Alternative atan2 (was Re: Motion 52: final ...)
P1788
On 2013 Nov 26, at 02:06, Vincent Lefevre wrote:
> On 2013-11-25 15:35:13 -0500, Michel Hack wrote:
>> I just skimmed the article, and if I understand it correctly, the point
>> it makes is that, for intervals, the restriction of the atan2() range
>> to [-\pi, +\pi] would force some evaluations to return the essentially
>> useless [-\pi, +\pi] instead of a sharp enclosure that straddles \pi.
>>
>> The same may apply to the other inverse-trig functions.
>
> I think that atan2 is a bit particular. Do you have an example
> with a conventional inverse-trig function (asin, acos, atan)?
I think atan2 is the only one that can be "improved" by this method. Basically, for any box (yy,xx) in R^2 that doesn't contain (0,0), but meets the usual branch cut of atan2, the idea is to rotate the branch cut out of the way of the box. Depending on the rule for which direction to rotate, one gets different answers for the range of the resulting function. Bill, is that right?
It's a neat idea. Jürgen, would you consider adding this to function to our list (recommended, I would say)? Who supports this?
John Pryce