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

.. currentmodule:: warp._src.lang

.. function:: spatial_cross_dual(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 force cross product of twist ``a`` and wrench ``b``.
   
   This is the wrench counterpart of :func:`~warp.spatial_cross`: the second operand and result are
   both wrenches. "Dual" refers to the wrench-twist dot product, which computes mechanical power.
   The operation is not antisymmetric, so its operands are not interchangeable. Both arguments
   must have the same scalar type.
   
   :param a: Twist represented as a spatial vector.
   :param b: Wrench represented as a spatial vector.
   
   :returns: The wrench ``(w x n + v x f, w x f)``, where ``a = (w, v)`` and ``b = (n, f)``.
   
   .. rubric:: Example
   
   .. testcode::
   
       @wp.kernel
       def compute_spatial_cross_dual(
           twists: wp.array[wp.spatial_vector],
           wrenches: wp.array[wp.spatial_vector],
           out: wp.array[wp.spatial_vector],
       ):
           i = wp.tid()
           out[i] = wp.spatial_cross_dual(twists[i], wrenches[i])
   
       twists = wp.array([wp.spatial_vector(0.0, 0.0, 1.0, 1.0, 0.0, 0.0)], dtype=wp.spatial_vector)
       wrenches = wp.array([wp.spatial_vector(0.0, 0.0, 0.0, 0.0, 1.0, 0.0)], dtype=wp.spatial_vector)
       out = wp.empty(1, dtype=wp.spatial_vector)
       wp.launch(compute_spatial_cross_dual, dim=1, inputs=[twists, wrenches], outputs=[out])
       print(out.numpy())
   
   .. testoutput::
   
       [[ 0.  0.  1. -1.  0.  0.]]