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Re: ListCurvePathPlot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg95935] Re: [mg95909] ListCurvePathPlot
  • From: Curtis Osterhoudt <cfo at lanl.gov>
  • Date: Fri, 30 Jan 2009 05:44:00 -0500 (EST)
  • Organization: LANL
  • References: <200901291058.FAA18253@smc.vnet.net>
  • Reply-to: cfo at lanl.gov

The following is rather interesting. I think it (with some imagination) conforms to the definition given in the Mathematica Documentation, but it wasn't what I was expecting. 

data = Table[RandomReal[{-1.3, 1.2}]*{Cos[t], Sin[t]}, 
       {t, 0, 6*Pi - 2*(Pi/6), Pi/6.1}]; 


{{0.25002688366379333, 0.}, {0.9356799430343185, 
  0.5295589611737038}, 
   {0.10118796319464748, 0.16851424646497157}, 
   {-0.029188553024956546, -1.1332520553860652}, 
   {-0.23082153680912088, 0.4335135296822279}, 
   {0.7576710364167465, -0.48192811086842924}, 
   {0.9705776190593385, -0.05003046313427862}, 
   {1.0962492703177467, 0.5479411095599908}, 
   {0.6370536297044893, 0.9468064433345135}, {0.03136422751102095, 
     0.4051894691695028}, {0.364963285556999, -0.7797519520786809}, 
   {-0.9341065689324766, 0.6640763628660812}, 
   {0.013137997466309304, -0.0013580598861936942}, 
   {-0.6906567258137415, -0.301834640354331}, 
   {0.566523954686374, 0.7549438704279434}, {0.07549928355009236, 
     0.5831410479690148}, {0.4000794379862568, -0.9837423213746447}, 
   {0.24638452631107208, -0.19500664556832673}, 
   {1.1421844045687481, -0.17789046644213574}, 
   {0.11779527337621096, 0.04440716210668134}, 
   {-0.10502847445807519, -0.12589786231771516}, 
   {0.20288991501930384, 1.1133525098565278}, 
   {0.19075826931350767, -0.54838931166244}, {-0.013717694614866967, 
     0.012056157937833439}, {0.8381916063026793, \
-0.17515740827734855}, 
   {-0.7711479671903417, -0.24617764515949736}, 
   {0.5886009181985181, 0.6359230898649515}, {-0.2787870392560766, 
     -1.1813146432588384}, {-0.04025184234997148, 0.1382818883263678}, 
   {0.29420624689007885, -0.2867261088679789}, 
   {0.6823920131526263, -0.17971101963053693}, 
   {1.1400162086445282, 0.3002284190055794}, {-0.13739394197848387, 
     -0.13390072706458242}, {0.00505513032785771, 
  0.017366483784624985}, 
   {0.10886543986338092, -0.4612995589701644}}

ListCurvePathPlot[data, Axes -> False]

                     --C.O.





On Thursday 29 January 2009 03:58:55 David Park wrote:
> I don't understand the new ListCurvePathPlot, which the Help page says:
> "attempts to reconstruct smooth curves defined by the specified set of
> points."
> 
>  
> 
> This plot routine also has the option: InterpolationOrder. And the word
> "Curve" appears not only in the name but repeatedly in the descriptions.
> But look at the following example:
> 
>  
> 
> data = Table[
> 
>    RandomReal[{.8, 1.2}] {Cos[t], Sin[t]}, {t, 0, 2 \[Pi] - 2 \[Pi]/6,
> 
>      2 \[Pi]/6}];
> 
> ListCurvePathPlot[data,
> 
>  InterpolationOrder -> 3,
> 
>  Axes -> False]
> 
>  
> 
> I don't see anything "smooth" or "curvy" about the results!  So it seems
> that these terms are a misdirection in understanding the use of the routine.
> It appears that what the routine actually does is reorder the points to give
> some simpler line (not curve) than the original set of points. But what is
> the criterion for this? Is this some well know computational geometry
> algorithm? Was InterpolationOrder included as an option by mistake? Did the
> implementation change from the original intention? What is the purpose of
> the routine? What is the relation of this and the spline functions?
> 
>  
> 
> David Park
> 
> djmpark at comcast.net
> 
>  <http://home.comcast.net/~djmpark> http://home.comcast.net/~djmpark/  
> 
> 



-- 
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Curtis Osterhoudt
cfo at remove_this.lanl.and_this.gov
PGP Key ID: 0x4DCA2A10
Please avoid sending me Word or PowerPoint attachments
See http://www.gnu.org/philosophy/no-word-attachments.html
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