Dear Fred, Where you say "uniformly distributed unit quaternions" I am confused. Uniformly distributed in what? I also don't know what "transitive in all four components" means. Clicked on the link to Stack Exchange and confronted a section of . . . I'm not sure what language of something by Ken Shoemake, but the question was not written in a way I can understand easily, so I don't care to read it. I certainly am reasonably familiar with quaternions and with probabilityt distributions, so if you give me just a few hints I can probably understand. Thanks, Dan P.S. Did you watch any of Wimbledon (on the telly) ? I don't care for spectator sports in general, but top-notch tennis I like a lot. On Jul 6, 2014, at 2:09 PM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
A feature of quaternions that is even more remarkable has not so far been explicitly discussed at all: the fact that uniformly distributed unit quaternions (transitive in all 4 components) correspond to "random" 3-space rotations (scalar angle unrelated to 3 axis vector components)!