xi

Spline coefficients as an Mx1 vector.

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Description

Real valued property with dimension \(coefficientIndex\) and no units.

Discussion

The coefficient vector weights the terminated B-spline basis in

\[f(t) = x_{\mathrm{Mean}} + x_{\mathrm{Std}} \sum_{j=1}^{M} \xi_j B_{j,S}(t;\tau).\]

So xi(j) is the weight on the jth basis function. The basis itself comes from matrixForDataPoints, and evaluation is handled by valueAtPoints. For a knot sequence tau and order K, the coefficient count is M = numel(knotPoints) - K.

  X = BSpline.matrixForDataPoints(t, knotPoints=knotPoints, S=3);
  xi = X \ x;
  spline = BSpline(S=3, knotPoints=knotPoints, xi=xi);