warp.quat\_from\_matrix
=======================

.. currentmodule:: warp._src.lang

.. function:: quat_from_matrix(mat: Matrix[Float, Literal[3], Literal[3]]) -> Quaternion[Float]

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

   Return the rotation quaternion of the rotation matrix ``mat``.
   
   :param mat: Rotation matrix that rotates column vectors as ``mat @ v``. It must be orthonormal with a
               determinant of ``+1``; otherwise, the result is unspecified. Matrices using row-vector
               conventions must be transposed first.
   
   :returns: A unit quaternion ``q`` such that ``quat_to_matrix(q)`` equals ``mat``. The sign of ``q`` is
             unspecified.
   

.. function:: quat_from_matrix(mat: Matrix[Float, Literal[4], Literal[4]]) -> Quaternion[Float]
   :noindex:

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

   Return the rotation quaternion of the top-left 3x3 block of ``mat``.
   
   :param mat: Transformation matrix whose top-left 3x3 block rotates column vectors. That block must be
               orthonormal with a determinant of ``+1``; otherwise, the result is unspecified. The
               remaining entries, such as a translation, are ignored.
   
   :returns: A unit quaternion ``q`` such that ``quat_to_matrix(q)`` equals the top-left 3x3 block of
             ``mat``. The sign of ``q`` is unspecified.