OpenEuphoria

Re: New proposal for math.e

• Posted by Juergen Luethje <j.lue at ??x.de> Aug 04, 2007
• 520 views

Colin Taylor wrote:

<snip>

> I would also like to add a couple of functions:
> 
> }}}
<eucode>
> 
> global function polar_to_rect(sequence xy)
> -- convert a rectangular coordinates to polar coordinates
>     atom angle, distance, x, y
>     x = xy[1]
>     y = xy[2]
>     distance = sqrt(power(x, 2)+power(y, 2))
>     if x > 0 then
>     	angle = arctan(y/x)
>     elsif x < 0 then
>     	if y < 0 then
>     	    angle = arctan(y/x)-PI
>     	else
>     	    angle = arctan(y/x)+PI
>     	end if
>     else
>     	if y < 0 then
>     	    angle = -HALF_PI
>     	else
>     	    angle = HALF_PI
>     	end if
>     end if
>     return {distance, angle}
> end function
> 
> global function rect_to_polar(sequence pol)
> -- convert a polar coordinates to rectangular coordinates
>     atom distance, angle, x, y
>     distance = pol[1]
>     angle = pol[2]
>     x = distance*cos(angle)
>     y = distance*sin(angle)
>     return {x, y}
> end function
> 
> </eucode>
{{{
 
>        
> In the above functions, angle is expressed in radians, increasing in a
> clockwise
> direction from east.
> 
> Regards,  Colin   (now returning to deep lurk mode)

I don't know what you mean by "east" in this context. However, the
normal math convention is: Increasing positive values of an angle
correspond to _counter_ clockwise rotation.

But I've seen now that different textbooks use different conventions
about the range of values that is used for the angle in Polar
Coordinates. Some books use -PI < a <= PI, while others use
0 <= a < 2*PI. Our implementation of the functions will depend on the
range that we'll allow for the angle.

Regards,
   Juergen