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Obtain smooth plot of free-hand contour

• To: mathgroup at smc.vnet.net
• Subject: [mg107174] Obtain smooth plot of free-hand contour
• From: "Dominic" <miliotodc at rtconline.com>
• Date: Fri, 5 Feb 2010 03:18:42 -0500 (EST)

Hi,

I'm working on a contour integral over a contour I'd like to draw 
free-hand via the graphics tools, then obtain a smooth plot of the 
curve.  So first I do a 
Show[mypoint,Axes-True,PlotRange->{{-2,2},{-2,2}}] to just get the 
graphics box of a single point.  Then I use the graphics tools to draw 
in the contour, then I select the contour and assign it to 
myfreehandcontour to obtain the x and y points.  Then I extract the 
points and then do a FindFit on the x and y values.  However, I cannot 
get the end-points to meet so the contour is not even close to closed.  
Here is the code I use once I have pasted the plot to myfreehandcontour 
and I don't know if it's ok to post JPEG images to the group but I'll 
try below of the points and resulting FindFit curve. Note the start and 
end points are not closing the contour in the contour of the resulting 
ParametricPlot[{xcod[t],{ycod[t]},{t,1,1100}].  I don't know, maybe this 
is too much.. 

Can you guys suggest a way to input a free-hand closed contour into 
Mathematica and obtain a nice smooth {x(t),y(t)} representation of it?

Thanks!

Dominic

lns = Cases[Normal[First[myfreehandcontour]], Line[pts_] -> pts,
{0, Infinity}];

lplot1 = ListPlot[lns]

myvals = First[lns];
myxval = (#1[[1]] & ) /@ myvals;
myyval = (#1[[2]] & ) /@ myvals;
nmax = 100;
myfun = Sum[Subscript[a, n]*t^n, {n, 0, nmax}];
mycoef = Table[Subscript[a, n], {n, 0, nmax}]
clist = FindFit[myxval, myfun, mycoef, t];
xcod[t_] = myfun /. clist
myyfun = Sum[Subscript[b, n]*t^n, {n, 0, nmax}];
myycoef = Table[Subscript[b, n], {n, 0, nmax}];
cylist = FindFit[myyval, myyfun, myycoef, t];
ycod[t_] = myyfun /. cylist

pp1 = ParametricPlot[{xcod[t], ycod[t]}, {t, 1, 1100}]

GraphicsGrid[{{lplot1, pp1}}]

• Follow-Ups:
  • Re: Obtain smooth plot of free-hand contour
    • From: Patrick Scheibe <pscheibe@trm.uni-leipzig.de>