What is the "area" of the general $n-1$ - box (hyperrectangle) projected onto the surface of the general $n$ - ball (hypersphere)?
Is there a known closed-form solution?
I'm just curious. Thanks!
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There a lot of different projections. What projection you are interested in? I suspect it is either central or orthogonal. Anyway, please, specify. – LRDPRDX Oct 28 '17 at 11:05
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I think you could just integrate a term depending on the angle over the rectangle. This works for all shapes and should lead to a 'closed form' if there is one. – Julian Quast Oct 30 '17 at 07:43