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edddZeedddZdS ) N)Tensor)KORNIA_CHECK_IS_TENSORcheck_is_tensor ) convert_points_from_homogeneous convert_points_to_homogeneous)compose_transformationsrelative_transformationinverse_transformationtransform_pointspoint_line_distance squared_norm)trans_01trans_12returnc C s t | s tdt| t |s8tdt| | dv rV| jdd dksftd| j| dv r|jdd dkstd|j| | kstd | d
| | d dd dd f }|d dd dd f }| d dd d
df }|d dd d
df }t ||}t ||| }t | }|d dd dd f |7 < |d dd d
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df d7 < |S )az Function that composes two homogeneous transformations.
.. math::
T_0^{2} = \begin{bmatrix} R_0^1 R_1^{2} & R_0^{1} t_1^{2} + t_0^{1} \\
\mathbf{0} & 1\end{bmatrix}
Args:
trans_01: tensor with the homogeneous transformation from
a reference frame 1 respect to a frame 0. The tensor has must have a
shape of :math:`(N, 4, 4)` or :math:`(4, 4)`.
trans_12: tensor with the homogeneous transformation from
a reference frame 2 respect to a frame 1. The tensor has must have a
shape of :math:`(N, 4, 4)` or :math:`(4, 4)`.
Returns:
the transformation between the two frames with shape :math:`(N, 4, 4)` or :math:`(4, 4)`.
Example::
>>> trans_01 = torch.eye(4) # 4x4
>>> trans_12 = torch.eye(4) # 4x4
>>> trans_02 = compose_transformations(trans_01, trans_12) # 4x4
/Input trans_01 type is not a torch.Tensor. Got z/Input trans_12 type is not a torch.Tensor. Got N r z:Input trans_01 must be a of the shape Nx4x4 or 4x4. Got {}z:Input trans_12 must be a of the shape Nx4x4 or 4x4. Got {}%Input number of dims must match. Got and .r r ?)
torch is_tensor TypeErrortypedimshape
ValueErrorformatmatmul
zeros_like) r r Zrmat_01rmat_12Ztvec_01tvec_12Zrmat_02Ztvec_02trans_02 r) _/var/www/html/stable-diffusion-webui/venv/lib/python3.9/site-packages/kornia/geometry/linalg.pyr s*
r c C s t | s tdt| | dv r:| jdd dksJtd| j | dddd df }| ddddd
f }t |d d}t | |}t | }|dddd df |7 < |dddd df |7 < |dd d df d 7 < |S )
a Function that inverts a 4x4 homogeneous transformation
:math:`T_1^{2} = \begin{bmatrix} R_1 & t_1 \\ \mathbf{0} & 1 \end{bmatrix}`
The inverse transformation is computed as follows:
.. math::
T_2^{1} = (T_1^{2})^{-1} = \begin{bmatrix} R_1^T & -R_1^T t_1 \\
\mathbf{0} & 1\end{bmatrix}
Args:
trans_12: transformation tensor of shape :math:`(N, 4, 4)` or :math:`(4, 4)`.
Returns:
tensor with inverted transformations with shape :math:`(N, 4, 4)` or :math:`(4, 4)`.
Example:
>>> trans_12 = torch.rand(1, 4, 4) # Nx4x4
>>> trans_21 = inverse_transformation(trans_12) # Nx4x4
z&Input type is not a torch.Tensor. Got r r Nr z'Input size must be a Nx4x4 or 4x4. Got .r r r r r )
r r r r r r! r" Z transposer$ r% )r r& r' Zrmat_21Ztvec_21Ztrans_21r) r) r* r
J s
r
)r r( r c C s t | s tdt| t |s8tdt| | dv rV| jdd dksftd| j| dv r|jdd dkstd|j| | kstd| d | t| }t ||}|S )
a Function that computes the relative homogeneous transformation from a
reference transformation :math:`T_1^{0} = \begin{bmatrix} R_1 & t_1 \\
\mathbf{0} & 1 \end{bmatrix}` to destination :math:`T_2^{0} =
\begin{bmatrix} R_2 & t_2 \\ \mathbf{0} & 1 \end{bmatrix}`.
The relative transformation is computed as follows:
.. math::
T_1^{2} = (T_0^{1})^{-1} \cdot T_0^{2}
Args:
trans_01: reference transformation tensor of shape :math:`(N, 4, 4)` or :math:`(4, 4)`.
trans_02: destination transformation tensor of shape :math:`(N, 4, 4)` or :math:`(4, 4)`.
Returns:
the relative transformation between the transformations with shape :math:`(N, 4, 4)` or :math:`(4, 4)`.
Example::
>>> trans_01 = torch.eye(4) # 4x4
>>> trans_02 = torch.eye(4) # 4x4
>>> trans_12 = relative_transformation(trans_01, trans_02) # 4x4
r z/Input trans_02 type is not a torch.Tensor. Got r r Nr z1Input must be a of the shape Nx4x4 or 4x4. Got {}r r )
r r r r r r! r" r# r
r )r r( Ztrans_10r r) r) r* r s s
r )r points_1r c C s2 t | t | | jd |jd ksJ| jd dkrJtd| j d|j | jd |jd d ksvtd| d| t|j}|d|jd |jd }| d| jd | jd } tj| |jd | jd dd} t|}t|| dd d}tj
|dd
}t |}|jd |d< |jd |d< ||}|S ) a4 Function that applies transformations to a set of points.
Args:
trans_01 (torch.Tensor): tensor for transformations of shape
:math:`(B, D+1, D+1)`.
points_1 (torch.Tensor): tensor of points of shape :math:`(B, N, D)`.
Returns:
torch.Tensor: tensor of N-dimensional points.
Shape:
- Output: :math:`(B, N, D)`
Examples:
>>> points_1 = torch.rand(2, 4, 3) # BxNx3
>>> trans_01 = torch.eye(4).view(1, 4, 4) # Bx4x4
>>> points_0 = transform_points(trans_01, points_1) # BxNx3
r r z)pointlineepsr c C s t | t | | jd dvr.td| j |jd dksLtd|j |d | d |d | d |d }|d d
d f jdd }||| S )
a] Return the distance from points to lines.
Args:
point: (possibly homogeneous) points :math:`(*, N, 2 or 3)`.
line: lines coefficients :math:`(a, b, c)` with shape :math:`(*, N, 3)`, where :math:`ax + by + c = 0`.
eps: Small constant for safe sqrt.
Returns:
the computed distance with shape :math:`(*, N)`.
r r z&pts must be a (*, 2 or 3) tensor. Got r z#lines must be a (*, 3) tensor. Got ).r ).r ).r .Nr r, )r r! r" absZnorm)r/ r0 r1 numerator denominatorr) r) r* r s ,r )xr c C s | ddS )z$Return the squared norm of a vector.r r )powsum)r5 r) r) r* r
s r
)r. )r r Zkornia.testingr r Z conversionsr r __all__r r
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