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### Re^2: Randomly biased, random numbers.

by salva (Abbot)
 on Dec 06, 2013 at 09:43 UTC ( #1065942=note: print w/replies, xml ) Need Help??

in reply to Re: Randomly biased, random numbers.
in thread Randomly biased, random numbers.

Math::Vector::Real::MultiNormalMixture generates density functions which may suit the OP case and that can also be randomly parametrized.

Anyway, one problem with this approach is that the ratio of a discarded points could be too high.

In that case, a more efficient way may be to divide the plane in regions (i.e. triangles), calculate the probability of every region and then generate the random points first picking a region and then a point inside the region with your proposed algorithm using the conditioned density function.

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Re^3: Randomly biased, random numbers.
by roboticus (Chancellor) on Dec 06, 2013 at 13:32 UTC

Yes, the discard rate can be a problem. For the table lookup version in 2D, I had a speedup that worked decently: Generate the first coordinate, then use the same technique to generate the remaining coordinate. It can still be a problem, though, in the event you choose a "mostly black" line, but I never needed made anything better than that.

I also tried to make a "transformational" technique that wouldn't reject any coordinates, but never got it working well enough to use. (Rather: the technique worked fine, but coming up with the warping functions for the project was more difficult (for me, at any rate), so I simply tended to run the density-mapping version before going to lunch, going home for the day, etc.

The intention was: Generate a random coordinate, and "remap" it based on a displacement function. I was hoping to be able to turn a density function into a space warping function. The difficulties I had were primarily coming up with functions to warp space appropriately, and ensuring that I could hit any point in the desired output space without too much overhang. (If the function moved the point outside the desired range, you had to reject the point and try again anyway.)

Update: Made edit above.

...roboticus

When your only tool is a hammer, all problems look like your thumb.

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