warp.transform\_inverse
=======================

.. currentmodule:: warp._src.lang

.. function:: transform_inverse(xform: Transformation[Float]) -> Transformation[Float]

   .. wp-function-tags::
      :kernel: true
      :python: true
      :differentiable: true

   Return the inverse of ``xform``.
   
   The inverse maps points transformed by ``xform`` back to their original coordinate frame.
   Because :func:`~warp.quat_inverse` returns the conjugate, ``xform.q`` must have unit length;
   normalize it first if needed.
   
   :param xform: Transformation to invert. Its rotation quaternion must have unit length.
   
   :returns: The inverse transformation, with rotation ``quat_inverse(xform.q)`` and translation
             ``-quat_rotate(quat_inverse(xform.q), xform.p)``.
   
   .. rubric:: Example
   
   .. testcode::
   
       @wp.kernel
       def to_local(
           xform: wp.transform, points: wp.array[wp.vec3], out: wp.array[wp.vec3]
       ):
           i = wp.tid()
           out[i] = wp.transform_point(wp.transform_inverse(xform), points[i])
   
       xform = wp.transform(wp.vec3(0.0, 0.0, 5.0), wp.quat_rpy(0.0, 0.0, wp.pi / 2.0))
       points = wp.array([wp.vec3(-2.0, 1.0, 8.0)], dtype=wp.vec3)
       out = wp.empty(1, dtype=wp.vec3)
       wp.launch(to_local, dim=1, inputs=[xform, points], outputs=[out])
       print(np.round(out.numpy(), 3))
   
   .. testoutput::
   
       [[1. 2. 3.]]