Post A85FoNSE7ZaDEFphMe by mwt@mathstodon.xyz
 (DIR) More posts by mwt@mathstodon.xyz
 (DIR) Post #A85FoM8L22518HWIj2 by jix@mathstodon.xyz
       2021-06-08T11:20:55Z
       
       0 likes, 0 repeats
       
       Does anyone know an efficiently implementable area-preserving homeomorphism between the n+1-cube boundary and the n-sphere? Not finding anything, and what I came up with, I don't know how to compute yet. Wouldn't be surprised if I just don't know the right keywords to find sth...
       
 (DIR) Post #A85FoMZHPrdATq7oie by jix@mathstodon.xyz
       2021-06-08T11:26:54Z
       
       0 likes, 0 repeats
       
       This would also give you one between the n-cube and the n-ball by mapping concentric cube boundaries to concentric spheres. I'm interested in this for low-discrepancy/quasirandom sequences on n-spheres and n-balls, which is also something where I'd have expected to find more...
       
 (DIR) Post #A85FoN1diQJdtnOSvI by jix@mathstodon.xyz
       2021-06-08T11:38:54Z
       
       0 likes, 0 repeats
       
       Ideally for that use case, the mapping should also approximately preserve distances locally, e.g. bounded by a constant factor (depending on n, I think there's no way around that).
       
 (DIR) Post #A85FoNSE7ZaDEFphMe by mwt@mathstodon.xyz
       2021-06-08T14:43:53Z
       
       0 likes, 0 repeats
       
       @jix what about translating to polar coordinates?
       
 (DIR) Post #A85FoNpyhGa8PuwfNw by 11011110@mathstodon.xyz
       2021-06-08T18:08:10Z
       
       0 likes, 1 repeats
       
       That would give an easy homeomorphism but not one that is area-preserving.