colour.kernel_cardinal_spline#

colour.kernel_cardinal_spline(x: ArrayLike, a: float = 0.5, b: float = 0.0) → NDArrayFloat[source]#

Return the cardinal spline kernel evaluated at given samples.

Notable cardinal spline \(a\) and \(b\) parameterizations:

Catmull-Rom: \((a=0.5, b=0)\)
Cubic B-Spline: \((a=0, b=1)\)
Mitchell-Netravalli: \((a=\cfrac{1}{3}, b=\cfrac{1}{3})\)

Parameters:

x (ArrayLike) – Samples at which to evaluate the cardinal spline kernel.
a (float) – \(a\) control parameter.
b (float) – \(b\) control parameter.

Returns:

The cardinal spline kernel evaluated at given samples.

Return type:

numpy.ndarray

References

[BB09]

Examples

>>> kernel_cardinal_spline(np.linspace(0, 1, 10))  
array([ 1.        ,  0.9711934...,  0.8930041...,  0.7777777...,  0.6378600...,
        0.4855967...,  0.3333333...,  0.1934156...,  0.0781893...,  0.        ])