warp.quaternion
===============

.. currentmodule:: warp._src.lang

.. function:: quaternion(dtype: Float = ...) -> Quaternion[Float]

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

   Construct a zero-initialized quaternion.
   
   Quaternions store their components in ``(x, y, z, w)`` order, where ``x``, ``y``, and ``z`` form
   the vector (imaginary) part and ``w`` is the scalar (real) part. For the identity rotation, use
   :func:`~warp.quat_identity`.
   
   :param dtype: Scalar type of the components. Defaults to ``float32``.
   
   :returns: The quaternion ``(0, 0, 0, 0)``.
   

.. function:: quaternion(x: Float, y: Float, z: Float, w: Float, dtype: Float = ...) -> Quaternion[Float]
   :noindex:

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

   Construct a quaternion from its components.
   
   All arguments must have the same scalar type, which must match ``dtype`` when it is given.
   
   :param x: ``x`` component of the vector (imaginary) part.
   :param y: ``y`` component of the vector (imaginary) part.
   :param z: ``z`` component of the vector (imaginary) part.
   :param w: Scalar (real) part.
   :param dtype: Scalar type of the components, inferred from the other arguments when omitted.
   
   :returns: The quaternion ``(x, y, z, w)``.
   

.. function:: quaternion(ijk: Vector[Float, Literal[3]], real: Float, dtype: Float = ...) -> Quaternion[Float]
   :noindex:

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

   Construct a quaternion from its vector and scalar parts.
   
   All arguments must have the same scalar type, which must match ``dtype`` when it is given.
   
   :param ijk: Vector (imaginary) part, stored as the ``x``, ``y``, and ``z`` components.
   :param real: Scalar (real) part, stored as the ``w`` component.
   :param dtype: Scalar type of the components, inferred from the other arguments when omitted.
   
   :returns: The quaternion ``(ijk[0], ijk[1], ijk[2], real)``.
   

.. function:: quaternion(quat: Quaternion[Float], dtype: Float = ...) -> Quaternion[Float]
   :noindex:

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

   Construct a copy of a quaternion, optionally converting its scalar type.
   
   :param quat: Quaternion to copy.
   :param dtype: Scalar type of the result. Defaults to the scalar type of ``quat``.
   
   :returns: A quaternion with the components of ``quat``, converted to ``dtype``.