rocket_league.math
==================

.. py:module:: rocket_league.math

.. autoapi-nested-parse::

   A set of useful mathematical operations.



Functions
---------

.. autoapisummary::

   rocket_league.math.euclidean_distance
   rocket_league.math.vector_projection
   rocket_league.math.scalar_projection
   rocket_league.math.magnitude
   rocket_league.math.normalize
   rocket_league.math.cosine_similarity
   rocket_league.math.quat_to_euler
   rocket_league.math.quat_to_rot_mtx
   rocket_league.math.rotation_to_quaternion
   rocket_league.math.euler_to_rotation
   rocket_league.math.rand_uvec3
   rocket_league.math.rand_vec3


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

.. py:function:: euclidean_distance(x: numpy.ndarray, y: numpy.ndarray) -> float

   Returns the Euclidean distance between two vectors.

   :param x: A numpy array of size n.
   :param y: A numpy array of size n.

   :return: A float representing the distance between the two vectors.


.. py:function:: vector_projection(a: numpy.ndarray, b: numpy.ndarray) -> numpy.ndarray

   Returns the vector projection of a vector `a` onto another vector `b`.

   :param a: A numpy array of size n.
   :param b: A numpy array of size n.

   :return: A numpy array of size n representing the vector projection.


.. py:function:: scalar_projection(a: numpy.ndarray, b: numpy.ndarray) -> float

   Returns the scalar projection of a vector `a` onto another vector `b`.

   :param a: A numpy array of size n.
   :param b: A numpy array of size n.

   :return: A float representing the scalar projection.


.. py:function:: magnitude(vec: numpy.ndarray) -> float

   Returns the magnitude of a vector.

   :param vec: A numpy array of size n.

   :return: A float representing the magnitude of the vector.


.. py:function:: normalize(vec: numpy.ndarray)

   Returns a unit vector with the same direction as the input vector.

   :param vec: A numpy array of size n.

   :return: A numpy array of size n.


.. py:function:: cosine_similarity(a: numpy.ndarray, b: numpy.ndarray) -> float

   Computes the cosine similarity between two vectors.

   :param a: A numpy array of size n.
   :param b: A numpy array of size n.

   :return: A float representing the cosine similarity.


.. py:function:: quat_to_euler(quat: numpy.ndarray) -> numpy.ndarray

   Converts a quaternion to Euler angles.

   :param quat: A numpy array of size 4 representing the quaternion.

   :return: A numpy array of size 3 representing the pitch, yaw, and roll angles.


.. py:function:: quat_to_rot_mtx(quat: numpy.ndarray) -> numpy.ndarray

   Converts a quaternion to a rotation matrix.

   :param quat: A numpy array of size 4 representing the quaternion.

   :return: A numpy array of size 3x3 representing the rotation matrix.


.. py:function:: rotation_to_quaternion(m: numpy.ndarray) -> numpy.ndarray

   Converts a rotation matrix to a quaternion.

   :param m: A numpy array of size 3x3 representing the rotation matrix.

   :return: A numpy array of size 4 representing the quaternion.


.. py:function:: euler_to_rotation(pyr: numpy.ndarray) -> numpy.ndarray

   Converts Euler angles to a rotation.

   :param pyr: A numpy array of size 3 representing the pitch, yaw, and roll angles.

   :return: A numpy array of size 3x3 representing the rotation matrix.


.. py:function:: rand_uvec3(rng: numpy.random.Generator = np.random) -> numpy.ndarray

   Generates a random 3-dimensional unit vector.

   :param rng: The random number generator to use.

   :return: A numpy array of size 3.


.. py:function:: rand_vec3(max_norm: float, rng: numpy.random.Generator = np.random) -> numpy.ndarray

   Generates a random 3-dimensional vector with a size between 0 and max_norm.

   :param max_norm: The maximum norm of the vector.
   :param rng: The random number generator to use.

   :return: A numpy array of size 3.