lsst::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 Eigen::Matrix3d	Matrix
typedef Eigen::Matrix< double, 6, 1 >	ParameterVector
typedef Eigen::Matrix< double, 2, 6 >	TransformDerivativeMatrix

Public Member Functions
	AffineTransform () noexcept
	Construct an empty (identity) AffineTransform.
	AffineTransform (Eigen::Matrix3d const &matrix) noexcept
	Construct an AffineTransform from a 3x3 matrix.
	AffineTransform (Eigen::Matrix2d const &linear) noexcept
	Construct an AffineTransform with no translation from a 2x2 matrix.
	AffineTransform (Eigen::Vector2d const &translation) noexcept
	Construct a translation-only AffineTransform from a vector.
	AffineTransform (Eigen::Matrix2d const &linear, Eigen::Vector2d const &translation) noexcept
	Construct an AffineTransform from a 2x2 matrix and vector.
	AffineTransform (LinearTransform const &linear) noexcept
	Construct an AffineTransform from a LinearTransform.
	AffineTransform (Extent2D const &translation) noexcept
	Construct a translation-only AffineTransform from an Extent2D.
	AffineTransform (LinearTransform const &linear, Extent2D const &translation) noexcept
	Construct an AffineTransform from a LinearTransform and Extent2D.
	AffineTransform (AffineTransform const &) noexcept=default
	AffineTransform (AffineTransform &&) noexcept=default
	~AffineTransform () noexcept=default
AffineTransform const	inverted () const
	Return the inverse transform.
bool	isIdentity () const noexcept
	Whether the transform is a no-op.
Point2D	operator() (Point2D const &p) const noexcept
	Transform a Point object.
Extent2D	operator() (Extent2D const &p) const noexcept
	Transform an Extent object.
double	applyX (double x, double y) const noexcept
	Transform a point given and returned as separate double values.
double	applyY (double x, double y) const noexcept
Extent2D const &	getTranslation () const noexcept
Extent2D &	getTranslation () noexcept
LinearTransform const &	getLinear () const noexcept
LinearTransform &	getLinear () noexcept
Matrix const	getMatrix () const noexcept
	Return the transform as a full 3x3 matrix.
ParameterVector const	getParameterVector () const noexcept
	Return the transform matrix elements as a parameter vector.
void	setParameterVector (ParameterVector const &vector) noexcept
	Set the transform matrix elements from a parameter vector.
double &	operator[] (int i)
double	operator[] (int i) const
AffineTransform	operator* (AffineTransform const &other) const noexcept
	Construct a new AffineTransform from two others: (B * A)(p) = B(A(p))
AffineTransform &	operator= (AffineTransform const &) noexcept=default
AffineTransform &	operator= (AffineTransform &&) noexcept=default
AffineTransform &	operator+= (AffineTransform const &other) noexcept
AffineTransform	operator+ (AffineTransform const &other) noexcept
AffineTransform &	operator-= (AffineTransform const &other) noexcept
AffineTransform	operator- (AffineTransform const &other) noexcept
TransformDerivativeMatrix	dTransform (Point2D const &input) const noexcept
	Take the derivative of (*this)(input) w.r.t the transform elements.
TransformDerivativeMatrix	dTransform (Extent2D const &input) const noexcept
	Take the derivative of (*this)(input) w.r.t the transform elements.

Static Public Member Functions
static AffineTransform	makeScaling (double s) noexcept
	Construct a new AffineTransform that represents a uniform scaling.
static AffineTransform	makeScaling (double s, double t) noexcept
	Construct a new AffineTransform that represents a non-uniform scaling.
static AffineTransform	makeRotation (Angle t) noexcept
	Construct a new AffineTransform that represents a CCW rotation in radians.
static AffineTransform	makeTranslation (Extent2D translation) noexcept
	Construct a new AffineTransform that represents a pure 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 75 of file AffineTransform.h.

Member Typedef Documentation

Matrix

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

Definition at line 79 of file AffineTransform.h.

ParameterVector

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

Definition at line 80 of file AffineTransform.h.

TransformDerivativeMatrix

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

Definition at line 81 of file AffineTransform.h.

Member Enumeration Documentation

Parameters

enum lsst::geom::AffineTransform::Parameters

Enumerator
XX
YX
XY
YY
X
Y

Definition at line 77 of file AffineTransform.h.

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

Constructor & Destructor Documentation

AffineTransform() [1/10]

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

inlinenoexcept

Construct an empty (identity) AffineTransform.

Definition at line 84 of file AffineTransform.h.

: _linear(), _translation() {}

AffineTransform() [2/10]

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

inlineexplicitnoexcept

Construct an AffineTransform from a 3x3 matrix.

Definition at line 87 of file AffineTransform.h.

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

AffineTransform() [3/10]

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

inlineexplicitnoexcept

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

Definition at line 91 of file AffineTransform.h.

: _linear(linear), _translation() {}

AffineTransform() [4/10]

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

inlineexplicitnoexcept

Construct a translation-only AffineTransform from a vector.

Definition at line 94 of file AffineTransform.h.

            : _linear(), _translation(translation) {}

AffineTransform() [5/10]

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

inlineexplicitnoexcept

Construct an AffineTransform from a 2x2 matrix and vector.

Definition at line 98 of file AffineTransform.h.

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

AffineTransform() [6/10]

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

inlinenoexcept

Construct an AffineTransform from a LinearTransform.

Definition at line 102 of file AffineTransform.h.

: _linear(linear), _translation() {}

AffineTransform() [7/10]

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

inlineexplicitnoexcept

Construct a translation-only AffineTransform from an Extent2D.

Definition at line 105 of file AffineTransform.h.

