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

• To: mathgroup at smc.vnet.net
• Subject: [mg116491] Re: 3D surface plots - non deletion of data inside undesirable
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Thu, 17 Feb 2011 05:17:13 -0500 (EST)

```Narasimham wrote:
> 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

What you contrast with looks to be not so closely related (has no points
of indeterminacy, that is, 0/0 singularities). Instead try something

a = 2; b = 1;
g2d = {a Cos[ph - th], b Sin[ph - th]}/Cos[ph + th];

g2d = ParametricPlot[gl2, {th, -Pi/4, Pi/4}, {ph, -Pi/4, Pi/4},
PlotRange -> {{-3, 3}, {-3, 3}}]

Then do:

g2db = ParametricPlot[gl2, {th, -Pi/3, Pi/3}, {ph, -Pi/4, Pi/4},
PlotRange -> {{-10, 10}, {-10, 10}}]

You will see a similar effect, in two dimensions, to what your original
function does in three dimensions.

Again, note (as a few respondents did) that your function takes on very
large values in the neighborhood of the singular points. The graph is
not incorrect in reflecting that fact.

This might be slightly closer to what you want to see, by the way.

GL3 = ParametricPlot3D[gl, {th, -Pi/2, Pi/2}, {ph, -Pi/4, Pi/4},
PlotRange -> {{-10, 10}, {-10, 10}, {-10, 10}}, PlotPoints -> 600]

Daniel Lichtblau
Wolfram Research

```

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