:py:mod:`rktl_planner.bezier_curve`
===================================

.. py:module:: rktl_planner.bezier_curve

.. autoapi-nested-parse::

   This module implements a Bezier curve class with various methods. A Bezier
   curve is defined by its order and control points.

   License:
     BSD 3-Clause License
     Copyright (c) 2023, Autonomous Robotics Club of Purdue (Purdue ARC)
     All rights reserved.



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

Classes
~~~~~~~

.. autoapisummary::

   rktl_planner.bezier_curve.BezierCurve




.. py:class:: BezierCurve(*args, **kwargs)

   A class representing a Bezier Curve and a duration. If `order` and `control_points` are given in
   kwargs, then it is used to initialize the instance. Otherwise, args is used to initialize the 
   instance. When not using kwargs, 4 options exist. Either a list of control points
   (geometry_msgs.msg.Points), the order of the bezier curve, both the order and the list of
   control points, or the control points as indiviudal arguments can be given.

   For example, All examples below give an instance of a `BezierCurve` of order 3. When points
   are specified, they are the control points used for the curve.

   ```python
   curve = BezierCurve(3)
   curve = BezierCurve(3, [Point(0, 0, 0), Point(1, 2, 3), Point(3, 2, 1), Point(4, 2, 0)])
   curve = BezierCurve([Point(0, 0, 0), Point(1, 2, 3), Point(3, 2, 1), Point(4, 2, 0)]))
   curve = BezierCurve(Point(0, 0, 0), Point(1, 2, 3), Point(3, 2, 1), Point(4, 2, 0)))
   curve = BezierCurve(order=3, control_points=[Point(0, 0, 0), Point(1, 2, 3), Point(3, 2, 1), Point(4, 2, 0)]))
   curve = BezierCurve(control_points=[Point(0, 0, 0), Point(1, 2, 3), Point(3, 2, 1), Point(4, 2, 0)]))```

   .. py:attribute:: _coefficients
      :value: [[1]]

      Table used internally to generate the coefficients of the bezier curve faster


   .. py:method:: __repr__()

      Returns a string representation of the instance.


   .. py:method:: __str__()

      Returns a string representation of the instance.


   .. py:method:: calc_coefficients()

      Calculates and returns the list of binomial coefficients for a given n.


   .. py:method:: at(t)

      Returns a Point object representing the location of the curve at the given parameter value `t`.


   .. py:method:: hodograph()

      Returns a `BezierCurve` object representing the hodograph (derivative) of the curve.


   .. py:method:: deriv(t)

      Returns a `geometry_msgs/Point` object representing the derivative of the curve at the given parameter value `t`.


   .. py:method:: de_casteljau(t)

      Splits this curve into 2 curves at the the point specified by `t`. Returns the two new `BezierCurve` objects.