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Is Voelker's dropped coordinates method for generating points in ball applicable to ellipsoid-ball?

A short write up is at section "method 22" on http://extremelearning.com.au/how-to-generate-uniformly-random-points-on-n-spheres-and-n-balls/ . I’m trying to get a more general case working, and so to say go from circle to any ellipse. However I’m starting to have doubts that this is even achievable with this method. Plotting results for 2d, I can see they’re all within area they should be, however they’re not uniformly distributed, and much more dense at center than at long ellipsis edges

Mathematics Asked by Coderino Javarino on December 10, 2021

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Supplementing my comment: The following picture shows the same $2000$ random points, once as original, and once stretched by $2$ in $x$-direction and by ${1over2}$ in $y$-direction.

enter image description here

Answered by Christian Blatter on December 10, 2021

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