	AffineTransform (Extent2D const &translation)
	AffineTransform (LinearTransform const &linear, Extent2D const &translation)
AffineTransform const	invert () const
bool	isIdentity () const
Point2D	operator() (Point2D const &p) const
Extent2D	operator() (Extent2D const &p) const
Extent2D const &	getTranslation () const
Extent2D &	getTranslation ()
LinearTransform const &	getLinear () const
LinearTransform &	getLinear ()
Matrix const	getMatrix () const
ParameterVector const	getParameterVector () const
void	setParameterVector (ParameterVector const &vector)
double &	operator[] (int i)
double	operator[] (int i) const
AffineTransform	operator* (AffineTransform const &other) const
AffineTransform &	operator= (AffineTransform const &other)
TransformDerivativeMatrix	dTransform (Point2D const &input) const
TransformDerivativeMatrix	dTransform (Extent2D const &input) const

Static Public Member Functions
static AffineTransform	makeScaling (double s)
	Construct a new AffineTransform that represents a uniform scaling. More...
static AffineTransform	makeScaling (double s, double t)
	Construct a new AffineTransform that represents a non-uniform scaling. More...
static AffineTransform	makeRotation (Angle t)
	Construct a new AffineTransform that represents a CCW rotation in radians. More...
static AffineTransform	makeTranslation (Extent2D translation)
	Construct a new AffineTransform that represents a pure translation. More...

Private Attributes
LinearTransform	_linear
Extent2D	_translation

Detailed Description

An affine coordinate transformation consisting of a linear transformation and an offset.

The transform is represented by a matrix \( \mathbf{M} \) such that

\[ \left[\begin{array}{ c } x_f \\ y_f \\ 1 \end{array}\right] = \mathbf{M} \left[\begin{array}{ c } x_i \\ y_i \\ 1 \end{array}\right] \]

where \((x_i,y_i)\) are the input coordinates and \((x_f,y_f)\) are the output coordinates.

If \( x_f(x_i,y_i) \) and \( y_f(x_i,y_i) \) are continuous differentiable functions, then

\[ \mathbf{M} = \left[\begin{array}{ c c c } \displaystyle\frac{\partial x_f}{\partial x_i} & \displaystyle\frac{\partial x_f}{\partial y_i} & x_f \\ \displaystyle\frac{\partial y_f}{\partial x_i} & \displaystyle\frac{\partial y_f}{\partial y_i} & y_f \\ \displaystyle 0 & \displaystyle 0 & \displaystyle 1 \end{array}\right] \]

evaluated at \((x_i,y_i)\).

The 2x2 upper left corner of \( \mathbf{M} \) is the linear part of the transform is simply the Jacobian of the mapping between \((x_i,y_i)\) and \((x_f,y_f)\).

Definition at line 77 of file AffineTransform.h.

Member Typedef Documentation

typedef boost::shared_ptr<AffineTransform const> lsst::afw::geom::AffineTransform::ConstPtr

Definition at line 80 of file AffineTransform.h.

typedef Eigen::Matrix3d lsst::afw::geom::AffineTransform::Matrix

Definition at line 84 of file AffineTransform.h.

typedef Eigen::Matrix<double,6,1> lsst::afw::geom::AffineTransform::ParameterVector

Definition at line 85 of file AffineTransform.h.

typedef boost::shared_ptr<AffineTransform> lsst::afw::geom::AffineTransform::Ptr

Definition at line 79 of file AffineTransform.h.

typedef Eigen::Matrix<double,2,6> lsst::afw::geom::AffineTransform::TransformDerivativeMatrix

Definition at line 86 of file AffineTransform.h.

Member Enumeration Documentation

enum lsst::afw::geom::AffineTransform::Parameters

Enumerator
XX
YX
XY
YY
X
Y

Definition at line 82 of file AffineTransform.h.

{XX=0,YX=1,XY=2,YY=3,X=4,Y=5};

Constructor & Destructor Documentation

lsst::afw::geom::AffineTransform::AffineTransform ( )

inline

Construct an empty (identity) AffineTransform.

