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

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

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 69 of file LinearTransform.h.

Member Typedef Documentation

Matrix

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

Definition at line 77 of file LinearTransform.h.

ParameterVector

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

Definition at line 73 of file LinearTransform.h.

ProductDerivativeMatrix

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

Definition at line 75 of file LinearTransform.h.

TransformDerivativeMatrix

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

Definition at line 74 of file LinearTransform.h.

Member Enumeration Documentation

Parameters

enum lsst::geom::LinearTransform::Parameters

Enumerator
XX
YX
XY
YY

Definition at line 71 of file LinearTransform.h.

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

Constructor & Destructor Documentation

LinearTransform() [1/4]

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

inlinenoexcept

Construct an empty (identity) LinearTransform.

Definition at line 80 of file LinearTransform.h.

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

LinearTransform() [2/4]

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

inlineexplicitnoexcept

Construct an LinearTransform from an Eigen::Matrix.

Definition at line 83 of file LinearTransform.h.

: _matrix(matrix) {}

LinearTransform() [3/4]

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

inlinenoexcept

Definition at line 86 of file LinearTransform.h.

: _matrix(other._matrix){};

LinearTransform() [4/4]

lsst::geom::LinearTransform::LinearTransform ( LinearTransform &&  other )

inlinenoexcept

Definition at line 87 of file LinearTransform.h.

: _matrix(std::move(other._matrix)){};

~LinearTransform()

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

defaultnoexcept

Member Function Documentation

applyX()

double lsst::geom::LinearTransform::applyX ( double  x, double  y  ) const

inlinenoexcept

Transform a point given and returned as separate double values.

This interface is intended primarily for use in Python (where it is vectorized to support NumPy array arguments).

Definition at line 195 of file LinearTransform.h.

{ return _matrix(0, 0)*x + _matrix(0, 1)*y; }

applyY()

double lsst::geom::LinearTransform::applyY ( double  x, double  y  ) const

inlinenoexcept

Definition at line 196 of file LinearTransform.h.

{ return _matrix(1, 0)*x + _matrix(1, 1)*y; }

computeDeterminant()

double lsst::geom::LinearTransform::computeDeterminant ( ) const

noexcept

Return the determinant of the 2x2 matrix.

Definition at line 54 of file LinearTransform.cc.

{ return getMatrix().determinant(); }

dTransform() [1/2]

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

inlinenoexcept

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

Definition at line 205 of file LinearTransform.h.

                                                                               {
        return dTransform(Point2D(input));
    }

dTransform() [2/2]

LinearTransform::TransformDerivativeMatrix lsst::geom::LinearTransform::dTransform ( Point2D const &  input ) const

noexcept

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

Definition at line 56 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;
}

getMatrix() [1/2]

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

inlinenoexcept

Definition at line 151 of file LinearTransform.h.

{ return _matrix; }

getMatrix() [2/2]

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

inlinenoexcept

Definition at line 152 of file LinearTransform.h.

{ return _matrix; }

getParameterVector()

LinearTransform::ParameterVector const lsst::geom::LinearTransform::getParameterVector ( ) const

noexcept

Return the transform matrix elements as a parameter vector.

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

Definition at line 32 of file LinearTransform.cc.

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

inverted()

LinearTransform const lsst::geom::LinearTransform::inverted

(

)

const

Return the inverse transform.

Exceptions

lsst::geom::SingularTransformException

if not invertible

Definition at line 45 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::geom::LinearTransform::isIdentity ( ) const

inlinenoexcept

Whether the transform is a no-op.

Definition at line 170 of file LinearTransform.h.

{ return getMatrix().isIdentity(); }

makeRotation()

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

inlinestaticnoexcept

Definition at line 102 of file LinearTransform.h.

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

makeScaling() [1/2]

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

inlinestaticnoexcept

Definition at line 94 of file LinearTransform.h.

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

makeScaling() [2/2]

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

inlinestaticnoexcept

Definition at line 98 of file LinearTransform.h.

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

operator()() [1/2]

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

inlinenoexcept

Transform a Extent2D object.

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

Definition at line 186 of file LinearTransform.h.

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

operator()() [2/2]

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

inlinenoexcept

Transform a Point2D object.

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

Definition at line 178 of file LinearTransform.h.

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

operator*()

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

inlinenoexcept

Definition at line 90 of file LinearTransform.h.

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

operator+()

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

inlinenoexcept

Definition at line 121 of file LinearTransform.h.

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

operator+=()

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

inlinenoexcept

Definition at line 116 of file LinearTransform.h.

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

operator-()

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

inlinenoexcept

Definition at line 132 of file LinearTransform.h.

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

operator-=()

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

inlinenoexcept

Definition at line 127 of file LinearTransform.h.

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

operator=() [1/2]

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

inlinenoexcept

Definition at line 111 of file LinearTransform.h.

                                                                 {
        _matrix = std::move(other._matrix);
        return *this;
    }

operator=() [2/2]

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

inlinenoexcept

Definition at line 107 of file LinearTransform.h.

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

operator[]() [1/2]

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

inline

Definition at line 154 of file LinearTransform.h.

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

operator[]() [2/2]

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

inline

Definition at line 155 of file LinearTransform.h.

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

setParameterVector()

void lsst::geom::LinearTransform::setParameterVector ( LinearTransform::ParameterVector const &  vector )

noexcept

Set the transform matrix elements from a parameter vector.

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

Definition at line 38 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:

• /j/snowflake/release/lsstsw/stack/lsst-scipipe-0.7.0/Linux64/geom/22.0.1-6-g8d3140d+720564cf76/include/lsst/geom/LinearTransform.h
• /j/snowflake/release/lsstsw/stack/lsst-scipipe-0.7.0/Linux64/geom/22.0.1-6-g8d3140d+720564cf76/src/LinearTransform.cc