Interesting question. If we don't know what x ^ y should mean for two quaternions, then maybe that is our answer. If there isn't a natural, meaningful and/or useful definition, why does it need to be defined?
It would be a shame to lose x^(y+z) = (x^y) * (x^z), could we keep a weaker version? I never thought much about quaternion exponentiation before, but I definitely will. Thanks! > -----Original Message----- > From: [email protected] [mailto:[email protected]] On > Behalf Of Raul Miller > Sent: Thursday, March 18, 2010 1:26 PM > To: Chat forum > Subject: [Jchat] j and quaternions > > I have in the past thought that quaternions would be a nice addition to > J. > > They are very useful, for example, for expressing rotations of > geometric models. > > However, J of course needs its implementation to be generally correct > and not just correct for some specific application. > > So I have been thinking of how to model J's primitives that would need > to interpret quaternion values. > > This leads to questions such as: what does x^y mean when x and y are > quaternions? > > Apparently, this is a hard problem: > > http://www.zipcon.net/~swhite/docs/math/quaternions/analysis.html > > I have been trying to find a definition of quaternion exponentials > that that does not do something silly (like assume that quaternion > multiplication is commutative). So far, I have not found anything I > feel I could implement a J model for transcendental functions from. > Also, x^y for quaternion x and quaternion y would often enough have an > infinite set of valid results, which complicates things. > > So... does anyone have an good ideas about how to handle > transcendental functions that work with quaternions? > > Thanks, > > -- > Raul > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
