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
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I don't know about Method 22. But when you have points $x_k$ $>(1\leq k\leq N)$ uniformly distributed in a $d$-ball then you can apply a diagonal matrix to the $x_k$ and obtain points uniformly distributed in an ellipsoid. – Christian Blatter Jul 21 '20 at 09:17
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@ChristianBlatter after such stretching would it truly be uniform? If I stretch something horizontally, then points going horizontally would be less dense than when going vertically. Excuse me for simplistic language, I hope you understand what I mean – Coderino Javarino Jul 22 '20 at 20:01
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1The "distribution" refers to the number of points per unit area in different parts of the figure. Since horizontal scaling multiplies all area parts with the same factor it leaves the set of chosen points uniformly distributed. – Christian Blatter Jul 23 '20 at 08:50
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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 ${1\over2}$ in $y$-direction.
Christian Blatter
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