donner::Transform2< T > Struct Template Reference

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

#include "donner/base/Transform.h"

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

Public Member Functions
	Transform2 ()
	Construct an identity transform.
	Transform2 (UninitializedTag)
	Construct an uninitialized transform.
	~Transform2 ()=default
	Destructor.
	Transform2 (const Transform2< T > &)=default
	Copy constructor.
	Transform2 (Transform2< T > &&)=default
	Move constructor.
Transform2< T > &	operator= (const Transform2< T > &)=default
	Copy assignment operator.
Transform2< T > &	operator= (Transform2< T > &&)=default
	Move assignment operator.
bool	isIdentity () const
	Returns true if this transform is equal to the identity matrix.
bool	isTranslation () const
	Returns true if this transform is a pure translation (no rotation, scale, or skew).
Vector2< T >	translation () const
	Returns the translation component of this transform as a vector.
T	determinant () const
	Returns the determinant.
Transform2< 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.
Box2< T >	transformBox (const Box2< T > &box) const
	Transform an axis-aligned bounding box, returning a new axis-aligned bounding box with the result.
Transform2< T >	operator* (const Transform2< T > &rhs) const
	Composes two transforms: the result applies this transform first, then rhs.
bool	operator== (const Transform2< T > &rhs) const
	Exact element-wise equality.

Static Public Member Functions
static Transform2	Rotate (T angleRadians)
	Return a 2D rotation matrix with the given angle, in radians.
static Transform2	Scale (T extent)
	Return a 2D scale matrix with uniform scaling.
static Transform2	Scale (const Vector2< T > &extent)
	Return a 2D scale matrix with horizontal and vertical scaling from a Vector2.
static Transform2	Scale (T x, T y)
	Return a 2D scale matrix with horizontal and vertical scaling, convenience API accepting two parameters.
static Transform2	Translate (const Vector2< T > &offset)
	Return a 2D translation matrix.
static Transform2	Translate (T x, T y)
	Return a 2D translation matrix, convenience API accepting two parameters.
static Transform2	SkewX (T theta)
	Returns a 2D skew transformation along the X axis.
static Transform2	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 const UninitializedTag	uninitialized = UninitializedTag()
	Tag value for constructing an uninitialized transform.

Friends
std::ostream &	operator<< (std::ostream &os, const Transform2< T > &t)
	Ostream output operator.

Detailed Description

template<typename T>
struct donner::Transform2< 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::Transform2::UninitializedTag

struct donner::Transform2::UninitializedTag

template<typename T>
struct donner::Transform2< T >::UninitializedTag

Tag type for constructing an uninitialized transform.

Constructor & Destructor Documentation

Transform2()

template<typename T>

donner::Transform2< T >::Transform2 ( UninitializedTag )

inlineexplicit

Construct an uninitialized transform.

Transform2<T> transform(Transform2::uninitialized);

Member Function Documentation

inverse()

template<typename T>

Transform2< T > donner::Transform2< T >::inverse ( ) const

inline

Returns the inverse of this transform.

If the determinant is zero, the result contains non-finite values.

isTranslation()

template<typename T>

bool donner::Transform2< T >::isTranslation ( ) const

inline

Returns true if this transform is a pure translation (no rotation, scale, or skew).

A pure translation has the form:

\[\begin{bmatrix} 1 & 0 & e \\ 0 & 1 & f \\ 0 & 0 & 1 \\ \end{bmatrix} \]

operator*()

template<typename T>

Transform2< T > donner::Transform2< T >::operator* ( const Transform2< T > & rhs ) const

inline

Composes two transforms: the result applies this transform first, then rhs.

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

A * T * R

Parameters

rhs	Transform applied after this one.

operator==()

template<typename T>

bool donner::Transform2< T >::operator== ( const Transform2< T > & rhs ) const

inline

Exact element-wise equality.

No epsilon: this is the comparison a cache key needs, where any difference in the producing transform means the cached derivative has to be rebuilt. Compare with an explicit tolerance instead when the two transforms went through different arithmetic.

Parameters

rhs	Other transform.

Rotate()

template<typename T>

Transform2 donner::Transform2< T >::Rotate ( T angleRadians )

inlinestatic

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

Parameters

angleRadians

Angle in radians.

Scale() [1/3]

template<typename T>

Transform2 donner::Transform2< 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>

Transform2 donner::Transform2< 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>

Transform2 donner::Transform2< 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>

Transform2 donner::Transform2< 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>

Transform2 donner::Transform2< 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>

Box2< T > donner::Transform2< T >::transformBox ( const Box2< 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::Transform2< 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::Transform2< 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>

Transform2 donner::Transform2< T >::Translate ( const Vector2< T > & offset )

inlinestatic

Return a 2D translation matrix.

Parameters

offset

Translation offset.

Translate() [2/2]

template<typename T>

Transform2 donner::Transform2< 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::Transform2< 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