aerosandbox.modeling.splines.hermite
====================================

.. py:module:: aerosandbox.modeling.splines.hermite


Attributes
----------

.. autoapisummary::

   aerosandbox.modeling.splines.hermite.x


Functions
---------

.. autoapisummary::

   aerosandbox.modeling.splines.hermite.linear_hermite_patch
   aerosandbox.modeling.splines.hermite.cubic_hermite_patch
   aerosandbox.modeling.splines.hermite.cosine_hermite_patch


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

.. py:function:: linear_hermite_patch(x, x_a, x_b, f_a, f_b)

   Computes the linear Hermite polynomial patch that passes through the given endpoints f_a and f_b.

   :param x: Scalar or array of values at which to evaluate the patch.
   :param x_a: The x-coordinate of the first endpoint.
   :param x_b: The x-coordinate of the second endpoint.
   :param f_a: The function value at the first endpoint.
   :param f_b: The function value at the second endpoint.

   :returns: The value of the patch evaluated at the input x. Returns a scalar if x is a scalar, or an array if x is an array.


.. py:function:: cubic_hermite_patch(x, x_a, x_b, f_a, f_b, dfdx_a, dfdx_b, extrapolation = 'continue')

   Computes the cubic Hermite polynomial patch that passes through the given endpoints and endpoint derivatives.

   :param x: Scalar or array of values at which to evaluate the patch.
   :param x_a: The x-coordinate of the first endpoint.
   :param x_b: The x-coordinate of the second endpoint.
   :param f_a: The function value at the first endpoint.
   :param f_b: The function value at the second endpoint.
   :param dfdx_a: The derivative of the function with respect to x at the first endpoint.
   :param dfdx_b: The derivative of the function with respect to x at the second endpoint.
   :param extrapolation: A string indicating how to handle extrapolation outside of the domain [x_a, x_b]. Valid values are
                         "continue", which continues the patch beyond the endpoints, and "clip", which clips the patch at the
                         endpoints. Default is "continue".

   :returns: The value of the patch evaluated at the input x. Returns a scalar if x is a scalar, or an array if x is an array.


.. py:function:: cosine_hermite_patch(x, x_a, x_b, f_a, f_b, dfdx_a, dfdx_b, extrapolation = 'continue')

   Computes a Hermite patch (i.e., values + derivatives at endpoints) that uses a cosine function to blend between
   linear segments.

   The end result is conceptually similar to a cubic Hermite patch, but computation is faster and the patch is
   $C^\infty$-continuous.

   :param x: Scalar or array of values at which to evaluate the patch.
   :param x_a: The x-coordinate of the first endpoint.
   :param x_b: The x-coordinate of the second endpoint.
   :param f_a: The function value at the first endpoint.
   :param f_b: The function value at the second endpoint.
   :param dfdx_a: The derivative of the function with respect to x at the first endpoint.
   :param dfdx_b: The derivative of the function with respect to x at the second endpoint.
   :param extrapolation: A string indicating how to handle extrapolation outside of the domain [x_a, x_b]. Valid values are
                         "continue", which continues the patch beyond the endpoints, and "linear", which extends the patch
                         linearly at the endpoints. Default is "continue".

   :returns: The value of the patch evaluated at the input x. Returns a scalar if x is a scalar, or an array if x is an array.


.. py:data:: x