cv::Affine3< T > Class Template Reference

Affine transform. More...

#include "affine.hpp"

Public Types
typedef T	float_type
typedef Matx< float_type, 3, 3 >	Mat3
typedef Matx< float_type, 4, 4 >	Mat4
typedef Vec< float_type, 3 >	Vec3

Public Member Functions
	Affine3 ()
	Default constructor. It represents a 4x4 identity matrix. More...
	Affine3 (const Mat4 &affine)
	Augmented affine matrix. More...
	Affine3 (const Mat3 &R, const Vec3 &t=Vec3::all(0))
	Affine3 (const Vec3 &rvec, const Vec3 &t=Vec3::all(0))
	Affine3 (const Mat &data, const Vec3 &t=Vec3::all(0))
	Affine3 (const float_type *vals)
	From 16-element array. More...
template<typename Y >
Affine3< Y >	cast () const
Affine3	concatenate (const Affine3 &affine) const
	a.concatenate(affine) is equivalent to affine * a; More...
Affine3	inv (int method=cv::DECOMP_SVD) const
void	linear (const Mat3 &L)
Mat3	linear () const
template<typename Y >
	operator Affine3< Y > () const
Affine3	rotate (const Mat3 &R) const
	a.rotate(R) is equivalent to Affine(R, 0) * a; More...
Affine3	rotate (const Vec3 &rvec) const
	a.rotate(rvec) is equivalent to Affine(rvec, 0) * a; More...
void	rotation (const Mat3 &R)
void	rotation (const Vec3 &rvec)
void	rotation (const Mat &data)
Mat3	rotation () const
Vec3	rvec () const
Affine3	translate (const Vec3 &t) const
	a.translate(t) is equivalent to Affine(E, t) * a, where E is an identity matrix More...
void	translation (const Vec3 &t)
Vec3	translation () const

Static Public Member Functions
static Affine3	Identity ()
	Create an 4x4 identity transform. More...

Public Attributes
Mat4	matrix

Detailed Description

template<typename T>
class cv::Affine3< T >

Affine transform.

It represents a 4x4 homogeneous transformation matrix \(T\)

\[T = \begin{bmatrix} R & t\\ 0 & 1\\ \end{bmatrix} \]

where \(R\) is a 3x3 rotation matrix and \(t\) is a 3x1 translation vector.

You can specify \(R\) either by a 3x3 rotation matrix or by a 3x1 rotation vector, which is converted to a 3x3 rotation matrix by the Rodrigues formula.

To construct a matrix \(T\) representing first rotation around the axis \(r\) with rotation angle \(|r|\) in radian (right hand rule) and then translation by the vector \(t\), you can use

cv::Vec3f r, t;
cv::Affine3f T(r, t);

If you already have the rotation matrix \(R\), then you can use

cv::Matx33f R;
cv::Affine3f T(R, t);

To extract the rotation matrix \(R\) from \(T\), use

cv::Matx33f R = T.rotation();

To extract the translation vector \(t\) from \(T\), use

cv::Vec3f t = T.translation();

To extract the rotation vector \(r\) from \(T\), use

cv::Vec3f r = T.rvec();

Note that since the mapping from rotation vectors to rotation matrices is many to one. The returned rotation vector is not necessarily the one you used before to set the matrix.

If you have two transformations \(T = T_1 * T_2\), use

cv::Affine3f T, T1, T2;
T = T2.concatenate(T1);

To get the inverse transform of \(T\), use

cv::Affine3f T, T_inv;
T_inv = T.inv();

Member Typedef Documentation

float_type

template<typename T>

typedef T cv::Affine3< T >::float_type

Mat3

template<typename T>

typedef Matx<float_type, 3, 3> cv::Affine3< T >::Mat3

Mat4

template<typename T>

typedef Matx<float_type, 4, 4> cv::Affine3< T >::Mat4

Vec3

template<typename T>

typedef Vec<float_type, 3> cv::Affine3< T >::Vec3

Constructor & Destructor Documentation

Affine3() [1/6]

template<typename T>

cv::Affine3< T >::Affine3

(

)

Default constructor. It represents a 4x4 identity matrix.

Affine3() [2/6]

template<typename T>

cv::Affine3< T >::Affine3

(

const Mat4 &

affine

)

Augmented affine matrix.

Affine3() [3/6]

template<typename T>

cv::Affine3< T >::Affine3	(	const Mat3 &	R,
		const Vec3 &	t = Vec3::all(0)
	)

The resulting 4x4 matrix is

\[ \begin{bmatrix} R & t\\ 0 & 1\\ \end{bmatrix} \]

Parameters

R	3x3 rotation matrix.
t	3x1 translation vector.

Affine3() [4/6]

template<typename T>

cv::Affine3< T >::Affine3	(	const Vec3 &	rvec,
		const Vec3 &	t = Vec3::all(0)
	)

Rodrigues vector.

The last row of the current matrix is set to [0,0,0,1].

Parameters

rvec	3x1 rotation vector. Its direction indicates the rotation axis and its length indicates the rotation angle in radian (using right hand rule).
t	3x1 translation vector.

