BSpline

Create a one-dimensional spline from degree, knots, and coefficients.

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Declaration

 spline = BSpline(options)

Parameters

• options.S spline degree
• options.knotPoints knot points
• options.xi (optional) spline coefficients
• options.Xtpp optional cached basis values at piecewise breakpoints
• options.xMean optional additive output offset
• options.xStd optional multiplicative output scale

Returns

• spline BSpline instance

Discussion

Use this constructor when you already know the terminated knot sequence knotPoints and the coefficient vector xi.

The constructed spline is

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

  knotPoints = [0; 0; 0; 0; 1; 1; 1; 1];
  xi = [1; -0.5; 0.25; 0];
  spline = BSpline(S=3, knotPoints=knotPoints, xi=xi);
  x = spline(linspace(0,1,50)');