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Re: Re: gaps in plot of piecewise function

• To: mathgroup at smc.vnet.net
• Subject: [mg108277] Re: [mg108220] Re: [mg108217] gaps in plot of piecewise function
• From: "Sjoerd C. de Vries" <sjoerd.c.devries at gmail.com>
• Date: Fri, 12 Mar 2010 07:11:42 -0500 (EST)
• References: <30604342.1268221205458.JavaMail.root@n11> <201003111134.GAA05875@smc.vnet.net> <1268313776.3447.120.camel@localhost>

The latter functions are equal for all x. Doesn't hold for the former two.

If you increase PlotPoints to well over a couple of hundred with
MaxRecursion at 15 I don't see a gap.

Cheers -- Sjoerd

> -----Original Message-----
> From: Patrick Scheibe [mailto:pscheibe at trm.uni-leipzig.de]
> Sent: 11 March 2010 14:23
> To: David Park; Benjamin Hell; Sjoerd C. de Vries; Peter Pein; gekko;
> Matthias Hunstig
> Cc: mathgroup at smc.vnet.net
> Subject: Re: [mg108220] Re: [mg108217] gaps in plot of piecewise
> function
> 
> Hi again,
> 
> I hope everyone saw now that Exclusions->None or using not Piecewise
> but
> e.g. Which will do the trick. In the documentation it sounds to me that
> many functions are generally connected to Piecewise (look at Properties
> and Relations in the Piecewise doc).
> 
> My question is, why would it be wrong to connect the plot in Piecewise
> when the Limits are the same? Following example:
> 
> Manipulate[
>  Plot[Piecewise[{{Exp[1] x, x < 1}}, Exp[x]], {x, 0, 3},
>   MaxRecursion -> mr, MeshStyle -> {Red, PointSize[0.005]},
>   Mesh -> All, PlotPoints -> pp,
>   ImageSize -> 500], {{pp, 5, "PlotPoints"}, 3, 30,
>   1}, {{mr, 1, "MaxRecursion"}, 1, 10, 1}]
> 
> The function has the same limit at x->1 and the same derivative. I
> would
> clearly expect a plot without a gap even without the Exclusions
> options.
> Where am I wrong?
> 
> Is it too unpredictable to check at least numerically the limits?
> But why is this working?
> 
> Manipulate[
>  Plot[Piecewise[{{Sin[x], x < 1.334}}, Cos[ x - Pi/2]], {x, 0, 3},
>   MaxRecursion -> mr, MeshStyle -> {Red, PointSize[0.005]},
>   Mesh -> All, PlotPoints -> pp,
>   ImageSize -> 500], {{pp, 5, "PlotPoints"}, 3, 30,
>   1}, {{mr, 1, "MaxRecursion"}, 1, 10, 1}]
> 
> What bothers me is that when using PiecewiseExpand you get an
> equivalent
> presentation of one and the same function but you get different plots
> in
> an, say not really predictable way.
> 
> Cheers
> Patrick
> 
> On Thu, 2010-03-11 at 06:34 -0500, David Park wrote:
> > I'm not certain of the exact underlying mechanics, but basically
> because of
> > the steep curve as x -> 2 from below, and the piecewise function,
> > Mathematica sees a discontinuity and leaves a gap. The way to
> overcome this
> > is to use the Exclusions option.
> >
> > s[x_] := Piecewise[{{-Sqrt[2]/2*Sqrt[-x + 0.5] + 2, x < 0.5}, {2,
> >      x >= 0.5}}];
> >
> > Plot[s[x], {x, 0, 1},
> >  Exclusions -> None,
> >  Frame -> True,
> >  PlotRangePadding -> .1]
> >
> >
> > David Park
> > djmpark at comcast.net
> > http://home.comcast.net/~djmpark/
> >
> >
> > From: Benjamin Hell [mailto:hell at exoneon.de]
> >
> > Hi,
> > I want to plot a piecewise function, but I don't want any gaps to
> appear
> > at the junctures. An easy example is:
> >
> > s[x_] := Piecewise[{{-Sqrt[2]/2*Sqrt[-x + 0.5] + 2, x < 0.5}, {2, x
> >=
> > 0.5}}];
> > Plot[s[x], {x, 0, 1}]
> >
> > It should be clear, that the piecewise function defined above is
> > continuous, even at x=0.5. So there should not be any gaps appearing
> in
> > the plot, but they do. Maybe it's a feature of mathematica, but
> > nevertheless I want to get rid of the gaps. Any suggestions on how to
> > achieve that.
> >
> >
> > Thanks in advance.
> >
> >
> >

• References:
  • Re: gaps in plot of piecewise function
    • From: "David Park" <djmpark@comcast.net>