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MathGroup Archive 2006

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Uniform arc length basis curve fitting

  • To: mathgroup at
  • Subject: [mg67348] Uniform arc length basis curve fitting
  • From: "Narasimham" <mathma18 at>
  • Date: Mon, 19 Jun 2006 00:01:05 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

How to find slopes, curvature etc. of cubic splines as a function of
arc length? With this example from Help,attempted to find piecewise
derivatives, but it cannot be right as the given pts need not be spaced
evenly on the arc. TIA.

<< NumericalMath`SplineFit`
pts = {{0,0},{1,2},{-1,3},{0,1},{3,0} };
spline = SplineFit[pts, Cubic] ;
plspl=ParametricPlot[spline[u], {u, 0, 4}, PlotRange -> All, Compiled
-> False];
"derivative components"
der[x_]:=( spline[x+10^-10]-spline[x-10^-10] ) /( 2 10^-10);
dxu[x_]:=der[x].{1,0}; dxv[x_]:=der[x].{0,1};
 ">>> slopes >>>"
Plot[ArcTan[dxu[v],dxv[v]] ,{v,0,4}] ;
plder=ParametricPlot[der[v],{v,0,4}] ;

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