CGAL users discussion list

[Marc Mörig <>]

Dear Cody,

the resulting normals in your example are linearly dependend, i.e. do 
point in the same direction. Even if Newells method returns a normalized 
vector (I don't know ...) the affine transformation may change its length.

Btw: I would still be very interested in comparing the performance of 
leda::real and Core::Expr to my number type within your application.

Regards,
Marc Mörig

On 29.03.2013 23:11, Cody Rose wrote:
> Hello,
>
> I've stumbled into some CGAL behavior I can't explain and I was hoping
> that someone could help me understand it. In my application, I'm using
> Newell's method to calculate the approximate normal for a polygon-like
> series of points (http://cs.haifa.ac.il/~gordon/plane.pdf). (The idea is
> that if all the points are actually coplanar, it will yield the true
> normal, but if they aren't quite, it will give a "best fit.") The
> problem I'm having is essentially this, given a particular affine
> transformation T and the kernel Cartesian<leda_real>:
>
> newell(T(points)) != T(newell(points))
>
> And I can't figure out why not, since I was under the impression that
> this kernel is exact (and that this should work in an exact kernel). I
> can't chalk it up to variations in how Newell's method approximates a
> plane fit before and after the transformation, because in the example I
> attached, all the points are actually coplanar after all. (Honestly that
> explanation wouldn't make sense to me anyway.)
>
> So I feel like I'm missing something about the way exactness (or this
> affine transformation) works. Can anyone clear this up?
>
> Cody Rose