warp.spatial\_cross
===================

.. currentmodule:: warp._src.lang

.. function:: spatial_cross(a: Vector[Float, Literal[6]], b: Vector[Float, Literal[6]]) -> Vector[Float, Literal[6]]

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

   Return the spatial cross product of ``a`` and ``b``, treating both as twists.
   
   The operation is antisymmetric: ``spatial_cross(a, b) == -spatial_cross(b, a)``. It computes
   velocity-product terms used in spatial-acceleration calculations for moving coordinate frames.
   Use :func:`~warp.spatial_cross_dual` when ``b`` is a wrench. Both arguments must have the same
   scalar type.
   
   :param a: First spatial vector, interpreted as a twist.
   :param b: Second spatial vector, interpreted as a twist.
   
   :returns: The spatial vector ``(w_a x w_b, v_a x w_b + w_a x v_b)``, where
             ``a = (w_a, v_a)`` and ``b = (w_b, v_b)``.
   
   .. rubric:: Example
   
   .. testcode::
   
       @wp.kernel
       def compute_spatial_cross(
           a: wp.array[wp.spatial_vector],
           b: wp.array[wp.spatial_vector],
           out: wp.array[wp.spatial_vector],
       ):
           i = wp.tid()
           out[i] = wp.spatial_cross(a[i], b[i])
   
       a = wp.array([wp.spatial_vector(0.0, 0.0, 1.0, 0.0, 0.0, 0.0)], dtype=wp.spatial_vector)
       b = wp.array([wp.spatial_vector(0.0, 0.0, 0.0, 1.0, 0.0, 0.0)], dtype=wp.spatial_vector)
       out = wp.empty(1, dtype=wp.spatial_vector)
       wp.launch(compute_spatial_cross, dim=1, inputs=[a, b], outputs=[out])
       print(out.numpy())
   
   .. testoutput::
   
       [[0. 0. 0. 0. 1. 0.]]