# DeepMind Robotics Transformations
Transformations is a pure python library for rigid-body transformations
including velocities and forces.
The objectives for this library are **simplicity** and **comprehensiveness**
across all canonical representations (euler, axis-angle, quaternion,
homogeneous matrices).
## Supported conversions:
* Quaternion to Rotation matrix, Axis-angle and Euler-angle
* Axis-angle to Quaternion, Rotation matrix and Euler-angle
* Rotation matrix to Quaternion, Axis-angle and Euler-angle
* Euler-angle to Quaternion, Rotation matrix and Axis-angle
## Quaternions:
Quaternions are represented with the scalar part (w) first, e.g.
```python
identity_quaternion = np.asarray([1, 0, 0, 0]) # w, i, j, k
```
Supported quaternion operations:
* Difference
* Distance
* Multiplication
* Inverse
* Conjugate
* Logarithm and Exponent
* Slerp (spherical linear interpolation)
* Rotation of a vector by a quaternion.
## Euler-angles
All 24 from-euler orderings are supported.
7 of 24 to-euler orderings are supported.
## Transforms
This library supports force and velocity transforms.
## Usage Example
```python
from dm_robotics.transformations import transformations as tr
# Convert a pose, euler angle into a homogeneous matrix (a 4x4 matrix):
hmat = tr.poseuler_to_hmat(
np.array([x, y, z, rot_x, rot_y, rot_z]), 'XYZ')
# Convert the homogeneous matrix to a twist (a 6 vector):
twist = tr.hmat_to_twist(hmat)
```
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"description": "# DeepMind Robotics Transformations\n\nTransformations is a pure python library for rigid-body transformations\nincluding velocities and forces.\n\nThe objectives for this library are **simplicity** and **comprehensiveness**\nacross all canonical representations (euler, axis-angle, quaternion,\nhomogeneous matrices).\n\n\n## Supported conversions:\n* Quaternion to Rotation matrix, Axis-angle and Euler-angle\n* Axis-angle to Quaternion, Rotation matrix and Euler-angle\n* Rotation matrix to Quaternion, Axis-angle and Euler-angle\n* Euler-angle to Quaternion, Rotation matrix and Axis-angle\n\n## Quaternions:\nQuaternions are represented with the scalar part (w) first, e.g.\n\n```python\nidentity_quaternion = np.asarray([1, 0, 0, 0]) # w, i, j, k\n```\n\nSupported quaternion operations:\n\n* Difference\n* Distance\n* Multiplication\n* Inverse\n* Conjugate\n* Logarithm and Exponent\n* Slerp (spherical linear interpolation)\n* Rotation of a vector by a quaternion.\n\n## Euler-angles\nAll 24 from-euler orderings are supported.\n7 of 24 to-euler orderings are supported.\n\n## Transforms\nThis library supports force and velocity transforms.\n\n## Usage Example\n\n```python\nfrom dm_robotics.transformations import transformations as tr\n\n# Convert a pose, euler angle into a homogeneous matrix (a 4x4 matrix):\nhmat = tr.poseuler_to_hmat(\n np.array([x, y, z, rot_x, rot_y, rot_z]), 'XYZ')\n\n# Convert the homogeneous matrix to a twist (a 6 vector):\ntwist = tr.hmat_to_twist(hmat)\n```\n\n",
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