donner::Transform< T > Struct Template Reference

A 2D matrix representing an affine transformation. More...

#include "donner/base/Transform.h"

Collaboration diagram for donner::Transform< T >:

Classes
struct	UninitializedTag
	Tag type for constructing an uninitialized transform. More...

Public Member Functions
	Transform ()
	Construct an identity transform.
	Transform (UninitializedTag)
	Construct an uninitialized transform.
	~Transform ()=default
	Destructor.
	Transform (const Transform< T > &)=default
	Copy constructor.
	Transform (Transform< T > &&)=default
	Move constructor.
Transform< T > &	operator= (const Transform< T > &)=default
	Copy assignment operator.
Transform< T > &	operator= (Transform< T > &&)=default
	Move assignment operator.
bool	isIdentity () const
	Returns true if this transform is equal to the identity matrix.
T	determinant () const
	Returns the determinant.
Transform< T >	inverse () const
	Returns the inverse of this transform.
Vector2< T >	transformVector (const Vector2< T > &v) const
	Transforms a column vector, applying rotations/scaling but not translation.
Vector2< T >	transformPosition (const Vector2< T > &v) const
	Transforms a position given as a vector.
Box< T >	transformBox (const Box< T > &box) const
	Transform an axis-aligned bounding box, returning a new axis-aligned bounding box with the result.
Transform< T >	operator* (const Transform< T > &rhs) const
	Post-multiplies rhs with this transform.

Static Public Member Functions
static Transform	Rotate (T angleRadians)
	Return a 2D rotation matrix with the given angle, in radians.
static Transform	Scale (T extent)
	Return a 2D scale matrix with uniform scaling.
static Transform	Scale (const Vector2< T > &extent)
	Return a 2D scale matrix with horizontal and vertical scaling from a Vector2.
static Transform	Scale (T x, T y)
	Return a 2D scale matrix with horizontal and vertical scaling, convenience API accepting two parameters.
static Transform	Translate (const Vector2< T > &offset)
	Return a 2D translation matrix.
static Transform	Translate (T x, T y)
	Return a 2D translation matrix, convenience API accepting two parameters.
static Transform	SkewX (T theta)
	Returns a 2D skew transformation along the X axis.
static Transform	SkewY (T theta)
	Returns a 2D skew transformation along the Y axis.

Public Attributes
T	data [6]
	Storage for a 3x2 matrix, in column-major order.

Static Public Attributes
static constexpr UninitializedTag	uninitialized = UninitializedTag()
	Tag value for constructing an uninitialized transform.

Friends
std::ostream &	operator<< (std::ostream &os, const Transform< T > &t)
	Ostream output operator.

Detailed Description

template<typename T>
struct donner::Transform< T >

A 2D matrix representing an affine transformation.

It stores six parameters, and is equivalent to the 3x3 matrix:

\[ \begin{bmatrix} a & c & e \\ b & d & f \\ 0 & 0 & 1 \\ \end{bmatrix} \]

Elements are stored in column-major order.

Template Parameters

T	Element type.

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Class Documentation

donner::Transform::UninitializedTag

struct donner::Transform::UninitializedTag

template<typename T>
struct donner::Transform< T >::UninitializedTag

Tag type for constructing an uninitialized transform.

Constructor & Destructor Documentation

Transform()

template<typename T >

donner::Transform< T >::Transform ( UninitializedTag )

inlineexplicit

Construct an uninitialized transform.

Transform<T> transform(Transform::uninitialized);

Member Function Documentation

operator*()

template<typename T >

Transform< T > donner::Transform< T >::operator* ( const Transform< T > & rhs ) const

inline

Post-multiplies rhs with this transform.

Example: Take A, transform by T, transform by R is written as

R * T * A

Parameters

rhs	Other transform.

Rotate()

template<typename T >

static Transform donner::Transform< T >::Rotate ( T angleRadians )

inlinestatic

Return a 2D rotation matrix with the given angle, in radians.

Parameters

theta

Angle in radians.

Scale() [1/3]

template<typename T >

static Transform donner::Transform< T >::Scale ( const Vector2< T > & extent )

inlinestatic

Return a 2D scale matrix with horizontal and vertical scaling from a Vector2.

Parameters

extent

Scale x/y parameters.

Scale() [2/3]

template<typename T >

static Transform donner::Transform< T >::Scale ( T extent )

inlinestatic

Return a 2D scale matrix with uniform scaling.

Parameters

extent

Scale x/y parameters.

Scale() [3/3]

template<typename T >

static Transform donner::Transform< T >::Scale ( T x, T y )

inlinestatic

Return a 2D scale matrix with horizontal and vertical scaling, convenience API accepting two parameters.

Parameters

x	Horizontal scale.
y	Vertical scale.

SkewX()

template<typename T >

static Transform donner::Transform< T >::SkewX ( T theta )

inlinestatic

Returns a 2D skew transformation along the X axis.

See also

https://www.w3.org/TR/css-transforms-1/#SkewXDefined

Parameters

theta

Angle in radians.

SkewY()

template<typename T >

static Transform donner::Transform< T >::SkewY ( T theta )

inlinestatic

Returns a 2D skew transformation along the Y axis.

See also

https://www.w3.org/TR/css-transforms-1/#SkewYDefined

Parameters

theta

Angle in radians.

transformBox()

template<typename T >

Box< T > donner::Transform< T >::transformBox ( const Box< T > & box ) const

inline

Transform an axis-aligned bounding box, returning a new axis-aligned bounding box with the result.

Parameters

box	Box to transform.

transformPosition()

template<typename T >

Vector2< T > donner::Transform< T >::transformPosition ( const Vector2< T > & v ) const

inline

Transforms a position given as a vector.

\[ v' = M \begin{bmatrix} v_x \\ v_y \\ 1 \end{bmatrix} \]

Parameters

v	Vector to transform.

Returns

Transformed vector.

transformVector()

template<typename T >

Vector2< T > donner::Transform< T >::transformVector ( const Vector2< T > & v ) const

inline

Transforms a column vector, applying rotations/scaling but not translation.

\[ v' = M \begin{bmatrix} v_x \\ v_y \\ 0 \end{bmatrix} \]

Parameters

v	Vector to transform.

Returns

Transformed vector.

Translate() [1/2]

template<typename T >

static Transform donner::Transform< T >::Translate ( const Vector2< T > & offset )

inlinestatic

Return a 2D translation matrix.

Parameters

offset

Translation offset.

Translate() [2/2]

template<typename T >

static Transform donner::Transform< T >::Translate ( T x, T y )

inlinestatic

Return a 2D translation matrix, convenience API accepting two parameters.

Parameters

x	Horizontal translation offset.
y	Vertical translation offset.

Member Data Documentation

data

template<typename T >

T donner::Transform< T >::data[6]

Storage for a 3x2 matrix, in column-major order.

Elements are stored in the following order:

• 0 = scaleX (a)
• 1 = skewY (b)
• 2 = skewX (c)
• 3 = scaleY (d)
• 4 = translateX (e)
• 5 = translateY (f)

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

• donner/base/Transform.h