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