Affine3() [5/6]

template<typename T>

cv::Affine3< T >::Affine3 ( const Mat &  data, const Vec3 &  t = Vec3::all(0)  )

explicit

Combines all constructors above. Supports 4x4, 3x4, 3x3, 1x3, 3x1 sizes of data matrix.

The last row of the current matrix is set to [0,0,0,1] when data is not 4x4.

Parameters

data	1-channel matrix. when it is 4x4, it is copied to the current matrix and t is not used. When it is 3x4, it is copied to the upper part 3x4 of the current matrix and t is not used. When it is 3x3, it is copied to the upper left 3x3 part of the current matrix. When it is 3x1 or 1x3, it is treated as a rotation vector and the Rodrigues formula is used to compute a 3x3 rotation matrix.
t	3x1 translation vector. It is used only when data is neither 4x4 nor 3x4.

Affine3() [6/6]

template<typename T>

cv::Affine3< T >::Affine3 ( const float_type *  vals )

explicit

From 16-element array.

Member Function Documentation

cast()

template<typename T>

template<typename Y >

Affine3<Y> cv::Affine3< T >::cast

(

)

const

concatenate()

template<typename T>

Affine3 cv::Affine3< T >::concatenate

(

const Affine3< T > &

affine

)

const

a.concatenate(affine) is equivalent to affine * a;

Identity()

template<typename T>

static Affine3 cv::Affine3< T >::Identity ( )

static

Create an 4x4 identity transform.

inv()

template<typename T>

Affine3 cv::Affine3< T >::inv

(

int

method = cv::DECOMP_SVD

)

const

Returns

the inverse of the current matrix.

linear() [1/2]

template<typename T>

void cv::Affine3< T >::linear

(

const Mat3 &

L

)

Copy the 3x3 matrix L to the upper left part of the current matrix

It sets the upper left 3x3 part of the matrix. The remaining part is unaffected.

Parameters

L	3x3 matrix.

linear() [2/2]

template<typename T>

Mat3 cv::Affine3< T >::linear

(

)

const

Returns

the upper left 3x3 part

operator Affine3< Y >()

template<typename T>

template<typename Y >

cv::Affine3< T >::operator Affine3< Y >

(

)

const

rotate() [1/2]

template<typename T>

Affine3 cv::Affine3< T >::rotate

(

const Mat3 &

R

)

const

a.rotate(R) is equivalent to Affine(R, 0) * a;

rotate() [2/2]

template<typename T>

Affine3 cv::Affine3< T >::rotate

(

const Vec3 &

rvec

)

const

a.rotate(rvec) is equivalent to Affine(rvec, 0) * a;

rotation() [1/4]

template<typename T>

void cv::Affine3< T >::rotation

(

const Mat3 &

R

)

Rotation matrix.

Copy the rotation matrix to the upper left 3x3 part of the current matrix. The remaining elements of the current matrix are not changed.

Parameters

R	3x3 rotation matrix.

rotation() [2/4]

template<typename T>

void cv::Affine3< T >::rotation

(

const Vec3 &

rvec

)

Rodrigues vector.

It sets the upper left 3x3 part of the matrix. The remaining part is unaffected.

Parameters

rvec	3x1 rotation vector. The direction indicates the rotation axis and its length indicates the rotation angle in radian (using the right thumb convention).

rotation() [3/4]

template<typename T>

void cv::Affine3< T >::rotation

(

const Mat &

data

)

Combines rotation methods above. Supports 3x3, 1x3, 3x1 sizes of data matrix.

It sets the upper left 3x3 part of the matrix. The remaining part is unaffected.

Parameters

data	1-channel matrix. When it is a 3x3 matrix, it sets the upper left 3x3 part of the current matrix. When it is a 1x3 or 3x1 matrix, it is used as a rotation vector. The Rodrigues formula is used to compute the rotation matrix and sets the upper left 3x3 part of the current matrix.

rotation() [4/4]

template<typename T>

Mat3 cv::Affine3< T >::rotation

(

)

const

Returns

the upper left 3x3 part

rvec()

template<typename T>

Vec3 cv::Affine3< T >::rvec

(

)

const

Rodrigues vector.

Returns

a vector representing the upper left 3x3 rotation matrix of the current matrix.

Warning

Since the mapping between rotation vectors and rotation matrices is many to one, this function returns only one rotation vector that represents the current rotation matrix, which is not necessarily the same one set by rotation(const Vec3& rvec).

translate()

template<typename T>

Affine3 cv::Affine3< T >::translate

(

const Vec3 &

t

)

const

a.translate(t) is equivalent to Affine(E, t) * a, where E is an identity matrix

translation() [1/2]

template<typename T>

void cv::Affine3< T >::translation

(

const Vec3 &

t

)

Copy t to the first three elements of the last column of the current matrix

It sets the upper right 3x1 part of the matrix. The remaining part is unaffected.

Parameters

t	3x1 translation vector.

translation() [2/2]

template<typename T>

Vec3 cv::Affine3< T >::translation

(

)

const

Returns

the upper right 3x1 part

Member Data Documentation

matrix

template<typename T>

Mat4 cv::Affine3< T >::matrix

---

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

• core/include/opencv2/core/affine.hpp