> As i have indicated in my post, it is non-trivial to implement a
> function that returns the positive angle of a vector. For example, it
> can be done with sign checking of the coordinate components (in total
> 4 cases, which can be done as 2 levels of nesting if, or simply 4
> if.), and or the evaluation of Min[Abs[ArcCos[x],Abs[ArcSin[x]]], or
> use clever ways with dot product, or ArcTan. It is not a trivial to
> know which algorithm is in general more efficient. (this is important,
> since finding the angle of a vector is a basic function, that may
> needs to be called millions times directly or indirectly) Further,
> consider the inverse trig function, it is likely 99.99% of people with
> a PH D in math wouldn't know how these are actually implemented. So,
> the question of whether calling one of the inverse trig function is
> more robust or efficient than another is a open question. And, besides
> the algorithmic level, the question also entails how the language
> actually implement the inverse trig functions.
>
> Besides efficiency concerns, there's also robustness concerns. For
> example, if the 2 vectors are {1,0} and {0,1}, a simplistic
> implementation will result in division by 0 or similar errors.
> Checking whether one of them lies on the x or y axis means more if
> statements, as well the non-trivial problem of determining if two
> numbers are equal. (e.g. is 0.000001 considered equal to 0.0001 )
>
>
> Xah
> [EMAIL PROTECTED]
> ∑http://xahlee.org/
Xah could you please post staff related to lisp programming like above
in separate thread from your personal things like someone banning you
from the IRC.
thanks
bobi
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