lsst::afw::geom::LinearTransform Class Reference

A 2D linear coordinate transformation. More...

#include <LinearTransform.h>

Public Types
enum	Parameters { XX = 0, YX = 1, XY = 2, YY = 3 }
typedef Eigen::Matrix< double, 4, 1 >	ParameterVector
typedef Eigen::Matrix< double, 2, 4 >	TransformDerivativeMatrix
typedef Eigen::Matrix< double, 4, 4 >	ProductDerivativeMatrix
typedef Eigen::Matrix< double, 2, 2, Eigen::DontAlign >	Matrix

Public Member Functions
	LinearTransform ()
	Construct an empty (identity) LinearTransform. More...
	LinearTransform (Matrix const &matrix)
	Construct an LinearTransform from an Eigen::Matrix. More...
	LinearTransform (LinearTransform const &)=default
	LinearTransform (LinearTransform &&)=default
	~LinearTransform ()=default
LinearTransform	operator* (LinearTransform const &other) const
LinearTransform &	operator= (LinearTransform const &)=default
LinearTransform &	operator= (LinearTransform &&)=default
LinearTransform &	operator+= (LinearTransform const &other)
LinearTransform	operator+ (LinearTransform const &other)
LinearTransform &	operator-= (LinearTransform const &other)
LinearTransform	operator- (LinearTransform const &other)
ParameterVector const	getParameterVector () const
	Return the transform matrix elements as a parameter vector. More...
void	setParameterVector (ParameterVector const &vector)
	Set the transform matrix elements from a parameter vector. More...
Matrix const &	getMatrix () const
Matrix &	getMatrix ()
double &	operator[] (int i)
double const &	operator[] (int i) const
LinearTransform const	invert () const
	Return the inverse transform. More...
double	computeDeterminant () const
	Return the determinant of the 2x2 matrix. More...
bool	isIdentity () const
	Whether the transform is a no-op. More...
Point2D	operator() (Point2D const &p) const
	Transform a Point2D object. More...
Extent2D	operator() (Extent2D const &p) const
	Transform a Extent2D object. More...
TransformDerivativeMatrix	dTransform (Point2D const &input) const
	Derivative of (*this)(input) with respect to the transform elements (for Point). More...
TransformDerivativeMatrix	dTransform (Extent2D const &input) const
	Derivative of (*this)(input) with respect to the transform elements (for Extent);. More...

Static Public Member Functions
static LinearTransform	makeScaling (double s)
static LinearTransform	makeScaling (double s, double t)
static LinearTransform	makeRotation (Angle t)

Detailed Description

A 2D linear coordinate transformation.

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

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

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

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

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

Definition at line 71 of file LinearTransform.h.

Member Typedef Documentation

Matrix

typedef Eigen::Matrix<double, 2, 2, Eigen::DontAlign> lsst::afw::geom::LinearTransform::Matrix

Definition at line 79 of file LinearTransform.h.

ParameterVector

typedef Eigen::Matrix<double, 4, 1> lsst::afw::geom::LinearTransform::ParameterVector

Definition at line 75 of file LinearTransform.h.

ProductDerivativeMatrix

typedef Eigen::Matrix<double, 4, 4> lsst::afw::geom::LinearTransform::ProductDerivativeMatrix

Definition at line 77 of file LinearTransform.h.

TransformDerivativeMatrix

typedef Eigen::Matrix<double, 2, 4> lsst::afw::geom::LinearTransform::TransformDerivativeMatrix

Definition at line 76 of file LinearTransform.h.

Member Enumeration Documentation

Parameters

enum lsst::afw::geom::LinearTransform::Parameters

Enumerator
XX
YX
XY
YY

Definition at line 73 of file LinearTransform.h.

{ XX = 0, YX = 1, XY = 2, YY = 3 };

Constructor & Destructor Documentation

LinearTransform() [1/4]

lsst::afw::geom::LinearTransform::LinearTransform ( )

inline

Construct an empty (identity) LinearTransform.

Definition at line 82 of file LinearTransform.h.

: _matrix(Matrix::Identity()) {}

LinearTransform() [2/4]

lsst::afw::geom::LinearTransform::LinearTransform ( Matrix const &  matrix )

inlineexplicit

Construct an LinearTransform from an Eigen::Matrix.

Definition at line 85 of file LinearTransform.h.

: _matrix(matrix) {}

LinearTransform() [3/4]

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

default

LinearTransform() [4/4]

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

default

~LinearTransform()

lsst::afw::geom::LinearTransform::~LinearTransform ( )

default

Member Function Documentation

computeDeterminant()

double lsst::afw::geom::LinearTransform::computeDeterminant

(

)

const

Return the determinant of the 2x2 matrix.

Definition at line 56 of file LinearTransform.cc.

                                                 {
    Eigen::MatrixXd const& m = getMatrix();
    return m(0, 0) * m(1, 1) - m(0, 1) * m(1, 0);
}

dTransform() [1/2]

LinearTransform::TransformDerivativeMatrix lsst::afw::geom::LinearTransform::dTransform

(

Point2D const &

input

)

const

Derivative of (*this)(input) with respect to the transform elements (for Point).

Definition at line 61 of file LinearTransform.cc.

                                                                                               {
    TransformDerivativeMatrix r = TransformDerivativeMatrix::Zero();
    r(0, XX) = input.getX();
    r(0, XY) = input.getY();
    r(1, YX) = input.getX();
    r(1, YY) = input.getY();
    return r;
}

dTransform() [2/2]

TransformDerivativeMatrix lsst::afw::geom::LinearTransform::dTransform ( Extent2D const &  input ) const

inline

Derivative of (*this)(input) with respect to the transform elements (for Extent);.

