CGAL users discussion list

Le Mer 7 mars 2007 0:45, Iosif Pinelis a écrit :
> Thank you again. This may address one of my 3 remaining questions. I am
> not quite sure, though, what exactly you mean here by:
>
>    1. a polygon (a closed piecewise-linear curve?)

I would define a polygon as a closed piecewise-linear curve with a set of
vertices on it, such that each singular point (i.e. with a discontinuous
derivative) is a vertex.

>    2. a flat polygon (a polygon for which some of the determinants are
>       zero?)

I would say a polygon which is contained in a line, in other words, a
polygon such that the determinant at each vertex is zero.

>    3. a vertex (where the determinant is nonzero?)

I would say the set of vertices is some finite set of points on the curve,
which contains the singular points.

> Given the definition of a polygon as a closed piecewise-linear curve,
> your nicer, topological definition would be clear. But the "biggest"
> question remains: is there a rigorous proof  that the CGAL convexity
> test exactly corresponds to the definition that you gave?

Check whether you are convinced by my sketch of proof (in the previous
message) or not.
-- 
Camille Wormser