Affine transformation class. More...

#include <geomc/linalg/AffineTransform.h>

Inheritance diagram for AffineTransform< T, N >:

Public Types
using	elem_t
	The coordinate type of this object.

using	point_t
	The type of a point in this object's space.

Public Member Functions
	AffineTransform ()
	Construct a new identity transform.

const AffineTransform< T, N >	apply (const AffineTransform< T, N > &xf) const
	Concatenation of transforms.

const VecType< T, N >	apply (const VecType< T, N > &p) const
	Transformation of a point.

const VecType< T, N >	apply_direction (const VecType< T, N > &v) const
	Transformation of a direction vector; ignores any translation.

const AffineTransform< T, N >	apply_inverse (const AffineTransform< T, N > &xf) const
	Application of inverse.

const VecType< T, N >	apply_inverse (const VecType< T, N > &p) const
	Inverse transformation of a point.

const VecType< T, N >	apply_inverse_direction (const VecType< T, N > &v) const
	Inverse transformation of a direction vector; ignores any translation.

const VecType< T, N >	apply_inverse_normal (const VecType< T, N > &n) const
	Inverse transformation of a normal.

const VecType< T, N >	apply_normal (const VecType< T, N > &n) const
	Transformation of a normal.

const SimpleMatrix< T, N, N >	direction_matrix () const
	Return the 3x3 matrix which transforms direction vectors.

const AffineTransform< T, N >	inverse () const

template<typename U>
	operator AffineTransform< U, N > () const
	Cast elements to a different type.

AffineTransform< T, N > &	operator*= (const AffineTransform< T, N > &xf)
	Concatenation of transforms.

AffineTransform< T, N > &	operator/= (const AffineTransform< T, N > &xf)
	Apply inverse transform.

bool	operator== (const AffineTransform< T, N > &xf) const
	Equality operator.

template<index_t M, typename U = T>
AffineTransform< U, M >	resized () const

Public Attributes
SimpleMatrix< T, N+1, N+1 >	inv
	Matrix representing the inverse of this transformation.

SimpleMatrix< T, N+1, N+1 >	mat
	Matrix representing this transformation.

Static Public Attributes
static constexpr index_t	N
	The dimension of this object.

Friends
Ray< T, N >	operator* (const AffineTransform< T, N > &xf, Ray< T, N > r)
	Transformation of a ray.

VecType< T, N >	operator* (const AffineTransform< T, N > &xf, VecType< T, N > p)
	Transformation of a point.

AffineTransform< T, N >	operator* (const AffineTransform< T, N > &xf1, const AffineTransform< T, N > &xf2)
	Concatenation of transforms.

AffineTransform< T, N >	operator/ (const AffineTransform< T, N > &xf1, const AffineTransform< T, N > &xf2)
	Inverse transform application.

Ray< T, N >	operator/ (Ray< T, N > r, const AffineTransform< T, N > &xf)
	Inverse transformation of a ray (`xf`^-1`* ray`)

VecType< T, N >	operator/ (VecType< T, N > p, const AffineTransform< T, N > &xf)
	Inverse transformation of a point (`xf`^-1`* pt`)

Related Symbols
(Note that these are not member symbols.)
template<typename T>
AffineTransform< T, 3 >	direction_align (const Vec< T, 3 > &dir, const Vec< T, 3 > &align_with)

template<typename T>
AffineTransform< T, 3 >	rotation (Quat< T > q)

template<typename T>
AffineTransform< T, 2 >	rotation (T radians)

template<typename T>
AffineTransform< T, 3 >	rotation (Vec< T, 3 > axis, const Vec< T, 3 > &center, T radians)

template<typename T>
AffineTransform< T, 3 >	rotation (Vec< T, 3 > axis, T radians)

template<typename T, index_t N>
AffineTransform< T, N >	scale (const Vec< T, N > &sx)

template<typename T>
AffineTransform< T, 2 >	scale (T sx, T sy)

template<typename T>
AffineTransform< T, 3 >	scale (T sx, T sy, T sz)

template<typename T, index_t N, MatrixLayout Lyt, StoragePolicy P>
AffineTransform< T, N >	transformation (const SimpleMatrix< T, N, N, Lyt, P > &mat)

template<typename T, index_t N>
AffineTransform< T, N >	translation (const Vec< T, N > &tx)

template<typename T>
AffineTransform< T, 2 >	translation (T tx, T ty)

template<typename T>
AffineTransform< T, 3 >	translation (T tx, T ty, T tz)

Detailed Description

template<typename T, index_t N>
class geom::AffineTransform< T, N >

Affine transformation class.

AffineTransforms may represent any linear transformation, including rotations, translations, nonuniform scales, and shears. They are represented by an (N+1) x (N+1) matrix, where the last row is [0,0,...,1].

AffineTransforms meet the Transform concept. For transforms that preserve angles and relative distances, see Similarity. For transforms that preserve distance, see Isometry. For pure rotations, see Rotation.

Vectors are assumed to be columns; therefore a transformation is ordered like:

T * v

and so:

A * B * v

applies B to v, then A to the result.

The transform which "undoes" a transform can be obtained with xf.inverse(). Because an AffineTransform internally stores both itself and its inverse, this construction is fairly inexpensive, as are all inverse-application functions.

Construction

Transforms are best constructed using the provided methods:

Vec<double,3> v = ... ;
AffineTransform<double,3> xf = rotation(axis, angle);
xf *= translation(v);
xf *= scale(v);
xf *= transformation(mat3x3);

These methods will generally be most efficient and robust, especially when constructing the internal inverse transformation matrix needed by AffineTransform objects.

Member Typedef Documentation

◆ point_t

using point_t

inherited

The type of a point in this object's space.

An N-vector of T if N > 1, otherwise a T.

