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Community Bot
Community Bot
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In case the goal is to draw points inside the sphere, the discussion Intuitive proof that the first $(n-2)$ coordinates on a sphere are uniform in a ballIntuitive proof that the first $(n-2)$ coordinates on a sphere are uniform in a ball seems relevant.

In other words, one simply draws random points on the 10-dimensional sphere (by drawing a normal vector and normalizing it) and discards the last two coordinates.

In case the goal is to draw points inside the sphere, the discussion Intuitive proof that the first $(n-2)$ coordinates on a sphere are uniform in a ball seems relevant.

In other words, one simply draws random points on the 10-dimensional sphere (by drawing a normal vector and normalizing it) and discards the last two coordinates.

In case the goal is to draw points inside the sphere, the discussion Intuitive proof that the first $(n-2)$ coordinates on a sphere are uniform in a ball seems relevant.

In other words, one simply draws random points on the 10-dimensional sphere (by drawing a normal vector and normalizing it) and discards the last two coordinates.

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Anthony Leverrier
Anthony Leverrier
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In case the goal is to draw points inside the sphere, the discussion Intuitive proof that the first $(n-2)$ coordinates on a sphere are uniform in a ball seems relevant.

In other words, one simply draws random points on the 10-dimensional sphere (by drawing a normal vector and normalizing it) and discards the last two coordinates.