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3D plot of hemisphere pushing into a triangular membrane or surface

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=A8 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.


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.

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