Defining a B-spline for a given set of control points

In the next section, we will look at how to solve B-splines given some controlled data.

Getting ready

We need to follow some instructions and install the prerequisites.

How to do it…

1. Univariate the spline in the B-spline basis
2. Execute the following: S(x)=∑j=0n−1cjBj,k;t(x)S(x)=∑j=0n−1cjBj,k;t(x)
3. Where it's Bj,k;tBj,k;t are B-spline basis functions of degree k and knots t

4. We can use the following parameters:

Parameters

t: ndarray, shape (n+k+1,) knots. c: ndarray, shape (>=n, ...). Spline coefficients. k: int. B-spline order. extrapolate: bool, optional. Whether to extrapolate beyond the base interval, t[k] .. t[n], or to return NaN values. If True, extrapolates the first and last polynomial pieces of B-spline functions active on the base interval. Default is True. axis: int; optional. Interpolation axis. The default is zero.

How it works ...

Here, we construct a quadratic spline function on the base interval 2 <= x <= 4 and compare it with...