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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,
> I liked your surface so much, I thought I might share this fun Manipulate:
>
> 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[3]], {{ls, 0}, 0, 1/2}]
>
> --
> W. Craig Carter
> 



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