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MathGroup Archive 2000

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Re: Equation of a "potato"

  • To: mathgroup at smc.vnet.net
  • Subject: [mg24594] Re: Equation of a "potato"
  • From: "Allan Hayes" <hay at haystack.demon.co.uk>
  • Date: Tue, 25 Jul 2000 00:56:26 -0400 (EDT)
  • References: <8l0pbk$dqo@smc.vnet.net> <8l3fdk$kvd@smc.vnet.net> <8lgr81$24a@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

David,
1) This trap does not arise for ParametricPlot3D, since it is not adaptive.
2) For 2D curvse we can avoid it by using ListPlot: for example
ListPlot[Table[Sin[t] + Random[], {t, 0, 2Pi, Pi/12}],
  PlotJoined -> True]

Allan
---------------------
Allan Hayes
Mathematica Training and Consulting
Leicester UK
www.haystack.demon.co.uk
hay at haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

"David Bailey" <db at salford-software.com> wrote in message
news:8lgr81$24a at smc.vnet.net...
>
> "Philip C Mendelsohn" <mend0070 at garnet.tc.umn.edu> wrote in message
> news:8l3fdk$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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