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 > > >