euler

A library for Euler angle computation and conversion.

Installation

You can install the library from PyPI as follows:

pip install -U euler

Usage

The library is designed to be imported directly, analogously to NumPy:

>>> from numpy import pi
>>> import euler

The 12 possible axis triples available for Euler angles can be accessed as follows:

>>> euler.AXIS_TRIPLES
('xzx', 'xyx', 'yxy', 'yzy', 'zyz', 'zxz', 'xzy', 'xyz', 'yxz', 'yzx', 'zyx', 'zxy')

For static typing purposes, the corresponding literal type alias is euler.AxisTriple.

The euler.matrix_<pqr> functions, where <pqr> is an axis triple, can be used to compute a rotation matrix from Euler angles:

>>> h = euler.matrix_zxz(pi/2, pi/2, pi/2)
>>> h.round(3)
array([[-0., -0.,  1.],
       [ 0., -1., -0.],
       [ 1.,  0.,  0.]])

The euler.angles_<pqr> functions, where <pqr> is an axis triple, can be used to compute Euler angles from a rotation matrix:

>>> a, b, c = euler.angles_xyz(h)
>>> a, b, c
(3.141592653589793, 1.5707963267948966, 0.0)

The euler.convert_<pqr>_<uvw> functions, finally, can be used to convert Euler angles from axis triple <pqr> to axis triple <uvw>:

>>> euler.convert_zxz_xyz(pi/2, pi/2, pi/2)
(3.141592653589793, 1.5707963267948966, 0.0)

The functions euler.matrix, euler.angles and euler.convert serve an analogous purpose, but take the axis triple(s) as string parameter(s):

>>> h = euler.matrix("zxz", pi/2, pi/2, pi/2)
>>> h.round(3)
array([[-0., -0.,  1.],
       [ 0., -1., -0.],
       [ 1.,  0.,  0.]])
>>> a, b, c = euler.angles("xyz", h)
>>> a, b, c
(3.141592653589793, 1.5707963267948966, 0.0)
>>> euler.convert("zxz", "xyz", pi/2, pi/2, pi/2)
(3.141592653589793, 1.5707963267948966, 0.0)

Matrix calculations are originally taken from https://ntrs.nasa.gov/citations/19770019231, and have been independently verified (see the test folder).

License

LGPLv3 © NeverLocal Ltd