Xtpp

Basis values and derivatives sampled at piecewise breakpoints.

Developer documentation: this item describes internal implementation details.

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Discussion

This cached array stores the basis and its derivatives evaluated at the piecewise-polynomial breakpoints t_pp:

\[\mathrm{Xtpp}(i,j,d+1) = B_{j,S}^{(d)}(t_{\mathrm{pp},i};\tau).\]

ppCoefficientsFromSplineCoefficients uses Xtpp to convert the spline coefficients xi into the cached interval coefficients C, and evaluateFromPPCoefficients consumes the resulting PP representation for fast evaluation.

  [C, tpp, Xtpp] = BSpline.ppCoefficientsFromSplineCoefficients( ...
      xi=spline.xi, knotPoints=spline.knotPoints, S=spline.S);
  size(Xtpp)
  % numel(tpp) x numel(xi) x (S+1)