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uniform sampling from n-ball #2

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chengyh23 opened this issue Jul 18, 2022 · 1 comment

chengyh23 commented Jul 18, 2022

sampling-based-path-finding/src/path_finder/include/path_finder/sampler.h

Line 81 in 242069e

double r = pow(uniform_rand_(gen_), 0.33333);

In infromed sampling, I‘m confused with uniform sampling from 3-ball

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chengyh23 commented Jul 18, 2022 •

edited

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As in Generate points uniformly inside a d-dimensional ball,

If Y is drawn from the uncorrelated multivariate normal distribution, then S = Y / ||Y|| has the uniform distribution on the unit d-sphere. Multiplying S by U^{1/d}, where U has the uniform distribution on the unit interval (0,1), creates the uniform distribution in the unit d-dimensional ball.

thus, normal sampling->vector normalization->multiply by a uniform sampled random number generates uniform sample from n-ball

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