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Adds a cosine hermite patch to spline modeling routines
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peterdsharpe committed Apr 9, 2024
1 parent 9dab4a0 commit 92ad4a4
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48 changes: 48 additions & 0 deletions aerosandbox/modeling/splines/hermite.py
Original file line number Diff line number Diff line change
Expand Up @@ -70,6 +70,54 @@ def cubic_hermite_patch(
)


def cosine_hermite_patch(
x: Union[float, np.ndarray],
x_a: float,
x_b: float,
f_a: float,
f_b: float,
dfdx_a: float,
dfdx_b: float,
extrapolation: str = 'continue',
) -> Union[float, np.ndarray]:
"""
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.
Args:
x: Scalar or array of values at which to evaluate the patch.
x_a: The x-coordinate of the first endpoint.
x_b: The x-coordinate of the second endpoint.
f_a: The function value at the first endpoint.
f_b: The function value at the second endpoint.
dfdx_a: The derivative of the function with respect to x at the first endpoint.
dfdx_b: The derivative of the function with respect to x at the second endpoint.
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.
"""
t = (x - x_a) / (x_b - x_a) # Nondimensional distance along the patch
if extrapolation == 'continue':
pass
elif extrapolation == 'linear':
t = np.clip(t, 0, 1)
else:
raise ValueError("Bad value of `extrapolation`!")

l1 = (x - x_a) * dfdx_a + f_a
l2 = (x - x_b) * dfdx_b + f_b

b = 0.5 + 0.5 * np.cos(np.pi * t)

return b * l1 + (1 - b) * l2


if __name__ == '__main__':
import matplotlib.pyplot as plt
import aerosandbox.tools.pretty_plots as p
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