[NTG-context] atan2 function

[Hans Hagen]

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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