Render Anmations in Python

This part describes the methods/classes we apply to render animations using Python’s PyRender interface.

render.python.utils._angle_from_tan(axis: str, other_axis: str, data: torch.Tensor, horizontal: bool, tait_bryan: bool) → torch.Tensor

Extract the first or third Euler angle from the two members of the matrix which are positive constant times its sine and cosine.

Parameters

• axis (str) – Axis label “X” or “Y or “Z” for the angle we are finding.

• other_axis (str) – Axis label “X” or “Y or “Z” for the middle axis in the convention.

• data (torch.Tensor) – Rotation matrices as tensor of shape (…, 3, 3).

• horizontal (bool) – Whether we are looking for the angle for the third axis, which means the relevant entries are in the same row of the rotation matrix. If not, they are in the same column.

• tait_bryan (bool) – Whether the first and third axes in the convention differ.

Returns

Euler Angles in radians for each matrix in data as a tensor of shape (…).

Return type

torch.Tensor

render.python.utils._axis_angle_rotation(axis: str, angle: torch.Tensor) → torch.Tensor

Return the rotation matrices for one of the rotations about an axis of which Euler angles describe, for each value of the angle given.

Parameters

• axis (str) – Axis label “X” or “Y or “Z”.

• angle (torch.Tensor) – any shape tensor of Euler angles in radians

Returns

Rotation matrices as tensor of shape (…, 3, 3).

Return type

torch.Tensor

render.python.utils._copysign(a: torch.Tensor, b: torch.Tensor) → torch.Tensor

Return a tensor where each element has the absolute value taken from the, corresponding element of a, with sign taken from the corresponding element of b. This is like the standard copysign floating-point operation, but is not careful about negative 0 and NaN.

Parameters

• a (torch.Tensor) – source tensor.

• b (torch.Tensor) – tensor whose signs will be used, of the same shape as a.

Returns

Tensor of the same shape as a with the signs of b.

Return type

torch.Tensor

render.python.utils._index_from_letter(letter: str) → int

return the index of axis from string

render.python.utils._sqrt_positive_part(x: torch.Tensor) → torch.Tensor

Returns torch.sqrt(torch.max(0, x)) but with a zero subgradient where x is 0.

Parameters

x (torch.Tensor) – input tensor

render.python.utils.axis_angle_to_matrix(axis_angle: torch.Tensor) → torch.Tensor

Convert rotations given as axis/angle to rotation matrices.

Parameters

axis_angle (torch.Tensor) – Rotations given as a vector in axis angle form, as a tensor of shape (…, 3), where the magnitude is the angle turned anticlockwise in radians around the vector’s direction.

Returns

Rotation matrices as tensor of shape (…, 3, 3).

Return type

torch.Tensor

render.python.utils.axis_angle_to_quaternion(axis_angle: torch.Tensor) → torch.Tensor

Convert rotations given as axis/angle to quaternions.

Parameters

axis_angle (torch.Tensor) – Rotations given as a vector in axis angle form, as a tensor of shape (…, 3), where the magnitude is the angle turned anticlockwise in radians around the vector’s direction.

Returns

quaternions with real part first, as tensor of shape (…, 4).

Return type

torch.Tensor

render.python.utils.euler_angles_to_matrix(euler_angles: torch.Tensor, convention: str) → torch.Tensor

Convert rotations given as Euler angles in radians to rotation matrices.

Parameters

• euler_angles (torch.Tensor) – Euler angles in radians as tensor of shape (…, 3).

• convention (str) – Convention string of three uppercase letters from {“X”, “Y”, and “Z”}.

Returns

Rotation matrices as tensor of shape (…, 3, 3).

Return type

torch.Tensor

render.python.utils.matrix_to_axis_angle(matrix: torch.Tensor) → torch.Tensor

Convert rotations given as rotation matrices to axis/angle.

Parameters

matrix (torch.Tensor) – Rotation matrices as tensor of shape (…, 3, 3).

Returns

Rotations given as a vector in axis angle form, as a tensor of shape (…, 3), where the magnitude is the angle turned anticlockwise in radians around the vector’s direction.

Return type

torch.Tensor

render.python.utils.matrix_to_euler_angles(matrix: torch.Tensor, convention: str) → torch.Tensor

Convert rotations given as rotation matrices to Euler angles in radians.

Parameters

• matrix (torch.Tensor) – Rotation matrices as tensor of shape (…, 3, 3).

• convention (str) – Convention string of three uppercase letters.

Returns

Euler angles in radians as tensor of shape (…, 3).

Return type

torch.Tensor

render.python.utils.matrix_to_quaternion(matrix: torch.Tensor) → torch.Tensor

Convert rotations given as rotation matrices to quaternions.

Parameters

matrix (torch.Tensor) – Rotation matrices as tensor of shape (…, 3, 3).

Returns

quaternions with real part first, as tensor of shape (…, 4).

Return type

torch.Tensor

render.python.utils.matrix_to_rotation_6d(matrix: torch.Tensor) → torch.Tensor

Converts rotation matrices to 6D rotation representation by Zhou et al. [1] by dropping the last row. Note that 6D representation is not unique.

Parameters

matrix (torch.Tensor) – batch of rotation matrices of size (x, 3, 3)

Returns

6D rotation representation, of size (x, 6)

Return type

torch.Tensor

[1] Zhou, Y., Barnes, C., Lu, J., Yang, J., & Li, H. On the Continuity of Rotation Representations in Neural Networks. IEEE Conference on Computer Vision and Pattern Recognition, 2019. Retrieved from http://arxiv.org/abs/1812.07035

render.python.utils.quaternion_apply(quaternion: torch.Tensor, point: torch.Tensor) → torch.Tensor

Apply the rotation given by a quaternion to a 3D point. Usual torch rules for broadcasting apply.

