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ZJU-FAST-Lab / sampling-based-path-finding

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uniform sampling from n-ball #2

Open chengyh23 opened 2 years ago

chengyh23 commented 2 years ago

https://github.com/ZJU-FAST-Lab/sampling-based-path-finding/blob/242069ee9691a919d913ad634111005b888b815f/src/path_finder/include/path_finder/sampler.h#L81

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

chengyh23 commented 2 years ago

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