evaluateFromPPCoefficients

Evaluate a cached piecewise-polynomial spline representation.

Developer documentation: this item describes internal implementation details.

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Declaration

 f = evaluateFromPPCoefficients(options)

Parameters

• options.queryPoints points at which to evaluate the splines
• options.C polynomial coefficients to be used in polyval, size(C) = [length(tpp)-1, K]
• options.tpp piece-wise polynomial intervals
• options.D number of derivatives

Returns

• f array the same size as queryPoints

Discussion

On interval i, let u = queryPoints - tpp(i). This function evaluates

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

where the interval coefficients \(c_{i,m}\) are stored in C.

  xq = BSpline.evaluateFromPPCoefficients(queryPoints=tQuery, C=C, tpp=tpp);
  dxq = BSpline.evaluateFromPPCoefficients(queryPoints=tQuery, C=C, tpp=tpp, D=1);