Uniform arc length basis curve fitting

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

```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};
Plot[{dxu[v],dxv[v]},{v,0,4}];
">>> slopes >>>"
Plot[ArcTan[dxu[v],dxv[v]] ,{v,0,4}] ;
plder=ParametricPlot[der[v],{v,0,4}] ;
der[2]
Show[plspl,plder];

```

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