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I would like to make a nice 3D graphic of a parabolic bowl, with a cylindrical rim. If I do the following:

Plot3D[x^2 + y^2, {x, -3, 3}, {y, -3, 3}]

I get a paraboloid, but the box is rectangular, so the edges come to points. I want a cylindrical bounding box. The best I've come up with is this:

Plot3D[Piecewise[{{x^2 + y^2, x^2 + y^2 < 1}}], {x, -1, 1}, {y, -1, 1}]

This creates a bowl, but there is also a "floor" to the graphic that I would like to get rid of. I might be able to play games with the coloring, but that seems like a poor hack. Does anyone have any suggestions?

More generally, is it possible to create a 3D bounding box of arbitrary shape?

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Plot3D[x^2 + y^2, {x, -3, 3}, {y, -3, 3}, 
       RegionFunction -> Function[{x, y, z}, x^2 + y^2 < 9]]

enter image description here

Re: " is it possible to create a 3D bounding box of arbitrary shape?" ... as arbitrary as your creativity for creating region functions is

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Thank you so much! That is exactly the option I had been unable to find. – jmizrahi Jun 18 '13 at 2:27
Alternatively, why not parametrize? ParametricPlot3D[{r Cos[t], r Sin[t], r^2}, {r, 0, 3}, {t, -π, π}] – J. M. Jun 18 '13 at 3:28
@0x4A4D Well, the title refers to Plot3D[] ... BTW: why the hex conversion? – Dr. belisarius Jun 18 '13 at 3:33
Well ,my message was more for the OP than you, but anyway... I got hexed, and now you're seeing the effects. – J. M. Jun 18 '13 at 3:57
@0x4A4D Please keep your true name concealed – Dr. belisarius Jun 18 '13 at 11:55

The shorter the better :) :

RevolutionPlot3D[t^2, {t, 0, 3}]

enter image description here

It is good to know RevolutionPlot3D in case of some axisimmetric figures but the true control is given by RegionFuntion introduced by belisarius.

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