warp.closest\_point\_edge\_edge
===============================

.. function:: warp._src.lang.closest_point_edge_edge(p1: vec3f, q1: vec3f, p2: vec3f, q2: vec3f, epsilon: float32) -> vec3f

   .. hlist::
      :columns: 8

      * Kernel
      * Differentiable

   Find the closest points between two edges (line segments) ``[p1, q1]`` and ``[p2, q2]``.
   
   All four endpoints must be in the same coordinate space.
   
   :param p1: Start point of the first edge
   :param q1: End point of the first edge
   :param p2: Start point of the second edge
   :param q2: End point of the second edge
   :param epsilon: An edge whose squared length is ``<= epsilon`` is treated as a single point
                   (degenerate); its barycentric weight is then returned as 0.
   
   :returns: ``s`` in [0, 1] is the barycentric weight of the closest point on
             the first edge (the point is ``p1 + s * (q1 - p1)``), ``t`` in [0, 1] is the barycentric
             weight on the second edge (``p2 + t * (q2 - p2)``), and ``d`` is the distance between those
             two closest points.
   :rtype: A ``vec3`` ``(s, t, d)``
   
   .. rubric:: Example
   
   .. testcode::
   
       @wp.kernel
       def edge_edge(out: wp.array[wp.vec3]):
           p1, q1 = wp.vec3(0.0, 0.0, 0.0), wp.vec3(1.0, 0.0, 0.0)
           p2, q2 = wp.vec3(0.5, 1.0, 1.0), wp.vec3(0.5, 1.0, -1.0)
           out[0] = wp.closest_point_edge_edge(p1, q1, p2, q2, 1.0e-6)
   
       out = wp.zeros(1, dtype=wp.vec3)
       wp.launch(edge_edge, dim=1, inputs=[out])
       s, t, d = out.numpy()[0]
       print(f"s={s:.1f} t={t:.1f} d={d:.1f}")
   
   .. testoutput::
   
       s=0.5 t=0.5 d=1.0