Composition and Inverses
========================

Use spatial operations to compose poses/transforms, apply poses to points,
rotate free vectors, and convert transforms into frameless pose offsets.

In Python, ``*`` composes poses/transforms or applies them to points. In
TypeScript, use ``multiply()`` for composition and ``apply()`` for points.
``Pose * Pose`` chains frameless poses; ``Transform * Pose`` re-expresses a
pose in a new frame; ``Transform * Transform`` chains stamped transforms when
frame ids match (empty ids act as wildcards). ``inverse()`` undoes a pose or
transform; for :class:`~olo.spatial.Transform` the frame ids are swapped as
well. ``as_pose()`` / ``asPose()`` returns the equivalent frameless
:class:`~olo.spatial.Pose`. Use ``rotate()`` for :class:`~olo.spatial.Vector`
values when translation should not be applied.

.. tab-set::
    :sync-group: sdk-language

    .. tab-item:: Python
        :sync: python

        .. literalinclude:: scripts/spatial-compose.py
           :language: python

    .. tab-item:: TypeScript
        :sync: typescript

        .. literalinclude:: scripts/spatial-compose.ts
           :language: typescript