# [NTG-context] atan2 function

Hans Hagen j.hagen at xs4all.nl
Fri Oct 14 10:07:19 CEST 2022

```On 10/14/2022 2:35 AM, Max Chernoff via ntg-context wrote:
>
> Hi,
>
>> The angle function doesn't appear to provide the same calculation as
>> my atantwo in all cases.
>
> They both give the same results, but "angle" gives a result in degrees
> while "atantwo" gives a result in radians. This demo:
>
>     \startMPpage
>         vardef atantwo( expr dy, dx ) =
>             save theta;
>
>             numeric theta;
>
>             theta := 0;
>
>             if (dx > 0):
>                 theta := atan( dy / dx );
>             elseif (dx < 0) and (dy >= 0):
>                 theta := atan( dy / dx ) + pi;
>             elseif (dx < 0) and (dy < 0):
>                 theta := atan( dy / dx ) - pi;
>             elseif (dx == 0) and (dy > 0):
>                 theta := pi / 2;
>             elseif (dx == 0) and (dy < 0):
>                 theta := -pi / 2;
>             fi;
>
>             theta
>         enddef;
>
>         def showangles(expr dx, dy) =
>             message "---------------"
>             message "atantwo " & decimal atantwo(dy, dx)
>             message "angle " & decimal (angle(dx, dy) * pi / 180)
>             message "angle " & decimal angle(dx, dy)
>             message "(" & decimal dx & ", " & decimal dy & ")"
>         enddef;
>
>         showangles(1, 0);
>         showangles(1, 1);
>         showangles(0, 1);
>         showangles(-1, 1);
>         showangles(-1, 0);
>         showangles(-1, -1);
>         showangles(0, -1);
>         showangles(1, -1);
>     \stopMPpage
So you suggest to add atantwo? As side note, you can redure your
definition to:

vardef atantwo( expr dy, dx ) =
if (dx > 0):
atan( dy / dx )
elseif (dx < 0) and (dy >= 0):
atan( dy / dx ) + pi
elseif (dx < 0) and (dy < 0):
atan( dy / dx ) - pi
elseif (dx == 0) and (dy > 0):
pi / 2
elseif (dx == 0) and (dy < 0):
-pi / 2
else :
0
fi
enddef ;

and then

vardef atantwo(expr dy, dx) =
if dx == 0 :
if dy < 0 : - fi pi / 2
else :
atan(dy/dx) if dx > 0 : if dy < 0 : - else : + fi pi fi
fi
enddef ;

going further makes us end up in an one-line obscurity

Hans

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