       Re: 3D surface plots - non deletion of data inside undesirable

• To: mathgroup at smc.vnet.net
• Subject: [mg116460] Re: 3D surface plots - non deletion of data inside undesirable
• From: Narasimham <mathma18 at hotmail.com>
• Date: Wed, 16 Feb 2011 04:34:57 -0500 (EST)
• References: <201102110919.EAA08103@smc.vnet.net> <ij5mnb\$jgq\$1@smc.vnet.net>

```On Feb 12, 3:17 pm, Daniel Lichtblau <d... at wolfram.com> wrote:
> Narasimham wrote:
> > a=2;b=1;c=3;gl={a Cos[ph-th],b Sin[ph-th],c Sin[ph+th]}/Cos[ph+=
th];
> > GL1=ParametricPlot3D[gl,{th,-Pi/4,Pi/4},{ph,-Pi/4,Pi/4},PlotRange-
> >> {{-3,3},{-3,3},{-3,3}}]
> > GL2=ParametricPlot3D[gl,{th,-Pi/3,Pi/3},{ph,-Pi/3,Pi/3},PlotRange-
> >> {{-3,3},{-3,3},{-3,3}}]
> > Show[GL1,GL2]
>
> > Extended plot limits in GL2 beyond those of GL1 result in 3D plot that
> > fail to delete undesiredspurioustracing/tracking data between points
> > not lying on the required surface.Like 'pen up' data in earlier
> > graphing s/w.
>
> What leads you to believe it isspurious?
>
> > It is OK may be to plot an enclosed solid, but not for a
> > surface. The difficulty also appeared in earlier Mathematica versions.
> > Is there then, no work around possible?
>
> > Best Regards
> > Narasimham
>
> Your denominator can vanish in the larger range. And there will be
> sampled points where it is quite small. So values will be huge. To see
> this, try
>
> eps = .01;
> GL1 = Table[
>    gl, {th, -Pi/4 - eps, -Pi/4 + eps,
>     eps/10}, {ph, -Pi/4 - eps, -Pi/4 + eps, eps/10}]
>
> So the plotting routine will be interpolating between values quite far
> apart. Sure, there may be a real pen-up situation e.g. getting points
> that go toward opposite infinities in a neighborhood of a singularity.
> But I think your surface will cause trouble even without that happening.
> Set the plot range a bit larger, as below, to see what I mean.
>
> GL1 = ParametricPlot3D[
>    gl, {th, -Pi/4 - eps, Pi/4 + eps}, {ph, -Pi/4 - eps, Pi/4 + eps},
>    PlotRange -> {{-10, 10}, {-10, 10}, {-10, 10}}]
>
> I don't think what I see is a "pen up" effect.
>
> Daniel Lichtblau
> Wolfram Research

Thanks.

GL3=ParametricPlot3D[gl,{th,-Pi,Pi},{ph,-Pi/4,Pi/4},PlotRange->{{-3,3},
{-3,3},{-3,3}}]

ep=1.73205;hb={Cos[t],Sin[t]}/(1-ep Cos[t]);
HB=ParametricPlot[hb,{t,0,2Pi},PlotRange->{{-3,3},{-3,3}}]

In 2-D plots we see a neat pair of asymptotic lines between the two
branches of a hyperbola where all the infinitely remote points are
effectively removed. In 3-D by the same token we can't see a single
neat asymptotic cone, but what appear as remnants of  a clutter of
packed planes.It may be tougher to handle the 3-D though.

Regards,
Narasimham

```

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