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Re: Re: Re: Re: ListCurvePathPlot
*To*: mathgroup at smc.vnet.net
*Subject*: [mg96039] Re: [mg96015] Re: [mg95995] Re: [mg95935] Re: [mg95909] ListCurvePathPlot
*From*: Murray Eisenberg <murray at math.umass.edu>
*Date*: Mon, 2 Feb 2009 06:22:01 -0500 (EST)
*Organization*: Mathematics & Statistics, Univ. of Mass./Amherst
*References*: <200901291058.FAA18253@smc.vnet.net> <200902010941.EAA22811@smc.vnet.net>
*Reply-to*: murray at math.umass.edu
With the possible exception of the very earliest versions, I'm not sure
that Mathematica was ever completely and authoritatively documented.
And this is a problem hardly unique to Mathematica.
Of course there IS authoritative documentation available, namely, what
the Mathematica interpreter actually does!
But I do agree that in the rush to get really, really, really useful new
features out to users, the documentation has sometimes lagged behind.
peter wrote:
> doesn't this just underline the impression that Wolfram are dropping
> the ball on documentation ? Doesn't matter how clever the programmers
> or the users are - unless the product is authoritatively documented,
> it is incomplete.
>
> Peter
>
> 2009/1/31 DrMajorBob <btreat1 at austin.rr.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
>>
>>
>
--
Murray Eisenberg murray at math.umass.edu
Mathematics & Statistics Dept.
Lederle Graduate Research Tower phone 413 549-1020 (H)
University of Massachusetts 413 545-2859 (W)
710 North Pleasant Street fax 413 545-1801
Amherst, MA 01003-9305
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