Equation of a "potato"

[Kevin J. McCann]

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?

Kevin

[Philip C Mendelsohn]

Kevin J. McCann (Kevin....@jhuapl.edu) wrote:
: I am doing some illustrations for class notes on vector calculus. I

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

[David Bailey]

"Philip C Mendelsohn" <mend...@garnet.tc.umn.edu> wrote in message
news:8l3fdk$k...@smc.vnet.net...

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

[Allan Hayes]

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
h...@haystack.demon.co.uk
Voice: +44 (0)116 271 4198
Fax: +44 (0)870 164 0565

"David Bailey" <d...@salford-software.com> wrote in message
news:8lgr81$2...@smc.vnet.net...

[adamizer]

You might try playing with the following:

f[t_, p_, pinch_] :=
(1 + pinch Cos[ p]^2){ Cos[t] Sin[ p] , Sin[t] Sin[ p], Cos[ p]}

ParametricPlot3D[ Evaluate[f[t,p,1.]],{t,0,2 Pi},{p,0,Pi}]

Changing the 3rd parameter "pinch" varies the amount the object
is "pinched" in the middle. It looks more like a peanut to me,
but it might be what you want.

Adam Smith

"Kevin J. McCann" <Kevin....@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?
>

>Kevin
>
>
>

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