OpenEuphoria

Re: Proposal for 'math.e' (2007-08-07)

• Posted by Colin Taylor <colinetaylor at ?mail.?om> Aug 07, 2007
• 510 views

Juergen Luethje wrote:
> 
> This is my current (2007-08-07) proposal for a "math.e" standard
> include file, according to the recent discussion here on EUforum.
> 
...
> 
> type point_pol (object x)
>    if sequence(x) and (length(x) = 2)
>    and atom(x[1]) and (x[1] >= 0)
>    and atom(x[2]) then
>       return 1 
>    end if
>    return 0
> end type
> 
> global function polar_to_rect (point_pol p)
>    -- convert polar coordinates to rectangular coordinates
>    -- in : sequence of two atoms: {distance, angle};
>    --      'distance' must be >= 0, 'angle' is in radians 
>    -- out: sequence of two atoms: {x, y}
>    atom distance, angle, x, y
> 
>    distance = p[1]
>    angle = p[2]
>    x = distance*cos(angle)
>    y = distance*sin(angle)
>    return {x, y}
> end function
> 
> type point_xy (object x)
>    if sequence(x) and (length(x) = 2)
>    and atom(x[1])
>    and atom(x[2]) then
>       return 1 
>    end if
>    return 0
> end type
> 
> global function rect_to_polar (point_xy p)
>    -- convert rectangular coordinates to polar coordinates
>    -- in : sequence of two atoms: {x, y}
>    -- out: sequence of two elements: {distance, angle}
>    --      - 'distance' is always an atom >= 0
>    --      - 'angle' is normally an atom that expresses radians,
>    --        and is in the half-closed interval ]-PI,+PI].
>    --        If 'distance' equals 0, then 'angle' is {},
>    --        meaning that it is undefined in this case.
>    object angle
>    atom distance, x, y
> 
>    x = p[1]
>    y = p[2]
>    distance = sqrt(x*x + y*y)
>    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
>       elsif y > 0 then
>          angle = HALF_PI
>       else
>          angle = {}            -- The angle is undefined in this case.
>       end if
>    end if
>    return {distance, angle}
> end function
> 
...
>
> Regards,
>    Juergen

Hi Juergen,

I disagree with your solution to the special case rect_to_polar({0,0}).  By
setting the undefined angle to {}, you create a situation where the result cannot
be translated back to rectangular coordinates.  You are creating a real problem
in order to solve what (imho) is an imagined problem.

Regards,  Colin