Somewhere in the E.U., le 26/11/2004 In article <98604e9d041123112135c8caae@mail.gmail.com>, Matt Austern <austern@gmail.com> wrote:
On Tue, 23 Nov 2004 10:55:19 +0100, Hubert Holin <hubert.holin@meteo.fr> wrote:
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 ;-) ? ).
I'm sure you'd want to use polar coordinates for that, yes. There are of problems for which you want to use polar coordinates of some sort or another.
But is it likely that you would want to use a package that provides complex numbers in polar form? My experience is that if you're
Basically, as I answered the OP, the answer is no ;-) .
working with complex numbers that you want to think of in the form r exp(i phi), then you'll probably just do the work of separating out the magnitude and phase ahead of time in your equations, and then compute with them separately. After all: if you're doing something
Yes.
where the magnitude-phase form is most convenient, it usually means that putting numbers in that form makes the equations simpler.
Yes (but it usually also means to watch out for the singularity).
--Matt
Still, from the discussion on comp.std.cpp a few years back, I recall that there was a feeling that having multiple representations (say cartesian and polar) at the same time would have been nice. Of course, it would have been a bloated beast (at least in a naive implementation), and a slow one at that (to keep track of the various changes, in a naive implementation still). Furthermore it clashed with the desire to have some layout guaranty which played nice with C (that line of reasoning seems to have flown out in limbo, however). This illustration is merely there as a reminder that the wish for concurrent multiple points of views of a given abstract entity is not a futile one, if one that I fear can't be translated from mathematics to CS. We've had another illustration of that recently with the affine space/vector space discussion in a GUI thread a few days back here (which also happens to be relevant to this discussion as well, at least in two dimensions). Merci Hubert Holin