kornia.geometry.conversions¶
- kornia.geometry.conversions.rad2deg(tensor)[source]¶
Function that converts angles from radians to degrees.
- Parameters
tensor (
Tensor) – Tensor of arbitrary shape.- Return type
- Returns
Tensor with same shape as input.
Example
>>> input = torch.tensor(3.1415926535) * torch.rand(1, 3, 3) >>> output = rad2deg(input)
- kornia.geometry.conversions.deg2rad(tensor)[source]¶
Function that converts angles from degrees to radians.
- Parameters
tensor (
Tensor) – Tensor of arbitrary shape.- Return type
- Returns
tensor with same shape as input.
Examples
>>> input = 360. * torch.rand(1, 3, 3) >>> output = deg2rad(input)
- kornia.geometry.conversions.pol2cart(rho, phi)[source]¶
Function that converts polar coordinates to cartesian coordinates.
- Parameters
- Return type
- Returns
Tensor with same shape as input.
Example
>>> rho = torch.rand(1, 3, 3) >>> phi = torch.rand(1, 3, 3) >>> x, y = pol2cart(rho, phi)
- kornia.geometry.conversions.cart2pol(x, y, eps=1e-08)[source]¶
Function that converts cartesian coordinates to polar coordinates.
- Parameters
rho – Tensor of arbitrary shape.
phi – Tensor of same arbitrary shape.
eps (
float, optional) – To avoid division by zero. Default:1e-08
- Return type
- Returns
Tensor with same shape as input.
Example
>>> x = torch.rand(1, 3, 3) >>> y = torch.rand(1, 3, 3) >>> rho, phi = cart2pol(x, y)
- kornia.geometry.conversions.convert_points_from_homogeneous(points, eps=1e-08)[source]¶
Function that converts points from homogeneous to Euclidean space.
- Parameters
- Return type
- Returns
the points in Euclidean space.
Examples
>>> input = torch.rand(2, 4, 3) # BxNx3 >>> output = convert_points_from_homogeneous(input) # BxNx2
- kornia.geometry.conversions.convert_points_to_homogeneous(points)[source]¶
Function that converts points from Euclidean to homogeneous space.
- Parameters
points (
Tensor) – the points to be transformed.- Return type
- Returns
the points in homogeneous coordinates.
Examples
>>> input = torch.rand(2, 4, 3) # BxNx3 >>> output = convert_points_to_homogeneous(input) # BxNx4
- kornia.geometry.conversions.convert_affinematrix_to_homography(A)[source]¶
Function that converts batch of affine matrices.
- Parameters
A (
Tensor) – the affine matrix with shape \((B,2,3)\).- Return type
- Returns
the homography matrix with shape of \((B,3,3)\).
Examples
>>> input = torch.rand(2, 2, 3) # Bx2x3 >>> output = convert_affinematrix_to_homography(input) # Bx3x3
- kornia.geometry.conversions.rotation_matrix_to_angle_axis(rotation_matrix)[source]¶
Convert 3x3 rotation matrix to Rodrigues vector in radians.
- Parameters
rotation_matrix (
Tensor) – rotation matrix.- Return type
- Returns
Rodrigues vector transformation.
- Shape:
Input: \((N, 3, 3)\)
Output: \((N, 3)\)
Example
>>> input = torch.rand(2, 3, 3) # Nx3x3 >>> output = rotation_matrix_to_angle_axis(input) # Nx3
- kornia.geometry.conversions.rotation_matrix_to_quaternion(rotation_matrix, eps=1e-08, order=QuaternionCoeffOrder.XYZW)[source]¶
Convert 3x3 rotation matrix to 4d quaternion vector.
The quaternion vector has components in (w, x, y, z) or (x, y, z, w) format.
Note
The (x, y, z, w) order is going to be deprecated in favor of efficiency.
- Parameters
- Return type
- Returns
the rotation in quaternion.
- Shape:
Input: \((*, 3, 3)\)
Output: \((*, 4)\)
Example
>>> input = torch.rand(4, 3, 3) # Nx3x3 >>> output = rotation_matrix_to_quaternion(input, eps=torch.finfo(input.dtype).eps, ... order=QuaternionCoeffOrder.WXYZ) # Nx4
- kornia.geometry.conversions.quaternion_to_angle_axis(quaternion, order=QuaternionCoeffOrder.XYZW)[source]¶
Convert quaternion vector to angle axis of rotation in radians.
The quaternion should be in (x, y, z, w) or (w, x, y, z) format.
Adapted from ceres C++ library: ceres-solver/include/ceres/rotation.h
- Parameters
quaternion (
Tensor) – tensor with quaternions.order (
QuaternionCoeffOrder, optional) – quaternion coefficient order. Note: ‘xyzw’ will be deprecated in favor of ‘wxyz’. Default:QuaternionCoeffOrder.XYZW
- Return type
- Returns
tensor with angle axis of rotation.
- Shape:
Input: \((*, 4)\) where * means, any number of dimensions
Output: \((*, 3)\)
Example
>>> quaternion = torch.rand(2, 4) # Nx4 >>> angle_axis = quaternion_to_angle_axis(quaternion) # Nx3
- kornia.geometry.conversions.quaternion_to_rotation_matrix(quaternion, order=QuaternionCoeffOrder.XYZW)[source]¶
Convert a quaternion to a rotation matrix.
The quaternion should be in (x, y, z, w) or (w, x, y, z) format.
- Parameters
quaternion (
Tensor) – a tensor containing a quaternion to be converted. The tensor can be of shape \((*, 4)\).order (
QuaternionCoeffOrder, optional) – quaternion coefficient order. Note: ‘xyzw’ will be deprecated in favor of ‘wxyz’. Default:QuaternionCoeffOrder.XYZW
- Return type
- Returns
the rotation matrix of shape \((*, 3, 3)\).
