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

• To: mathgroup at smc.vnet.net
• Subject: [mg116361] Re: 3D surface plots - non deletion of data inside undesirable
• From: Daniel Lichtblau <danl at wolfram.com>
• Date: Sat, 12 Feb 2011 05:17:19 -0500 (EST)
• References: <201102110919.EAA08103@smc.vnet.net>

```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 undesired spurious tracing/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 is spurious?

> 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

```

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