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. More...
	AffineTransform (Eigen::Matrix3d const &matrix) noexcept
	Construct an AffineTransform from a 3x3 matrix. More...
	AffineTransform (Eigen::Matrix2d const &linear) noexcept
	Construct an AffineTransform with no translation from a 2x2 matrix. More...
	AffineTransform (Eigen::Vector2d const &translation) noexcept
	Construct a translation-only AffineTransform from a vector. More...
	AffineTransform (Eigen::Matrix2d const &linear, Eigen::Vector2d const &translation) noexcept
	Construct an AffineTransform from a 2x2 matrix and vector. More...
	AffineTransform (LinearTransform const &linear) noexcept
	Construct an AffineTransform from a LinearTransform. More...
	AffineTransform (Extent2D const &translation) noexcept
	Construct a translation-only AffineTransform from an Extent2D. More...
	AffineTransform (LinearTransform const &linear, Extent2D const &translation) noexcept
	Construct an AffineTransform from a LinearTransform and Extent2D. More...
	AffineTransform (AffineTransform const &) noexcept=default
	AffineTransform (AffineTransform &&) noexcept=default
	~AffineTransform () noexcept=default
bool	isIdentity () const noexcept
	Whether the transform is a no-op. More...
Point2D	operator() (Point2D const &p) const noexcept
	Transform a Point object. More...
Extent2D	operator() (Extent2D const &p) const noexcept
	Transform an Extent object. More...
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. More...
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...
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)) More...
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. More...
TransformDerivativeMatrix	dTransform (Extent2D const &input) const noexcept
	Take the derivative of (*this)(input) w.r.t the transform elements. More...
AffineTransform const	inverted () const
	Return the inverse transform. More...

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

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

dTransform() [1/2]

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;
}

dTransform() [2/2]

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;
}

getLinear() [1/2]

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

inlinenoexcept

Definition at line 144 of file AffineTransform.h.

{ return _linear; }

getLinear() [2/2]

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

inlinenoexcept

Definition at line 145 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 141 of file AffineTransform.h.

{ return _translation; }

getTranslation() [2/2]

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

inlinenoexcept

Definition at line 142 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 247 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 215 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 232 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 263 of file AffineTransform.h.

                                                                          {
        return AffineTransform(translation);
    }

operator()() [1/2]

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()() [2/2]

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*()

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 171 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 185 of file AffineTransform.h.

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

operator+=()

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

inlinenoexcept

Definition at line 179 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 197 of file AffineTransform.h.

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

operator-=()

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

inlinenoexcept

Definition at line 191 of file AffineTransform.h.

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

operator=() [1/2]

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

defaultnoexcept

operator=() [2/2]

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

defaultnoexcept

operator[]() [1/2]

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

inline

Definition at line 165 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 166 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/Linux64/geom/17.0.1-1-gb9095d2+7/include/lsst/geom/AffineTransform.h
• /j/snowflake/release/lsstsw/stack/Linux64/geom/17.0.1-1-gb9095d2+7/src/AffineTransform.cc