: _linear(), _translation(translation) {}

AffineTransform() [8/10]

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

inlineexplicitnoexcept

Construct an AffineTransform from a LinearTransform and Extent2D.

Definition at line 108 of file AffineTransform.h.

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

AffineTransform() [9/10]

lsst::geom::AffineTransform::AffineTransform ( AffineTransform const & )

defaultnoexcept

AffineTransform() [10/10]

lsst::geom::AffineTransform::AffineTransform ( AffineTransform && )

defaultnoexcept

~AffineTransform()

lsst::geom::AffineTransform::~AffineTransform ( )

defaultnoexcept

Member Function Documentation

applyX()

double lsst::geom::AffineTransform::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 148 of file AffineTransform.h.

{ return _linear.applyX(x, y) + _translation.getX(); }

applyY()

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

inlinenoexcept

Definition at line 149 of file AffineTransform.h.

{ return _linear.applyY(x, y) + _translation.getY(); }

dTransform() [1/2]

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

noexcept

Take the derivative of (*this)(input) w.r.t the transform elements.

Definition at line 66 of file AffineTransform.cc.

                                                                                                         {
    TransformDerivativeMatrix r = TransformDerivativeMatrix::Zero();
    r.block<2, 4>(0, 0) = getLinear().dTransform(input);
    return r;
}

dTransform() [2/2]

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

noexcept

Take the derivative of (*this)(input) w.r.t the transform elements.

Definition at line 58 of file AffineTransform.cc.

                                                                                                        {
    TransformDerivativeMatrix r = TransformDerivativeMatrix::Zero();
    r.block<2, 4>(0, 0) = getLinear().dTransform(input);
    r(0, X) = 1.0;
    r(1, Y) = 1.0;
    return r;
}

getLinear() [1/2]

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

inlinenoexcept

Definition at line 155 of file AffineTransform.h.

{ return _linear; }

getLinear() [2/2]

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

inlinenoexcept

Definition at line 156 of file AffineTransform.h.

{ return _linear; }

getMatrix()

AffineTransform::Matrix const lsst::geom::AffineTransform::getMatrix ( ) const

noexcept

Return the transform as a full 3x3 matrix.

Definition at line 47 of file AffineTransform.cc.

                                                                      {
    Matrix r;
    r << (*this)[XX], (*this)[XY], (*this)[X], (*this)[YX], (*this)[YY], (*this)[Y], 0.0, 0.0, 1.0;
    return r;
}

getParameterVector()

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

noexcept

Return the transform matrix elements as a parameter vector.

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

Definition at line 32 of file AffineTransform.cc.

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

getTranslation() [1/2]

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

inlinenoexcept

Definition at line 152 of file AffineTransform.h.

{ return _translation; }

getTranslation() [2/2]

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

inlinenoexcept

Definition at line 153 of file AffineTransform.h.

{ return _translation; }

inverted()

AffineTransform const lsst::geom::AffineTransform::inverted

(

)

const

Return the inverse transform.

Exceptions

lsst::geom::SingularTransformException

if not invertible

Definition at line 53 of file AffineTransform.cc.

                                                      {
    LinearTransform inv(getLinear().inverted());
    return AffineTransform(inv, -inv(getTranslation()));
}

isIdentity()

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

inlinenoexcept

Whether the transform is a no-op.

Definition at line 125 of file AffineTransform.h.

{ return getMatrix().isIdentity(); }

makeRotation()

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

inlinestaticnoexcept

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 258 of file AffineTransform.h.

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

makeScaling() [1/2]

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

inlinestaticnoexcept

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 226 of file AffineTransform.h.

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

makeScaling() [2/2]

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

inlinestaticnoexcept

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 243 of file AffineTransform.h.

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

makeTranslation()

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

inlinestaticnoexcept

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 274 of file AffineTransform.h.

                                                                          {
        return AffineTransform(translation);
    }

operator()() [1/2]

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

inlinenoexcept

Transform an Extent object.

The result is unaffected by the translation parameters of the transform

Definition at line 139 of file AffineTransform.h.

{ return Extent2D(_linear(p)); }

operator()() [2/2]

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

inlinenoexcept

Transform a Point object.

The result is affected by the translation parameters of the transform

Definition at line 132 of file AffineTransform.h.

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

operator*()

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

inlinenoexcept

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

Definition at line 182 of file AffineTransform.h.

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

operator+()

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

inlinenoexcept

Definition at line 196 of file AffineTransform.h.

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

operator+=()

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

inlinenoexcept

Definition at line 190 of file AffineTransform.h.

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

operator-()

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

inlinenoexcept

Definition at line 208 of file AffineTransform.h.

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

operator-=()

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

inlinenoexcept

Definition at line 202 of file AffineTransform.h.

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

operator=() [1/2]

AffineTransform & lsst::geom::AffineTransform::operator= ( AffineTransform && )

defaultnoexcept

operator=() [2/2]

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

defaultnoexcept

operator[]() [1/2]

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

inline

Definition at line 176 of file AffineTransform.h.

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

operator[]() [2/2]

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

inline

Definition at line 177 of file AffineTransform.h.

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

setParameterVector()

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

noexcept

Set the transform matrix elements from a parameter vector.

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

Definition at line 38 of file AffineTransform.cc.

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

---

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

• /j/snowflake/release/lsstsw/stack/lsst-scipipe-9.0.0/Linux64/geom/g414038480c+077ccc18e7/include/lsst/geom/AffineTransform.h
• /j/snowflake/release/lsstsw/stack/lsst-scipipe-9.0.0/Linux64/geom/g414038480c+077ccc18e7/src/AffineTransform.cc