       Re: Cropping a surface to a sphere (fun Manipulate example)

• To: mathgroup at smc.vnet.net
• Subject: [mg88236] Re: Cropping a surface to a sphere (fun Manipulate example)
• From: "David Park" <djmpark at comcast.net>
• Date: Tue, 29 Apr 2008 06:49:13 -0400 (EDT)
• References: <fv42mu\$624\$1@smc.vnet.net>

```This is nice Craig, but unfortunately ContourPlot3D is not the fastest of
routines. So, on my machine at least, the response is quite slow.

But, looking at the plot, there is obvious symmetry. There appears to be
only one fundamental surface which is present in 12 copies. So would it be
possible to use Reduce to obtain a parametrization of one of the surfaces
and use rotation/reflection geometric transformations to generate all the
other surfaces? This might then be much faster. For those who are experts in
group theory, how would one start with the polynomial and then generate the
set of transformations to create all the surfaces?

I put this forward as a challenge problem for those who might care to take
it up.

--
David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/

"W_Craig Carter" <ccarter at mit.edu> wrote in message
news:fv42mu\$624\$1 at smc.vnet.net...
> HellO Szabolcs,
>
> sphere[ls_] := Function[{x, y, z}, x^2 + y^2 + z^2 < ls^2]
>
> Manipulate[
> ContourPlot3D[-x^4*y^2 + x^2*y^4 + x^4*z^2 - y^4*z^2 - x^2*z^4 +
>    y^2*z^4 == ls, {x, -3, 3}, {y, -3, 3}, {z, -3, 3},
>  RegionFunction -> sphere], {{ls, 0}, 0, 1/2}]
>
> --
> W. Craig Carter
>

```

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