# Source code for kornia.geometry.linalg

import torch

from kornia.testing import check_is_tensor

from .conversions import convert_points_from_homogeneous, convert_points_to_homogeneous

__all__ = [
"compose_transformations",
"relative_transformation",
"inverse_transformation",
"transform_points",
]

[docs]def compose_transformations(trans_01: torch.Tensor, trans_12: torch.Tensor) -> torch.Tensor:
r"""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

"""
if not torch.is_tensor(trans_01):
raise TypeError(f"Input trans_01 type is not a torch.Tensor. Got {type(trans_01)}")

if not torch.is_tensor(trans_12):
raise TypeError(f"Input trans_12 type is not a torch.Tensor. Got {type(trans_12)}")

if not ((trans_01.dim() in (2, 3)) and (trans_01.shape[-2:] == (4, 4))):
raise ValueError("Input trans_01 must be a of the shape Nx4x4 or 4x4." " Got {}".format(trans_01.shape))

if not ((trans_12.dim() in (2, 3)) and (trans_12.shape[-2:] == (4, 4))):
raise ValueError("Input trans_12 must be a of the shape Nx4x4 or 4x4." " Got {}".format(trans_12.shape))

if not trans_01.dim() == trans_12.dim():
raise ValueError(f"Input number of dims must match. Got {trans_01.dim()} and {trans_12.dim()}")

# unpack input data
rmat_01: torch.Tensor = trans_01[..., :3, :3]  # Nx3x3
rmat_12: torch.Tensor = trans_12[..., :3, :3]  # Nx3x3
tvec_01: torch.Tensor = trans_01[..., :3, -1:]  # Nx3x1
tvec_12: torch.Tensor = trans_12[..., :3, -1:]  # Nx3x1

# compute the actual transforms composition
rmat_02: torch.Tensor = torch.matmul(rmat_01, rmat_12)
tvec_02: torch.Tensor = torch.matmul(rmat_01, tvec_12) + tvec_01

# pack output tensor
trans_02: torch.Tensor = torch.zeros_like(trans_01)
trans_02[..., :3, 0:3] += rmat_02
trans_02[..., :3, -1:] += tvec_02
trans_02[..., -1, -1:] += 1.0
return trans_02

[docs]def inverse_transformation(trans_12):
r"""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
"""
if not torch.is_tensor(trans_12):
raise TypeError(f"Input type is not a torch.Tensor. Got {type(trans_12)}")
if not ((trans_12.dim() in (2, 3)) and (trans_12.shape[-2:] == (4, 4))):
raise ValueError(f"Input size must be a Nx4x4 or 4x4. Got {trans_12.shape}")
# unpack input tensor
rmat_12: torch.Tensor = trans_12[..., :3, 0:3]  # Nx3x3
tvec_12: torch.Tensor = trans_12[..., :3, 3:4]  # Nx3x1

# compute the actual inverse
rmat_21: torch.Tensor = torch.transpose(rmat_12, -1, -2)
tvec_21: torch.Tensor = torch.matmul(-rmat_21, tvec_12)

# pack to output tensor
trans_21: torch.Tensor = torch.zeros_like(trans_12)
trans_21[..., :3, 0:3] += rmat_21
trans_21[..., :3, -1:] += tvec_21
trans_21[..., -1, -1:] += 1.0
return trans_21

[docs]def relative_transformation(trans_01: torch.Tensor, trans_02: torch.Tensor) -> torch.Tensor:
r"""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
"""
if not torch.is_tensor(trans_01):
raise TypeError(f"Input trans_01 type is not a torch.Tensor. Got {type(trans_01)}")
if not torch.is_tensor(trans_02):
raise TypeError(f"Input trans_02 type is not a torch.Tensor. Got {type(trans_02)}")
if not ((trans_01.dim() in (2, 3)) and (trans_01.shape[-2:] == (4, 4))):
raise ValueError("Input must be a of the shape Nx4x4 or 4x4." " Got {}".format(trans_01.shape))
if not ((trans_02.dim() in (2, 3)) and (trans_02.shape[-2:] == (4, 4))):
raise ValueError("Input must be a of the shape Nx4x4 or 4x4." " Got {}".format(trans_02.shape))
if not trans_01.dim() == trans_02.dim():
raise ValueError(f"Input number of dims must match. Got {trans_01.dim()} and {trans_02.dim()}")
trans_10: torch.Tensor = inverse_transformation(trans_01)
trans_12: torch.Tensor = compose_transformations(trans_10, trans_02)
return trans_12

[docs]def transform_points(trans_01: torch.Tensor, points_1: torch.Tensor) -> torch.Tensor:
r"""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
"""
check_is_tensor(trans_01)
check_is_tensor(points_1)
if not trans_01.shape == points_1.shape and trans_01.shape != 1:
raise ValueError(
"Input batch size must be the same for both tensors or 1."
f"Got {trans_01.shape} and {points_1.shape}"
)
if not trans_01.shape[-1] == (points_1.shape[-1] + 1):
raise ValueError(
"Last input dimensions must differ by one unit"
f"Got{trans_01} and {points_1}"
)

# We reshape to BxNxD in case we get more dimensions, e.g., MxBxNxD
shape_inp = list(points_1.shape)
points_1 = points_1.reshape(-1, points_1.shape[-2], points_1.shape[-1])
trans_01 = trans_01.reshape(-1, trans_01.shape[-2], trans_01.shape[-1])
# We expand trans_01 to match the dimensions needed for bmm
trans_01 = torch.repeat_interleave(trans_01, repeats=points_1.shape // trans_01.shape, dim=0)
# to homogeneous
points_1_h = convert_points_to_homogeneous(points_1)  # BxNxD+1
# transform coordinates
points_0_h = torch.bmm(points_1_h, trans_01.permute(0, 2, 1))
points_0_h = torch.squeeze(points_0_h, dim=-1)
# to euclidean
points_0 = convert_points_from_homogeneous(points_0_h)  # BxNxD
# reshape to the input shape
shape_inp[-2] = points_0.shape[-2]
shape_inp[-1] = points_0.shape[-1]
points_0 = points_0.reshape(shape_inp)
return points_0

# TODO:
# - project_points: from opencv