splinebox.basis_functions.

B2

class splinebox.basis_functions.B2

Basis function for a quadratic (\(2^{\text{nd}}\) order) polynomial basis spline.

For a detailed theoretical description – including the equation and a plot of the function – refer to the Polynomial basis (B-spline) section in the documentation.

The constructor does not require any arguments.

Methods

__call__(t[, derivative])	Evaluate the function at position(s) t.
filter_periodic(s)	Returns a filtered version of the input s, used to convert knots into control points for a closed spline.
filter_symmetric(s)	Returns a filtered version of the input s, used to convert knots into control points for an open spline.
refinement_mask()	This function is needed for local refinement (see [Badoual2016]).

Examples

>>> import splinebox
>>> import numpy as np
>>> import matplotlib.pyplot as plt

Create a basis function object:

>>> basis_function = splinebox.basis_functions.B2()

Evaluate the basis function at a single position:

>>> basis_function(0.5)
0.5

Evaluate the basis function at multiple positions simultaneously:

>>> t = np.array([-0.2, 0, 0.5])
>>> basis_function(t)
array([0.71, 0.75, 0.5 ])

Compute the first derivative of the basis function at multiple positions:

>>> basis_function(t, derivative=1)
array([ 0.4, -0. , -1. ])

>>> t = np.linspace(-2.1, 2.1, 500)
>>> plt.plot(t, basis_function(t))
>>> plt.show()