e3x.so3.rotations.alignment_rotation

e3x.so3.rotations.alignment_rotation(u, v)[source]

Rotation matrix that aligns \(\vec{u}\) with \(\vec{v}\).

Calculates the \(3\times3\) rotation matrix that aligns the vector \(\vec{u}\) with the vector \(\vec{v}\) using the shortest possible arc. When \(\vec{u}\) and \(\vec{v}\) are exactly antiparallel, there are infinitely many paths with the same arc length and one of them is chosen at random.

Example

>>> import jax.numpy as jnp
>>> import e3x
>>> u = jnp.asarray([1., 0., 0.])  # Unit vector in x-direction.
>>> v = jnp.asarray([0., 1., 0.])  # Unit vector in y-direction.
>>> jnp.round(u @ e3x.so3.alignment_rotation(u, v), decimals=3)
Array([0., 1., 0.], dtype=float32)

Parameters:

u (<class 'Float[Array, '... 3']'>) – Vector \(\vec{u}\).
v (<class 'Float[Array, '... 3']'>) – Vector \(\vec{v}\).

Return type:

<class 'Float[Array, '... 3 3']'>

Returns:

The \(3\times3\) rotation matrix.