C

Piecewise-polynomial coefficients for interval evaluation.

Developer documentation: this item describes internal implementation details.

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Discussion

For interval i, let u = t - t_pp(i). The cached PP form stores

\[f_i(u) = \sum_{m=0}^{S} \frac{c_{i,m}}{m!} u^m,\]

where row i of C contains the coefficients in descending power order so they can be passed to polyval after factorial scaling. The helper ppCoefficientsFromSplineCoefficients builds C, and evaluateFromPPCoefficients evaluates it.

  [C, tpp] = BSpline.ppCoefficientsFromSplineCoefficients( ...
      xi=spline.xi, knotPoints=spline.knotPoints, S=spline.S);
  xq = BSpline.evaluateFromPPCoefficients(queryPoints=tQuery, C=C, tpp=tpp);

  size(C) = [length(t_pp)-1, K]