Example
>>> quaternion = torch.tensor((0., 0., 0., 1.)) >>> quaternion_to_rotation_matrix(quaternion, order=QuaternionCoeffOrder.WXYZ) tensor([[-1., 0., 0.], [ 0., -1., 0.], [ 0., 0., 1.]])
- kornia.geometry.conversions.quaternion_log_to_exp(quaternion, eps=1e-08, order=QuaternionCoeffOrder.XYZW)[source]¶
Apply exponential map to log quaternion.
The quaternion should be in (x, y, z, w) or (w, x, y, z) format.
- Parameters
quaternion (
Tensor) – a tensor containing a quaternion to be converted. The tensor can be of shape \((*, 3)\).order (
QuaternionCoeffOrder, optional) – quaternion coefficient order. Note: ‘xyzw’ will be deprecated in favor of ‘wxyz’. Default:QuaternionCoeffOrder.XYZW
- Return type
- Returns
the quaternion exponential map of shape \((*, 4)\).
Example
>>> quaternion = torch.tensor((0., 0., 0.)) >>> quaternion_log_to_exp(quaternion, eps=torch.finfo(quaternion.dtype).eps, ... order=QuaternionCoeffOrder.WXYZ) tensor([1., 0., 0., 0.])
- kornia.geometry.conversions.quaternion_exp_to_log(quaternion, eps=1e-08, order=QuaternionCoeffOrder.XYZW)[source]¶
Apply the log map to a quaternion.
The quaternion should be in (x, y, z, w) format.
- Parameters
quaternion (
Tensor) – a tensor containing a quaternion to be converted. The tensor can be of shape \((*, 4)\).eps (
float, optional) – A small number for clamping. Default:1e-08order (
QuaternionCoeffOrder, optional) – quaternion coefficient order. Note: ‘xyzw’ will be deprecated in favor of ‘wxyz’. Default:QuaternionCoeffOrder.XYZW
- Return type
- Returns
the quaternion log map of shape \((*, 3)\).
Example
>>> quaternion = torch.tensor((1., 0., 0., 0.)) >>> quaternion_exp_to_log(quaternion, eps=torch.finfo(quaternion.dtype).eps, ... order=QuaternionCoeffOrder.WXYZ) tensor([0., 0., 0.])
- kornia.geometry.conversions.angle_axis_to_quaternion(angle_axis, order=QuaternionCoeffOrder.XYZW)[source]¶
Convert an angle axis to a quaternion.
The quaternion vector has components in (x, y, z, w) or (w, x, y, z) format.
Adapted from ceres C++ library: ceres-solver/include/ceres/rotation.h
- Parameters
angle_axis (
Tensor) – tensor with angle axis in radians.order (
QuaternionCoeffOrder, optional) – quaternion coefficient order. Note: ‘xyzw’ will be deprecated in favor of ‘wxyz’. Default:QuaternionCoeffOrder.XYZW
- Return type
- Returns
tensor with quaternion.
- Shape:
Input: \((*, 3)\) where * means, any number of dimensions
Output: \((*, 4)\)
Example
>>> angle_axis = torch.rand(2, 3) # Nx3 >>> quaternion = angle_axis_to_quaternion(angle_axis, order=QuaternionCoeffOrder.WXYZ) # Nx4
- kornia.geometry.conversions.angle_axis_to_rotation_matrix(angle_axis)[source]¶
Convert 3d vector of axis-angle rotation to 3x3 rotation matrix.
- Parameters
angle_axis (
Tensor) – tensor of 3d vector of axis-angle rotations in radians.- Return type
- Returns
tensor of 3x3 rotation matrices.
- Shape:
Input: \((N, 3)\)
Output: \((N, 3, 3)\)
Example
>>> input = torch.rand(1, 3) # Nx3 >>> output = angle_axis_to_rotation_matrix(input) # Nx3x3
- kornia.geometry.conversions.denormalize_pixel_coordinates(pixel_coordinates, height, width, eps=1e-08)[source]¶
Denormalize pixel coordinates.
The input is assumed to be -1 if on extreme left, 1 if on extreme right (x = w-1).
- Parameters
- Return type
- Returns
the denormalized pixel coordinates.
- kornia.geometry.conversions.normalize_pixel_coordinates(pixel_coordinates, height, width, eps=1e-08)[source]¶
Normalize pixel coordinates between -1 and 1.
Normalized, -1 if on extreme left, 1 if on extreme right (x = w-1).
- Parameters
- Return type
- Returns
the normalized pixel coordinates.
- kornia.geometry.conversions.denormalize_pixel_coordinates3d(pixel_coordinates, depth, height, width, eps=1e-08)[source]¶
Denormalize pixel coordinates.
The input is assumed to be -1 if on extreme left, 1 if on extreme right (x = w-1).
- Parameters
- Return type
- Returns
the denormalized pixel coordinates.
- kornia.geometry.conversions.normalize_pixel_coordinates3d(pixel_coordinates, depth, height, width, eps=1e-08)[source]¶
Normalize pixel coordinates between -1 and 1.
Normalized, -1 if on extreme left, 1 if on extreme right (x = w-1).
- Parameters
- Return type
- Returns
the normalized pixel coordinates.
- kornia.geometry.conversions.normalize_quaternion(quaternion, eps=1e-12)[source]¶
Normalize a quaternion.
The quaternion should be in (x, y, z, w) format.
- Parameters
- Return type
- Returns
the normalized quaternion of shape \((*, 4)\).
Example
>>> quaternion = torch.tensor((1., 0., 1., 0.)) >>> normalize_quaternion(quaternion) tensor([0.7071, 0.0000, 0.7071, 0.0000])