Definition at line 90 of file AffineTransform.h.

: _linear(), _translation() {}

lsst::afw::geom::AffineTransform::AffineTransform ( Eigen::Matrix3d const &  matrix )

inlineexplicit

Construct an AffineTransform from a 3x3 matrix.

Definition at line 93 of file AffineTransform.h.

      : _linear(matrix.block<2,2>(0,0)), 
        _translation(matrix.block<2,1>(0,2)) 
    {}

lsst::afw::geom::AffineTransform::AffineTransform ( Eigen::Matrix2d const &  linear )

inlineexplicit

Construct an AffineTransform with no translation from a 2x2 matrix.

Definition at line 99 of file AffineTransform.h.

      : _linear(linear), _translation() {}

lsst::afw::geom::AffineTransform::AffineTransform ( Eigen::Vector2d const &  translation )

inlineexplicit

Construct a translation-only AffineTransform from a vector.

Definition at line 103 of file AffineTransform.h.

      : _linear(), _translation(translation) {}

lsst::afw::geom::AffineTransform::AffineTransform ( Eigen::Matrix2d const &  linear, Eigen::Vector2d const &  translation  )

inlineexplicit

Construct an AffineTransform from a 2x2 matrix and vector.

Definition at line 107 of file AffineTransform.h.

      : _linear(linear), _translation(translation) {}

lsst::afw::geom::AffineTransform::AffineTransform ( LinearTransform const &  linear )

inlineexplicit

Construct an AffineTransform from a LinearTransform.

Definition at line 112 of file AffineTransform.h.

      : _linear(linear), _translation() {}

lsst::afw::geom::AffineTransform::AffineTransform ( Extent2D const &  translation )

inlineexplicit

Construct a translation-only AffineTransform from an Extent2D.

Definition at line 116 of file AffineTransform.h.

      : _linear(), _translation(translation) {}

lsst::afw::geom::AffineTransform::AffineTransform ( LinearTransform const &  linear, Extent2D const &  translation  )

inlineexplicit

Construct an AffineTransform from a LinearTransform and Extent2D.

Definition at line 120 of file AffineTransform.h.

      : _linear(linear), _translation(translation) {}

Member Function Documentation

TransformDerivativeMatrix lsst::afw::geom::AffineTransform::dTransform

(

Point2D const &

input

)

const

TransformDerivativeMatrix lsst::afw::geom::AffineTransform::dTransform

(

Extent2D const &

input

)

const

LinearTransform const& lsst::afw::geom::AffineTransform::getLinear ( ) const

inline

Definition at line 152 of file AffineTransform.h.

{return _linear;}

LinearTransform& lsst::afw::geom::AffineTransform::getLinear ( )

inline

Definition at line 153 of file AffineTransform.h.

{return _linear;}

Matrix const lsst::afw::geom::AffineTransform::getMatrix

(

)

const

ParameterVector const lsst::afw::geom::AffineTransform::getParameterVector

(

)

const

Extent2D const& lsst::afw::geom::AffineTransform::getTranslation ( ) const

inline

Definition at line 149 of file AffineTransform.h.

{return _translation;}

Extent2D& lsst::afw::geom::AffineTransform::getTranslation ( )

inline

Definition at line 150 of file AffineTransform.h.

{return _translation;}

AffineTransform const lsst::afw::geom::AffineTransform::invert

(

)

const

bool lsst::afw::geom::AffineTransform::isIdentity ( ) const

inline

Whether the transform is a no-op.

Definition at line 128 of file AffineTransform.h.

{ return getMatrix().isIdentity(); }

static AffineTransform lsst::afw::geom::AffineTransform::makeRotation ( Angle  t )

inlinestatic

Construct a new AffineTransform that represents a CCW rotation in radians.

Returns

An AffineTransform with matrix \( \left[\begin{array}{ c c c } \cos t & -\sin t & 0 \\ \sin t & \cos t & 0 \\ 0 & 0 & 1 \\ \end{array}\right] \)

Definition at line 227 of file AffineTransform.h.

