K

Spline order K, where polynomial degree is S = K - 1.

---

Discussion

The order is the number of coefficients in each local polynomial piece. On any one interval, a spline of order K is a polynomial of the form

\[p_i(t) = a_{i,0} + a_{i,1}(t-t_i) + \cdots + a_{i,K-1}(t-t_i)^{K-1}.\]

So K=1 gives piecewise constants, K=2 gives piecewise linear splines, and K=4 gives cubic splines. The matching degree property is S, with S = K - 1.

  spline = BSpline(S=3, knotPoints=knotPoints, xi=xi);
  spline.K
  % returns 4, meaning each piece is cubic