[NTG-context] atan2 function

Taco Hoekwater taco at bittext.nl
Fri Oct 14 14:58:31 CEST 2022



> On 14 Oct 2022, at 14:26, Alan Braslau via ntg-context <ntg-context at ntg.nl> wrote:
> 
> Are you using MP in scaled integer or in doubleprecision mode?
> 
> I have not looked into the MP angle operator code, but my suspicion is that it is based on some super-clever John Hobby scheme optimized for scaled integer calculations.

The scaled version of “angle” is a handwritten approximation in web, not using
any math library. I really doubt that that code is faster than calling atan2()
on a modern machine, but I’ve kept it in because using a lib might give slightly 
different results.

The double version of “angle" uses atan2() internally already, so that the 
atantwo macro is just duplicating the internals for that case.

The decimal version of “angle’ uses a dedicated decNumberAtan2() library call.

> 
> Hans has integrated the entire math library (and more) into lmtx.
> 
> On 13/10/22 13/10/22, 13:51, Thangalin via ntg-context wrote:
>> Thank you, Max.
>> The angle function doesn't appear to provide the same calculation as
>> my atantwo in all cases.
>> https://pdfhost.io/v/Oqj7XmibJ_scaled
>> The shorter line segment should be directed towards the vertex closest
>> to the longer line segment. I tried using both:
>>     theta := angle( dx, dy );
>>     theta := angle( dy, dx );
>> Neither made a difference, in some cases the angle differs from what I'd expect.
>> My implementation is based on the first version given here:
>> https://en.wikipedia.org/wiki/Atan2#Definition_and_computation
>> I have something that works, so this is more of a curiosity as to
>> there being a difference between my implementation of atantwo and the
>> angle function.
>> Here's an example with many lines and the angle function:
>> https://pdfhost.io/v/1T4jgBnxh_scaled
>> On Wed, Oct 12, 2022 at 11:42 PM Max Chernoff <mseven at telus.net> wrote:
>>> 
>>> Hi,
>>> 
>>>> How is atan2 called? I rolled my own as follows:
>>> 
>>>> Is atan with two parameters supposed to behave like atan2?
>>> 
>>> At mp-math.mpxl:167 there is:
>>> 
>>>        vardef atan   primary x = angle(1,x)       enddef ;
>>> 
>>> The MetaPost manual says:
>>> 
>>>    The angle operator takes a pair and computes the two-argument
>>>    arctangent; i.e., angle is the inverse of the dir operator
>>> 
>>> So it looks like "angle" is the function that you want for "atan2".
>>> 
>>> Thanks,
>>> -- Max
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— 
Taco Hoekwater              E: taco at bittext.nl
genderfluid (all pronouns)





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