Member Function Documentation

◆ apply()

template<typename T, index_t N>

const AffineTransform< T, N > apply ( const AffineTransform< T, N > & xf ) const

inline

Concatenation of transforms.

Returns: A transformation representing a transform by this followed by a transform by xf.

◆ apply_inverse()

template<typename T, index_t N>

const AffineTransform< T, N > apply_inverse ( const AffineTransform< T, N > & xf ) const

inline

Application of inverse.

Returns: A transformation representing a transform by this followed by the inverse of xf.

◆ apply_normal()

template<typename T, index_t N>

const VecType< T, N > apply_normal ( const VecType< T, N > & n ) const

inline

Transformation of a normal.

Preserves surface direction of geometry transformed by this.

◆ inverse()

template<typename T, index_t N>

const AffineTransform< T, N > inverse ( ) const

inline

Returns: The inverse transform of this.

◆ operator*=()

template<typename T, index_t N>

AffineTransform< T, N > & operator*= ( const AffineTransform< T, N > & xf )

inline

Concatenation of transforms.

Assign a transform representing an application of this followed by xf.

◆ operator/=()

template<typename T, index_t N>

AffineTransform< T, N > & operator/= ( const AffineTransform< T, N > & xf )

inline

Apply inverse transform.

Assign a transform representing an application of this followed by the inverse of xf.

Friends And Related Symbol Documentation

◆ direction_align()

template<typename T>

AffineTransform< T, 3 > direction_align	(	const Vec< T, 3 > &	dir,
		const Vec< T, 3 > &	align_with )

Rotation to align one vector with another.

Parameters

dir	Unit direction to be realigned.
align_with	Unit direction to align with.

Returns: A rotation transform aligning dir with align_with.

◆ operator*

template<typename T, index_t N>

AffineTransform< T, N > operator*	(	const AffineTransform< T, N > &	xf1,
		const AffineTransform< T, N > &	xf2 )

friend

Concatenation of transforms.

Returns: A transformation representing an application of xf2 followed by xf1.

◆ operator/

template<typename T, index_t N>

AffineTransform< T, N > operator/	(	const AffineTransform< T, N > &	xf1,
		const AffineTransform< T, N > &	xf2 )

friend

Inverse transform application.

Returns: A transformation representing an application of xf1 followed by the inverse of xf2.

◆ rotation() [1/4]

template<typename T>

AffineTransform< T, 3 > rotation ( Quat< T > q )

Rotation from a quaternion.

Parameters

q	Rotation quaternion.

Returns: A rotation transformation.

◆ rotation() [2/4]

template<typename T>

AffineTransform< T, 2 > rotation ( T radians )

2D rotation about the origin by angle radians.

Parameters

radians Angle of rotation in the counterclockwise direction

Returns: A 2D rotation transformation.

◆ rotation() [3/4]

template<typename T>

AffineTransform< T, 3 > rotation	(	Vec< T, 3 >	axis,
		const Vec< T, 3 > &	center,
		T	radians )

Rotation about a point.

This transformation will not be a pure rotation; it will include a translation component.

Parameters

axis	Axis of rotation.
center	Center of rotation.
radians	Angle of rotation.

Returns: A transformation representing a rotation around the point center by angle radians and axis axis.

◆ rotation() [4/4]

template<typename T>

AffineTransform< T, 3 > rotation	(	Vec< T, 3 >	axis,
		T	radians )

Rotation about an axis.

Parameters

axis	Axis of rotation.
radians	Angle of rotation.

Returns: A transformation representing a rotation about axis by angle radians.

◆ scale() [1/3]

template<typename T, index_t N>

AffineTransform< T, N > scale ( const Vec< T, N > & sx )

Scale transform.

Parameters

sx	Vector whose elements describe a scaling along each axis.

Returns: A transform representing a non-uniform scale along each axis.

◆ scale() [2/3]

template<typename T>

AffineTransform< T, 2 > scale	(	T	sx,
		T	sy )

Per-axis 2D scale

◆ scale() [3/3]

template<typename T>

AffineTransform< T, 3 > scale	(	T	sx,
		T	sy,
		T	sz )

Per-axis 3D scale

◆ transformation()

template<typename T, index_t N, MatrixLayout Lyt, StoragePolicy P>

AffineTransform< T, N > transformation ( const SimpleMatrix< T, N, N, Lyt, P > & mat )

Arbitrary transformation.

Parameters

mat	`N x N` matrix representing an arbitrary transformation.

Returns: A transformation by mat

◆ translation() [1/3]

template<typename T, index_t N>

AffineTransform< T, N > translation ( const Vec< T, N > & tx )

Translation transform

◆ translation() [2/3]

template<typename T>

AffineTransform< T, 2 > translation	(	T	tx,
		T	ty )

2D translation

◆ translation() [3/3]

template<typename T>

AffineTransform< T, 3 > translation	(	T	tx,
		T	ty,
		T	tz )

3D translation

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

geomc/linalg/AffineTransform.h

Public Types

Public Member Functions

Public Attributes

Static Public Attributes

Friends

Related Symbols

Detailed Description

Construction

Member Typedef Documentation

◆ point_t

Member Function Documentation

◆ apply()

◆ apply_inverse()

◆ apply_normal()

◆ inverse()

◆ operator*=()

◆ operator/=()

Friends And Related Symbol Documentation

◆ direction_align()

◆ operator*

◆ operator/

◆ rotation() [1/4]

◆ rotation() [2/4]

◆ rotation() [3/4]

◆ rotation() [4/4]

◆ scale() [1/3]

◆ scale() [2/3]

◆ scale() [3/3]

◆ transformation()

◆ translation() [1/3]

◆ translation() [2/3]

◆ translation() [3/3]