[cairo] Shouldn't Cairo use/offer degrees rather than radians?

[Bill Spitzak]

David's code seems to be an alternative to atan2 that returns degrees.
It has a bunch of kludges to hide the fact that the atan2d he is
calling internally apparently just calls atan2 and multiplies by
180/pi. He then has another function that is in effect calculating
sin() and cos() and has even more kludges to detect multiples of 45
degrees.

The work needed in the second function indicates that passing degrees
does not really help.

Although it seems like it helps as far as I can tell if you don't want
discontinuities then adjusting the sin/cos results for N*pi/2 is
exactly the same difficulty whether degrees or radians are used.
Basically it amounts to detecting if a/90 or a/M_PI_2 is near an
integer, and is thus exactly the same problem.


On Thu, Jun 29, 2017 at 11:38 PM, David Kastrup <dak at gnu.org> wrote:
> David Kastrup <dak at gnu.org> writes:
>
>> Lawrence D'Oliveiro <ldo at geek-central.gen.nz> writes:
>>
>>> On Fri, 30 Jun 2017 07:02:36 +0200, David Kastrup wrote:
>>>
>>>> Lawrence D'Oliveiro <ldo at geek-central.gen.nz> writes:
>>>>
>>>>> On Thu, 29 Jun 2017 08:08:04 +0200, David Kastrup wrote:
>>>>>
>>>>>> It replaces a sin(x)/cos(x) pair by a sin(x)/sin(pi/2-x) pair.  The
>>>>>> largest cumulative effect is at pi/4.
>>>>>
>>>>> So you introduce a kink at π/4. How is this any better, again?
>>>>
>>>> There is no kink.  None at all.
>>>
>>> No kink? Have a look--here’s your kink, at π/4.
>>
>> I have no idea what you are plotting here.  Your "fake" does not look
>> like a _function_ of either axis, and it also doesn't have the symmetry
>> of the sin/cos pairing of my code.  So if it is neither a function in
>> isolation nor the actual value pair, what is it?
>>
>> Care to show the program you are generating your plots with?
>
> And show the units it is working with?
>
> Cutting this a bit short: can we actually skip the part where you are
> trying to show, using bravado and ad-hoc arguments, to show that I am
> incompetent and don't know what I am talking about?
>
> If you are worried about the added jitter due to the _internal_
> implementation using the built-in sin/cos with radians as arguments,
> I can of course add a post-correction stage (about doubling the
> computational cost, of course) that will use the addition theorem in
> order to get the full resolution of angles provided by the different
> rasterization of degrees and radians.  But that's sort of pointless as
> it will add precision amounting to something like 2^-53 .
>
> --
> David Kastrup
>
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