I have just completed basic research on Bézier curves, mainly focused on the characteristics of Bernstein polynomials and the de Casteljau algorithm. Now I am supposed to approximate $\sin(x)$ and $\frac{\sin(x)}{x}$ using Bézier curves. How is approximation made using Bézier curves? Thank you.

  • $\begingroup$ Often the method for choosing a Bézier curve to approximate a smooth function is to interpolate values of that function (and possibly its derivatives as well) at selected nodes. Until you choose a finite interval on which you want to do the approximation, there's not a lot of further advice I can give you. $\endgroup$ – hardmath May 27 '18 at 15:59
  • $\begingroup$ So, if I want to do from x=0 to x=pi/2 the Bézier curve should interpolate sin(x) at those points (and the derivatives too), but which others? Thank you. $\endgroup$ – Diego Ibarra May 27 '18 at 16:19

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