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MathGroup Archive 2000

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Re: Equation of a "potato"

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24532] Re: Equation of a "potato"
  • From: "David Bailey" <db at salford-software.com>
  • Date: Mon, 24 Jul 2000 03:04:11 -0400 (EDT)
  • Organization: University of Salford, Salford, Manchester, UK
  • References: <8l0pbk$dqo@smc.vnet.net> <8l3fdk$kvd@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

"Philip C Mendelsohn" <mend0070 at garnet.tc.umn.edu> wrote in message
news:8l3fdk$kvd at smc.vnet.net...
> Kevin J. McCann (Kevin.McCann at jhuapl.edu) wrote:
> : I am doing some illustrations for class notes on vector calculus. I
> : would be nice to have some drawings for a "random" 3d shape, i.e.
> : something that is fairly rounded and regular like a potato, but not as
> : simple as a sphere. Any ideas for the an equation that would draw
> : something like this?
>
> What about making a ParametricPlot of a Sphere where the radius varies
> by a small random coefficient?
>
> I'll see if I can play with this when I get near the computer.
>
> Phil M
> --
> Lottery:    a tax on people who are bad at math
>

There is a trap here. If you plot something like Plot[Sin[t]+Random[],{t,0,2
Pi}] you get a graph which is really just an artifact. The point is that
Plot assumes a continuous function and repeatedly divides the interval
trying to fit a smooth curve to something that is randomly varying.
ParametricPlot3D will behave similarly! I think this will result in a very
hairy sphere! I think you could use ParametricPlot3D, but you would have to
generate a function r[theta,phi] that was (say) fitted to a number of random
values or r for particular theta and phi. This would still suffer from rapid
variation near the poles of the sphere.

I suspect this problem is a bit more subtle than it looks!

David Bailey
Salford Software




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