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];