OpenEuphoria

Re: New proposal for math.e

• Posted by Juergen Luethje <j.lue at ??x.de> Aug 05, 2007
• 699 views

Colin Taylor wrote:

> Juergen Luethje wrote:
> > 
> > Colin Taylor wrote:
> > 
> > <snip>
> > >        
> > > 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
> 
> When I wrote these functions some years ago I wanted them to be perfectly 
> reversable so that data could be transformed in both directions without 
> any corruption.  I think I also wanted to adopt the same angle notation 
> which was used by another application (don't remember which - possibly 
> AutoCAD) so that I could easily import and export data.
> 
> I leave it to Juergen or someone else to recommend an angle notation which 
> works best with Euphoria, and (if necessary) modify the functions to suit.
> 
> Regards,  Colin

Helo Colin,

in the meantime, I've looked closer to this stuff, and I think
when rect_to_polar() returns an angle between -PI and +PI, like
yours code does, this is probably the most straightforward way.
I'd like to read an opinion of a mathematician, though.

What I'd actually like to change in rect_to_polar() is the return
value for the angle, when both x and y are 0. In this case the angle
is undefined. This would be again a good case for having 'nil' or
'nan' available in Euphoria. We don't have it, but I think at least
it's better to assign 0 to the angle in this case, rather than HALF_PI.
And the docs should contain something like this:
| Note: A calling program should firstly check the
|       'distance' value of the result. If it is 0, then the
|       'angle' value of the result is actually undefined.

Regards,
   Juergen