aerosandbox.modeling.splines.bezier
===================================

.. py:module:: aerosandbox.modeling.splines.bezier


Functions
---------

.. autoapisummary::

   aerosandbox.modeling.splines.bezier.quadratic_bezier_patch_from_tangents


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

.. py:function:: quadratic_bezier_patch_from_tangents(t, x_a, x_b, y_a, y_b, dydx_a, dydx_b)

   Computes sampled points in 2D space from a quadratic Bezier spline defined by endpoints and end-tangents.

   Note: due to the inherent nature of a quadratic Bezier curve, curvature will be strictly one-sided - in other
   words, this will not make "S"-shaped curves. This means that you should be aware that bad values of dydx at
   either endpoint might cause this curvature to flip, which would result in the curve "going backwards" at one
   endpoint.

   Also, note that, in general, points will not be spaced evenly in x, y, or arc length s.

   :param t:
   :param x_a: The x-coordinate of the first endpoint.
   :param x_b: The x-coordinate of the second endpoint.
   :param y_a: The y-coordinate of the first endpoint.
   :param y_b: The y-coordinate of the second endpoint.
   :param dydx_a: The derivative of y with respect to x at the first endpoint.
   :param dydx_b: The derivative of y with respect to x at the second endpoint.

   :returns: A scalar or numpy array of scalars representing the x-coordinates of the sampled points.
             y: A scalar or numpy array of scalars representing the y-coordinates of the sampled points.
   :rtype: x

   Usage:
       >>> x_a, x_b = 0, 10
       >>> y_a, y_b = 0, 5
       >>> dydx_a, dydx_b = 0.5, -0.5
       >>>
       >>> t = np.linspace(0, 1, 50)
       >>> x, y = quadratic_bezier_patch_from_tangents(
       >>>     t=t,
       >>>     x_a=x_a,
       >>>     x_b=x_b,
       >>>     y_a=y_a,
       >>>     y_b=y_b,
       >>>     dydx_a=dydx_a,
       >>>     dydx_b=dydx_b
       >>> )