CGAL users discussion list

[Cody Rose <>]

Thank you for your replies. I still do not understand your diagnoses of 
my problem exactly, but I think it might be helpful for me to take a 
step back to explain better what I'm doing.

The actual transformations in my application are defined by inexact 
tuples in the form (new x-axis, new y-axis, new z-axis, new origin). (I 
have no control over this -  it is my input.) I have been generating 
each tuple into a CGAL Aff_transformation by first converting it to 
exact representation and then placing each normalized tuple member into 
the corresponding column of the Aff_transformation. (Obviously I don't 
normalize the new origin, and I understand that the sample code I 
provided skips the normalization step, but I just added it and the 
result is the same.)

Is this not an acceptable way to go about this? If not, how should I be 
doing it? And if so, I really feel the need to understand why the 
commutativity I'm looking for does not exist, so I'd appreciate some 
pointers towards further reading I can do (within the CGAL documentation 
or elsewhere) so I don't keep cluttering up this list with questions.

Thank you,
Cody

On 4/1/2013 11:58 PM, Marc Mörig wrote:
> Now I was confused for a moment, since I had checked that the vectors 
> do point in the same direction. However I had only printed the 
> quotients not checked they are actually equal ...
>
> Still, you explanation is incorrect. Regardless of what coefficients 
> you write into the matrix, the transformation will preserve 
> coplanarity. It does however not preserve angles or orthogonality. As 
> you correctly pointed out, it can not be an exact rotation. That is 
> why newell and T do not commute.
>
> Marc
>
> On 04/02/2013 08:22 AM, Sebastien Loriot (GeometryFactory) wrote:
> > The problem comes from your transformation that is not exactly an affine
> > one (you have a limited precision cosinus and sinus in your example).
> > Thus the points transformed no longer lie in a plane which implies that
> > the direction are not the same.
> >
> > Sebastien.