Definition at line 188 of file LinearTransform.h.

{ return dTransform(Point2D(input)); }

getMatrix() [1/2]

Matrix const& lsst::afw::geom::LinearTransform::getMatrix ( ) const

inline

Definition at line 145 of file LinearTransform.h.

{ return _matrix; }

getMatrix() [2/2]

Matrix& lsst::afw::geom::LinearTransform::getMatrix ( )

inline

Definition at line 146 of file LinearTransform.h.

{ return _matrix; }

getParameterVector()

LinearTransform::ParameterVector const lsst::afw::geom::LinearTransform::getParameterVector

(

)

const

Return the transform matrix elements as a parameter vector.

The elements will be ordered XX, YX, XY, YY

Definition at line 34 of file LinearTransform.cc.

                                                                               {
    ParameterVector r;
    r << (*this)[XX], (*this)[YX], (*this)[XY], (*this)[YY];
    return r;
}

invert()

LinearTransform const lsst::afw::geom::LinearTransform::invert

(

)

const

Return the inverse transform.

Exceptions

lsst::afw::geom::SingularTransformException

Definition at line 47 of file LinearTransform.cc.

                                                    {
    Eigen::FullPivLU<Matrix> lu(getMatrix());
    if (!lu.isInvertible()) {
        throw LSST_EXCEPT(SingularTransformException, "Could not compute LinearTransform inverse");
    }
    Matrix inv = lu.inverse();
    return LinearTransform(inv);
}

isIdentity()

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

inline

Whether the transform is a no-op.

Definition at line 164 of file LinearTransform.h.

{ return getMatrix().isIdentity(); }

makeRotation()

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

inlinestatic

Definition at line 103 of file LinearTransform.h.

                                                 {
        return LinearTransform(Matrix(Eigen::Rotation2D<double>(t.asRadians())));
    }

makeScaling() [1/2]

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

inlinestatic

Definition at line 95 of file LinearTransform.h.

                                                 {
        return LinearTransform((Matrix() << s, 0.0, 0.0, s).finished());
    }

makeScaling() [2/2]

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

inlinestatic

Definition at line 99 of file LinearTransform.h.

                                                           {
        return LinearTransform((Matrix() << s, 0.0, 0.0, t).finished());
    }

operator()() [1/2]

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

inline

Transform a Point2D object.

This operation is equivalent to applying the LinearTransform to an lsst::afw::geom::Extent

Definition at line 172 of file LinearTransform.h.

{ return Point2D(getMatrix() * p.asEigen()); }

operator()() [2/2]

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

inline

Transform a Extent2D object.

This operation is equivalent to applying the LinearTransform to an lsst::afw::geom::Point

Definition at line 180 of file LinearTransform.h.

{ return Extent2D(getMatrix() * p.asEigen()); }

operator*()

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

inline

Definition at line 91 of file LinearTransform.h.

                                                                  {
        return LinearTransform(getMatrix() * other.getMatrix());
    }

operator+()

LinearTransform lsst::afw::geom::LinearTransform::operator+ ( LinearTransform const &  other )

inline

Definition at line 115 of file LinearTransform.h.

                                                            {
        LinearTransform tmp(*this);
        tmp += other;
        return tmp;
    }

operator+=()

LinearTransform& lsst::afw::geom::LinearTransform::operator+= ( LinearTransform const &  other )

inline

Definition at line 110 of file LinearTransform.h.

                                                              {
        _matrix += other._matrix;
        return *this;
    }

operator-()

LinearTransform lsst::afw::geom::LinearTransform::operator- ( LinearTransform const &  other )

inline

Definition at line 126 of file LinearTransform.h.

                                                            {
        LinearTransform tmp(*this);
        tmp -= other;
        return tmp;
    }

operator-=()

LinearTransform& lsst::afw::geom::LinearTransform::operator-= ( LinearTransform const &  other )

inline

Definition at line 121 of file LinearTransform.h.

                                                              {
        _matrix -= other._matrix;
        return *this;
    }

operator=() [1/2]

LinearTransform& lsst::afw::geom::LinearTransform::operator= ( LinearTransform const &  )

default

operator=() [2/2]

LinearTransform& lsst::afw::geom::LinearTransform::operator= ( LinearTransform &&  )

default

operator[]() [1/2]

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

inline

Definition at line 148 of file LinearTransform.h.

{ return _matrix(i % 2, i / 2); }

operator[]() [2/2]

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

inline

Definition at line 149 of file LinearTransform.h.

{ return const_cast<Matrix&>(_matrix)(i % 2, i / 2); }

setParameterVector()

void lsst::afw::geom::LinearTransform::setParameterVector

(

LinearTransform::ParameterVector const &

vector

)

Set the transform matrix elements from a parameter vector.

The parameter vector is ordered XX, YX, XY, YY

Definition at line 40 of file LinearTransform.cc.

                                                                                     {
    (*this)[XX] = vector[XX];
    (*this)[XY] = vector[XY];
    (*this)[YX] = vector[YX];
    (*this)[YY] = vector[YY];
}

---

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

• /home/jenkins-slave/snowflake/release/lsstsw/stack/Linux64/afw/15.0-29-ga12a2b06e/include/lsst/afw/geom/LinearTransform.h
• /home/jenkins-slave/snowflake/release/lsstsw/stack/Linux64/afw/15.0-29-ga12a2b06e/src/geom/LinearTransform.cc