t_pp

Piecewise-polynomial breakpoint locations.

Developer documentation: this item describes internal implementation details.

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Discussion

These are the breakpoints of the cached interval representation. If Nk = numel(knotPoints), then

\[t_{\mathrm{pp}} = \tau_{K:(N_k-K+1)}.\]

On interval i, the PP cache works in the local coordinate u = t - t_pp(i) for t \in [t_pp(i), t_pp(i+1)]. The functions ppCoefficientsFromSplineCoefficients and evaluateFromPPCoefficients are the main consumers of this breakpoint vector.

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

  size(t_pp) = length(knotPoints) - 2*K + 1