warp.spatial\_vector
====================

.. currentmodule:: warp._src.lang

.. function:: spatial_vector(dtype: Float = ...) -> Vector[Float, Literal[6]]

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

   Return a zero 6D spatial vector.
   
   See the overload that accepts ``w`` and ``v`` for an example.
   
   :param dtype: Scalar type of the components. Defaults to ``float32``.
   
   :returns: The zero spatial vector.
   

.. function:: spatial_vector(w: Vector[Float, Literal[3]], v: Vector[Float, Literal[3]], dtype: Float = ...) -> Vector[Float, Literal[6]]
   :noindex:

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

   Construct a 6D spatial vector from the two 3D vectors ``w`` and ``v``.
   
   A spatial vector can represent a twist ``(angular velocity, linear velocity)`` or a wrench
   ``(torque, force)``. Warp does not distinguish these interpretations at the type level. Both
   vectors must have the same scalar type.
   
   :param w: First 3D part: angular velocity for a twist or torque for a wrench.
   :param v: Last 3D part: linear velocity for a twist or force for a wrench.
   :param dtype: Scalar type of the components, inferred from ``w`` and ``v`` when omitted.
   
   :returns: The spatial vector ``(w.x, w.y, w.z, v.x, v.y, v.z)``.
   
   .. rubric:: Example
   
   .. testcode::
   
       @wp.kernel
       def make_twists(out: wp.array[wp.spatial_vector]):
           # spinning about the z axis while moving along x
           out[0] = wp.spatial_vector(wp.vec3(0.0, 0.0, 2.0), wp.vec3(1.0, 0.0, 0.0))
           out[1] = wp.spatial_vector(0.0, 0.0, 2.0, 1.0, 0.0, 0.0)
   
       out = wp.empty(2, dtype=wp.spatial_vector)
       wp.launch(make_twists, dim=1, outputs=[out])
       print(out.numpy())
   
   .. testoutput::
   
       [[0. 0. 2. 1. 0. 0.]
        [0. 0. 2. 1. 0. 0.]]
   

.. function:: spatial_vector(wx: Float, wy: Float, wz: Float, vx: Float, vy: Float, vz: Float, dtype: Float = ...) -> Vector[Float, Literal[6]]
   :noindex:

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

   Construct a 6D spatial vector from six scalar components.
   
   See the overload that accepts ``w`` and ``v`` for the twist and wrench interpretations. All
   values must have the same scalar type.
   
   :param wx: First component of the first 3D part.
   :param wy: Second component of the first 3D part.
   :param wz: Third component of the first 3D part.
   :param vx: First component of the last 3D part.
   :param vy: Second component of the last 3D part.
   :param vz: Third component of the last 3D part.
   :param dtype: Scalar type of the components, inferred from the arguments when omitted.
   
   :returns: The spatial vector ``(wx, wy, wz, vx, vy, vz)``.
   
   See the overload that accepts ``w`` and ``v`` for an example.