boinor.core.util
================

.. py:module:: boinor.core.util

.. autoapi-nested-parse::

   module containing auxiliary functions for the core sub-package



Functions
---------

.. autoapisummary::

   boinor.core.util.rotation_matrix
   boinor.core.util.alinspace
   boinor.core.util.spherical_to_cartesian
   boinor.core.util.cartesian_to_spherical
   boinor.core.util.planetocentric_to_AltAz


Module Contents
---------------

.. py:function:: rotation_matrix(angle, axis)

   create 3D rotation matrix for rotation by angle around axis


.. py:function:: alinspace(start, stop=None, num=50, endpoint=True)

   Return increasing, evenly spaced angular values over a specified interval.


.. py:function:: spherical_to_cartesian(v)

   Compute cartesian coordinates from spherical coordinates (norm, colat, long). This function is vectorized.

   .. math::

      v = norm \cdot \begin{bmatrix}
      \sin(colat)\cos(long)\\
      \sin(colat)\sin(long)\\
      \cos(colat)\\
      \end{bmatrix}

   :param v: Spherical coordinates in 3D (norm, colat, long). Angles must be in radians.
   :type v: numpy.ndarray

   :returns: **v** -- Cartesian coordinates (x,y,z)
   :rtype: numpy.ndarray


.. py:function:: cartesian_to_spherical(v)

   Compute spherical coordinates (norm, colat, long) from cartesian coordinates (x,y,z).
   This function is vectorized. The coordinates are also called (radius, inclination, azimuth).

   .. math::

      norm = \sqrt{x^2 + y^2 + z^2}

      colat = \arccos{\frac{z}{norm}}

      lon = \arctan2(y,x) \mod 2 \pi

   :param v: Cartesian coordinates in 3D (x, y, z).
   :type v: np.array

   :returns: **v** -- Spherical coordinates in 3D (norm, colat, long) where norm in [0, inf),
             colat in [0, pi] and long in [0, 2pi).
   :rtype: np.array


.. py:function:: planetocentric_to_AltAz(theta, phi)

   Defines transformation matrix to convert from Planetocentric coordinate system
   to the Altitude-Azimuth system.

   .. math::
      t\_matrix = \begin{bmatrix}
      -\sin(theta) & \cos(theta) & 0\\
      -\sin(phi)\cdot\cos(theta) & -\sin(phi)\cdot\sin(theta) & \cos(phi)\\
      \cos(phi)\cdot\cos(theta) & \cos(phi)\cdot\sin(theta) & \sin(phi)
      \end{bmatrix}

   :param theta: Local sidereal time
   :type theta: float
   :param phi: Planetodetic latitude
   :type phi: float

   :returns: **t_matrix** -- Transformation matrix
   :rtype: numpy.ndarray