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Re: Re: ListCurvePathPlot

  • To: mathgroup at smc.vnet.net
  • Subject: [mg95995] Re: [mg95935] Re: [mg95909] ListCurvePathPlot
  • From: DrMajorBob <btreat1 at austin.rr.com>
  • Date: Sat, 31 Jan 2009 06:44:47 -0500 (EST)
  • References: <200901291058.FAA18253@smc.vnet.net>
  • Reply-to: drmajorbob at longhorns.com

Interesting? Yes.

Useful? I don't see how!

Bobby

On Fri, 30 Jan 2009 04:44:00 -0600, Curtis Osterhoudt <cfo at lanl.gov> wrote:

> 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/
>>
>>
>
>
>



-- 
DrMajorBob at longhorns.com


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