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Class Affine3

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();

Source: opencv2/core/affine.hpp.

Hierarchy

  • Affine3

Index

Constructors

Properties

Methods

Constructors

constructor

  • The resulting 4x4 matrix is Rodrigues vector. Combines all constructors above. Supports 4x4, 3x4, 3x3, 1x3, 3x1 sizes of data matrix.

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

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

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

    Returns Affine3

  • The resulting 4x4 matrix is Rodrigues vector. Combines all constructors above. Supports 4x4, 3x4, 3x3, 1x3, 3x1 sizes of data matrix.

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

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

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

    Parameters

    Returns Affine3

  • The resulting 4x4 matrix is

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

    Parameters

    • R: Mat3

      3x3 rotation matrix.

    • Optional t: Vec3

      3x1 translation vector.

    Returns Affine3

  • Rodrigues vector.

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

    Parameters

    • rvec: Vec3

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

    • Optional t: Vec3

      3x1 translation vector.

    Returns Affine3

  • 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: Mat

      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.

    • Optional t: Vec3

      3x1 translation vector.

    Returns Affine3

  • The resulting 4x4 matrix is Rodrigues vector. Combines all constructors above. Supports 4x4, 3x4, 3x3, 1x3, 3x1 sizes of data matrix.

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

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

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

    Parameters

    Returns Affine3

Properties

matrix

matrix: Mat4

Methods

cast

concatenate

inv

linear

rotate

rotation

  • 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: Mat3

      3x3 rotation matrix.

    Returns Mat3

  • Rodrigues vector.

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

    Parameters

    • rvec: Vec3

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

    Returns Vec3

  • 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: Mat

      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.

    Returns Mat

  • the upper left 3x3 part

    Returns Mat3

rvec

  • Rodrigues vector.

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

    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)].

    Returns Vec3

translate

translation

  • 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: Vec3

      3x1 translation vector.

    Returns Vec3

  • the upper right 3x1 part

    Returns Vec3

Static Identity

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