CGAL users discussion list

[Cody Rose <>]

Marc,

Thank you for your reply. Given that they do, in fact, point the same 
direction, do you know why CGAL is considering them unequal? Equality in this 
case is, as I understand it, the entire reason you would use directions 
instead of vectors.

I will contact you directly later today regarding your number type.

Thanks,
Cody

On Mar 30, 2013, at 6:59 AM, Marc Mörig 
<>
 wrote:

> 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
> 
> 
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