algorithm - Random point within oval with higher probability for a point closer to the centre? -

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i feel question quite descriptive illustrate in words.

picture radial gradient (black in centre, white on edge) want generate random point more fall in black, less fall in grey, , less fall in white.

could point me in right direction? i'm quite stumped :/

if b matrix such y = c + bx affine transformation maps unit circle ellipse (which assume mean "oval"), probability distribution looks seem want given y ~ n(c, bb^t) b^t transpose of b.

you can sample distribution generating column vector x of 2 distributed variables , applying transformation y = c + bx. there many libraries generating pair of distributed variables; in java, x0=rand.nextgaussian(); x1=rand.nextgaussian() work.

this generate points outside ellipse. can avoid rejecting such points. test whether x0*x0 + x1*x1 > 1 , reject if true.

one more thing: if want "more white" near edge of ellipse, can change standard deviation of gaussians generate number less 1:

sd = 0.5;     x0 = sd * rand.nextgaussian();    x1 = sd * rand.nextgaussian(); while (x0*x0 + x1*x1 > 1); y0 = c0 + b[0][0] * x0 + b[0][1] * x1 y1 = c1 + b[1][0] * x0 + b[1][1] * x1

if want "less white", set sd number greater 1.


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