                                                 {
        return AffineTransform(LinearTransform::makeRotation(t));
    }

static AffineTransform lsst::afw::geom::AffineTransform::makeScaling ( double  s )

inlinestatic

Construct a new AffineTransform that represents a uniform scaling.

Returns

An AffineTransform with matrix \( \left[\begin{array}{ c c c } s & 0 & 0 \\ 0 & s & 0 \\ 0 & 0 & 1 \\ \end{array}\right] \)

Definition at line 195 of file AffineTransform.h.

                                                 { 
        return AffineTransform(LinearTransform::makeScaling(s));
    }

static AffineTransform lsst::afw::geom::AffineTransform::makeScaling ( double  s, double  t  )

inlinestatic

Construct a new AffineTransform that represents a non-uniform scaling.

Returns

An AffineTransform with matrix \( \left[\begin{array}{ c c c } s & 0 & 0 \\ 0 & t & 0 \\ 0 & 0 & 1 \\ \end{array}\right] \)

Definition at line 212 of file AffineTransform.h.

                                                           { 
        return AffineTransform(LinearTransform::makeScaling(s, t));
    }

static AffineTransform lsst::afw::geom::AffineTransform::makeTranslation ( Extent2D  translation )

inlinestatic

Construct a new AffineTransform that represents a pure translation.

Returns

An AffineTransform with matrix \( \left[\begin{array}{ c c c } 0 & 0 & translation.getX() \\ 0 & 0 & translation.getY() \\ 0 & 0 & 1 \\ \end{array}\right] \)

Definition at line 243 of file AffineTransform.h.

                                                                 { 
        return AffineTransform(translation);
    }

Point2D lsst::afw::geom::AffineTransform::operator() ( Point2D const &  p ) const

inline

Transform a Point object.

The result is affected by the translation parameters of the transform

Definition at line 136 of file AffineTransform.h.

                                               {         
        return Point2D(_linear(p) + _translation);
    }

Extent2D lsst::afw::geom::AffineTransform::operator() ( Extent2D const &  p ) const

inline

Transform an Extent object.

The result is unaffected by the translation parameters of the transform

Definition at line 145 of file AffineTransform.h.

                                                 {         
        return Extent2D(_linear(p));
    }

AffineTransform lsst::afw::geom::AffineTransform::operator* ( AffineTransform const &  other ) const

inline

Construct a new AffineTransform from two others: (B * A)(p) = B(A(p))

Definition at line 170 of file AffineTransform.h.

                                                                   {
        return AffineTransform(
            getLinear()*other.getLinear(),
            getLinear()(other.getTranslation()) + getTranslation()
        );
    }

AffineTransform& lsst::afw::geom::AffineTransform::operator= ( AffineTransform const &  other )

inline

Definition at line 177 of file AffineTransform.h.

                                                                {
        _linear = other._linear;
        _translation = other._translation;
        return *this;
    }

double& lsst::afw::geom::AffineTransform::operator[] ( int  i )

inline

Definition at line 160 of file AffineTransform.h.

                               { 
        return (i < 4) ? _linear[i] : _translation[i - 4]; 
    }

double lsst::afw::geom::AffineTransform::operator[] ( int  i ) const

inline

Definition at line 163 of file AffineTransform.h.

                                   { 
        return (i < 4) ? _linear[i] : _translation[i - 4]; 
    }

void lsst::afw::geom::AffineTransform::setParameterVector

(

ParameterVector const &

vector

)

Member Data Documentation

LinearTransform lsst::afw::geom::AffineTransform::_linear

private

Definition at line 252 of file AffineTransform.h.

Extent2D lsst::afw::geom::AffineTransform::_translation

private

Definition at line 253 of file AffineTransform.h.

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

• /home/lsstsw/stack/Linux64/afw/11.0-2-g04d2804/include/lsst/afw/geom/AffineTransform.h