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Use S^3 for unit sphere
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AlexanderFabisch committed Oct 28, 2024
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2 changes: 1 addition & 1 deletion doc/source/user_guide/rotations.rst
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Expand Up @@ -314,7 +314,7 @@ Read `this paper <https://arxiv.org/pdf/1801.07478.pdf>`_ for details about
the two conventions and why Hamilton's convention should be used. Section VI A
gives further useful hints to identify which convention is used.

The unit quaternion space :math:`\mathbb{S}^3` can be used to represent
The unit quaternion space :math:`S^3` can be used to represent
orientations with an encoding based on the rotation axis and angle.
A rotation quaternion is a four-dimensional unit vector (versor)
:math:`\boldsymbol{\hat{q}}`.
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2 changes: 1 addition & 1 deletion pytransform3d/rotations/_quaternions.py
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Expand Up @@ -158,7 +158,7 @@ def q_prod_vector(q, v):
We use Hamilton's quaternion multiplication.
To apply the rotation defined by a unit quaternion :math:`\boldsymbol{q}
\in \mathbb{S}^3` to a vector :math:`\boldsymbol{v} \in \mathbb{R}^3`, we
\in S^3` to a vector :math:`\boldsymbol{v} \in \mathbb{R}^3`, we
first represent the vector as a quaternion: we set the scalar part to 0 and
the vector part is exactly the original vector
:math:`\left(\begin{array}{c}0\\\boldsymbol{v}\end{array}\right) \in
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