[Fwd: Re: [ardour-dev] questions about panner.cc ...]

[fons adriaensen]

On Fri, Aug 26, 2005 at 12:32:58AM +0200, Marc Vinyes wrote:
> > The scheme used is a (good) approximation to sin(), cos().
>
> Uow, during my degree I only used taylor series to aproximate sin() and
> cos() and this aproximation is just fantastic in the range of [0,pi/2]!
> Do you know how did they get it? (does it minimize the norm error
> between the parabola and the sin() perhaps?)

Yes, it is a very good approximation. How to compute it ? You want
f(0) = 0 and f(1) = 1, so there's only one free parameter. The rest
is 'an exercise for the reader' :-)

An even simpler one, accurate enough for pannning, is x * (2 - x).
Replace x by 1 - x for the other channel.

-- 
FA