Ioannis
Posts:
2,014
Registered:
12/13/04


Re: How to make weighted random numbers?
Posted:
Feb 27, 2009 10:30 PM


Rich Grise wrote:
> Say, I want to fill a sphere uniformly with random dots; the logical way > to do that in r,theta format; otherwise to make a sphere, you'd have to > do some heroic math on the three dimension (or is there some > quickndirty formula that can do it in one flop, that they don't tell > us high school (and Tech School, don't forget!) ? > > Either way. I don't want a uniform sphere  more like density through the > center looks like a bellshaped curve, i.e., denser in the middle? > > It's got to be computable, maybe with iterations, but that's what I > do best! I just have no idea what the algorithm would be. > > What I'm up to is I have a 3d drafting program and I want to approximate > a translucent ball effect. I can enter coordinates by copying the output > and paste it into the command line to automatically place n dots. ;)
With Maple you can do it in a jiffy. Here's some code and the result:
> with(plots): > with(stats): > L1:=[stats[random, normald](1000)]: #1000 points with normal distribution > L2:=[stats[random, normald](1000)]: #1000 more with normal distribution > > L:=[]; > for n from 1 to 1000 do > L:=[op(L),[L1[n],L2[n]]]; > od: > plot(L, style=point);
#result:
http://misc.virtualcomposer2000.com/Normal2D.gif
Now generalize to 3D.
> Thanks! > Rich  Ioannis  "There's _always_ a mistake, somewhere"

