# Problem: Polygon Representation

Chee Yap yap at cs.nyu.edu
Mon Oct 18 17:15:33 PDT 1999

```Glenn,

Irrationalities that are only algebraic
can be handled.  If the irrationalities
are non-algebraic, this is impossible (in
the sense of being undecidable) in general.
Mixing (algebraic) angles and, say, (algebraic)
lengths in the same setting
is also generally impossible.  The best way
out of this is to assume angles as computed
values and they are implicitly represented.

Two current libraries can handle nested square-roots,
which is the kind of irrationality that
suffices for many basic applications:

(1) LEDA Library:  I think what you want is their
underlying arithmetic called leda_reals.
Leda offers many other useful algorithms
and data structures besides leda_reals.

http://www.mpi-sb.mpg.de/LEDA/

(2) The Core Library

http://cs.nyu.edu/exact/core/

Speed may be an issue if your application
has high algebraic degree, but at least in principle,
these systems can do it.  These are current topics
of research.  Both systems are described
in papers in the proceedings of the 15th
ACM Symp.on Computational Geometry (June 1999) (and
can be found in the respective sites).

--Chee Yap

> From compgeom-owner at research.bell-labs.com Sun Oct 17 22:01 EDT 1999
> Date: Wed, 6 Oct 1999 23:27:38 -0400 (EDT)
> X-Authentication-Warning: paul.rutgers.edu: rhoads set sender to rhoads at paul.rutgers.edu using -f
> To: compgeom-discuss at research.bell-labs.com
> Subject: Problem: Polygon Representation
>
>
> Hi everybody,
>
> I've written a program where polygons are represented as a sequence
> of edges and I need to generalize my representation to handle polygons
> where both the angles and edge lengths could be *irrational*.  At the
> moment, I'm stuck on how to do this.  I would really appreciate it if
> somebody would give me an idea, suggestion, or a useful reference on
> representing polygons with irrational angles and edge lengths.
>
> Regards,
>
> Glenn
>
> ---
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