[boost] Re: Gauging Interest: polar_complex

From: Hubert Holin (Hubert.Holin_at_[hidden])
Date: 2004-11-23 04:55:19

Somewhere in the E.U., le 23/11/2004

   Bonjour

In article <41A1D3A7.70609_at_[hidden]>,
 Roland Schwarz <roland.schwarz_at_[hidden]> wrote:

> Mickey Moore wrote:
> 
> >  For some applications, polar complex numbers have significant 
> > advantages over Cartesian complex (e.g., std::complex) in efficiency 
> > and numerical accuracy. 
> 
> Just out of curiosity: Can you give me an example of an algorithm where 
> this would be of advantage?
> 
> Roland

      It is interesting if, for instance, you have to track an object 
along an orbit for a very long time. Using the canonical ("cartesian") 
representation usually entails transcendental functions (say sine and 
cosine), for which it is very hard to guaranty the accuracy (of a given, 
one-size-fits-all, implementation) for big values of the argument. If 
you integrate numerically, you all the more want to stay in the polar 
domain (unless we cross the singularity, but we are not modeling 
missiles, are we ;-)  ?  ).

   Merci

         Hubert Holin