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Re: How does Plot work?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg115235] Re: How does Plot work?
  • From: DrMajorBob <btreat1 at austin.rr.com>
  • Date: Tue, 4 Jan 2011 18:50:45 -0500 (EST)

To me, "initially sampled at equally spaced points as specified by  
PlotPoints" seems pretty darn specific... and equally inaccurate.

Bobby

On Tue, 04 Jan 2011 03:24:48 -0600, Bill Rowe <readnews at sbcglobal.net>  
wrote:

> On 1/3/11 at 3:56 AM, lshifr at gmail.com (Leonid Shifrin) wrote:
>
>> Not that this  answers the question, but it looks to me like this
>> behavior has to do with the exact periodicity of Sin and the plot
>> limits being multiples of 2 Pi. Somehow, for PlotPoints being
>> exactly 50, this breaks the algorithm (I think this is either a bug,
>> or at least the algorithm used is unstable in some cases like this
>> one). You can see that changing any of the above would result in a
>> normal plot:
>
> I don't believe the intent of the original poster was to produce
> a normal plot of Sin[x] but instead to learn more about how Plot
> sampled the function to be plotted.
>
> The documentation for Plot states the function to be plotted is
> initially sampled at equally spaced points as specified by
> PlotPoints. This suggests if the plot range is specified to be 0
> to n and the number of plot points is specified to be n+1, the
> function will be initially sampled at integer values. But this
> is clearly not what is happening as can be seen from:
>
> In[58]:= Reap[
>    Plot[Sin[Sow[x]], {x, 0, 9}, MaxRecursion -> 0,
>     PlotPoints -> 10]][[-1, -1, 3 ;;]]
>
> Out[58]=  
> {1.*10^-6,0.961804,2.00451,2.97812,3.93262,4.96803,5.93435,6.98156,8.00968,9.}
>
> I don't believe this is evidence of a bug or instability of the
> algorithm used by Plot. Perhaps it can be seen as an example
> where the documentation isn't complete or is misleading. My
> guess is the documentation was intended to give an user a
> reasonable understanding of what Plot does without going into
> all of the details.
>
>


-- 
DrMajorBob at yahoo.com


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