Parameters

• quaternion (torch.Tensor) – Tensor of quaternions, real part first, of shape (…, 4).

• point (torch.Tensor) – Tensor of 3D points of shape (…, 3).

Returns

Tensor of rotated points of shape (…, 3).

Return type

torch.Tensor

render.python.utils.quaternion_invert(quaternion: torch.Tensor) → torch.Tensor

Given a quaternion representing rotation, get the quaternion representing its inverse.

Param

quaternion: Quaternions as tensor of shape (…, 4), with real part first, which must be versors (unit quaternions).

Returns

The inverse, a tensor of quaternions of shape (…, 4).

Return type

torch.Tensor

render.python.utils.quaternion_multiply(a: torch.Tensor, b: torch.Tensor) → torch.Tensor

Multiply two quaternions representing rotations, returning the quaternion representing their composition, i.e. the versor with nonnegative real part. Usual torch rules for broadcasting apply.

Parameters

• a (torch.Tensor) – Quaternions as tensor of shape (…, 4), real part first.

• b (torch.Tensor) – Quaternions as tensor of shape (…, 4), real part first.

Returns

The product of a and b, a tensor of quaternions shape (…, 4).

Return type

torch.Tensor

render.python.utils.quaternion_raw_multiply(a: torch.Tensor, b: torch.Tensor) → torch.Tensor

Multiply two quaternions. Usual torch rules for broadcasting apply.

Parameters

• a (torch.Tensor) – Quaternions as tensor of shape (…, 4), real part first.

• b (torch.Tensor) – Quaternions as tensor of shape (…, 4), real part first.

Returns

The product of a and b, a tensor of quaternions shape (…, 4).

Return type

torch.Tensor

render.python.utils.quaternion_to_axis_angle(quaternions: torch.Tensor) → torch.Tensor

Convert rotations given as quaternions to axis/angle.

Parameters

quaternions (torch.Tensor) – quaternions with real part first, as tensor of shape (…, 4).

Returns

Rotations given as a vector in axis angle form, as a tensor of shape (…, 3), where the magnitude is the angle turned anticlockwise in radians around the vector’s direction.

Return type

torch.Tensor

render.python.utils.quaternion_to_matrix(quaternions: torch.Tensor) → torch.Tensor

Convert rotations given as quaternions to rotation matrices.

Parameters

quaternions (torch.Tensor) – quaternions as tensor of shape (…, 4), with real part first

Returns

Rotation matrices as tensor of shape (…, 3, 3).

Return type

torch.Tensor

render.python.utils.random_quaternions(n: int, dtype: Optional[torch.dtype] = None, device=None, requires_grad=False) → torch.Tensor

Generate random quaternions representing rotations, i.e. versors with nonnegative real part.

Parameters

• n (int) – Number of quaternions in a batch to return.

• dtype (Optional[torch.dtype]) – Type to return.

• device (str) – Desired device of returned tensor. Default: uses the current device for the default tensor type.

• requires_grad (bool) – Whether the resulting tensor should have the gradient flag set.

Returns

Quaternions as tensor of shape (N, 4).

Return type

torch.Tensor

render.python.utils.random_rotation(dtype: Optional[torch.dtype] = None, device=None, requires_grad=False) → torch.Tensor

Generate a single random 3x3 rotation matrix.

Parameters

• dtype (Optional[torch.dtype]) – Type to return

• device (str) – Device of returned tensor. Default: if None, uses the current device for the default tensor type

• requires_grad (bool) – Whether the resulting tensor should have the gradient flag set

Returns

Rotation matrix as tensor of shape (3, 3).

Return type

torch.Tensor

render.python.utils.random_rotations(n: int, dtype: Optional[torch.dtype] = None, device=None, requires_grad=False) → torch.Tensor

Generate random rotations as 3x3 rotation matrices.

Parameters

• n (int) – Number of rotation matrices in a batch to return.

• dtype (Optional[torch.dtype]) – Type to return.

• device (str) – Device of returned tensor. Default: if None, uses the current device for the default tensor type.

• requires_grad (bool) – Whether the resulting tensor should have the gradient flag set.

Returns

Rotation matrices as tensor of shape (n, 3, 3).

Return type

torch.Tensor

render.python.utils.rotation_6d_to_matrix(d6: torch.Tensor) → torch.Tensor

Converts 6D rotation representation by Zhou et al. [1] to rotation matrix using Gram–Schmidt orthogonalisation per Section B of [1].

Parameters

d6 (torch.Tensor) – 6D rotation representation, of size (x, 6)

Returns

batch of rotation matrices of size (x, 3, 3)

Return type

torch.Tensor

[1] Zhou, Y., Barnes, C., Lu, J., Yang, J., & Li, H. On the Continuity of Rotation Representations in Neural Networks. IEEE Conference on Computer Vision and Pattern Recognition, 2019. Retrieved from http://arxiv.org/abs/1812.07035

render.python.utils.standardize_quaternion(quaternions: torch.Tensor) → torch.Tensor

Convert a unit quaternion to a standard form: one in which the real part is non negative.

Parameters

quaternions (torch.Tensor) – Quaternions with real part first, as tensor of shape (…, 4).

Returns

Standardized quaternions as tensor of shape (…, 4).

Return type

torch.Tensor