       Re: 3D plot of hemisphere pushing into a triangular membrane or

• To: mathgroup at smc.vnet.net
• Subject: [mg110324] Re: 3D plot of hemisphere pushing into a triangular membrane or
• From: Narasimham <mathma18 at hotmail.com>
• Date: Sun, 13 Jun 2010 04:11:29 -0400 (EDT)
• References: <husjud\$6go\$1@smc.vnet.net>

```On Jun 11, 11:09 am, Garapata <warsaw95... at mypacks.net> wrote:
> I'd like to create a 3D plot of some kind with 2 key elements.
>
> 1. something that looks like a membrane stretched across a unit
> triangle with coordinates {{1,0,0}, {0,1,0},{0,0,1}}
>
> 2. a hemisphere that would press up from behind the membrane
>
> Basically a hemisphere pushing up through or intersecting a plane.
>
> I'll then set up a Manipulate so I can control 3 parameters:
>
>         diameter of the sphere;
>         how far it penetrates through the plane defined by the triangle;  and
>         where it penetrates the plane of the triangle.
>
> The Manipulate should be straight forward, I think I can handle that
> part easily enough.  But the plot part has eluded me.
>
> I've searched the documentation for anything that looked relevant.
>
> Graphics3D[{Sphere[{0, 0, 1}, 1], Sphere[{1, 0, 1}, 1/2]}, =E2=80=A=
8 BoxSty=
> le -
>
> > Directive[LightGray]]
>
> Which shows 2 spheres intersecting and
>
> Plot3D[UnitTriangle[x, y], {x, -1, 1}, {y, -1, 1}, PlotRange -> All,
> BoxStyle -> Directive[LightGray]]
>
> which shows something one could think of as a membrane both look
> promising, but
> I can't figure out where to go next.
>
> I haven't done a lot of graphics with Mathematica and just need an
> idea of where to start.
>
> Any thoughts appreciated.
>
> Thanks,
> G
>
> P.S. I made a couple of responses to thank forum participants for
> their help on previous posts that never appeared in the forum.  Not
> certain what happened, but belatedly, many many thanks.

The x,y,z plot limits have to be mentioned for PlotRange.
One way of depicting may be:
aa = Plot3D[1 - x - y, {x, -1, 1}, {y, -1, 1},
PlotRange -> {{-1, 1}, {-1, 1}, {-1, 2}} ] ;
shift = 0.3;
sphXYZ = { shift + Cos[ph] Cos[t], Cos[ph] Sin[t], Sin[ph]};
sph = ParametricPlot3D[sphXYZ, {ph, 0, 1.5}, {t, 0, 2 Pi},
PlotRange -> {{-1, 1}, {-1, 1}, {0, 1}}] ;
Show[{aa, sph}, PlotRange -> {{-1, 1}, {-1, 1}, {0, 1}},
AspectRatio -> Automatic]

Narasimham

```

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