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MWB
MWB
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There is a simple algorithm to pick a random point ON an $n$-dimensional hypersphere.

Is there one to sample a point from inside it? (Sampling points from a hypercube and rejecting them if they are not inside the hypersphere would scale extremely poorly with $n$, as the vast majority of points would be rejected)

There is a simple algorithm to pick a random point ON an $n$-dimensional hypersphere.

Is there one to sample a point from inside it? (Sampling points from a hypercube and rejecting them if they are not inside the hypersphere would scale extremely poorly with $n$ as the vast majority of points would be rejected)

There is a simple algorithm to pick a random point ON an $n$-dimensional hypersphere.

Is there one to sample a point from inside it? (Sampling points from a hypercube and rejecting them if they are not inside the hypersphere would scale extremely poorly with $n$, as the vast majority of points would be rejected)

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MWB
MWB
  • 1.7k
  • 2
  • 11
  • 20

Sampling a uniformly distributed point INSIDE a hypersphere?

There is a simple algorithm to pick a random point ON an $n$-dimensional hypersphere.

Is there one to sample a point from inside it? (Sampling points from a hypercube and rejecting them if they are not inside the hypersphere would scale extremely poorly with $n$ as the vast majority of points would be rejected)