CGAL users discussion list

[Sylvain Pion <>]

Alejandro Aragon a écrit :
> I see your point but as soon as you start using double precision, the 
> "mathematical sense" is out of question, right?

That's the naive view.  A double value has a real (exact) value
(except NaNs and infinities).  That is a fact.
Most (if not all) CGAL algorithms are designed with the model that the
input is known exactly, and compute the exact answer.  They are proved
in the literature in this model.

Defining computational geometry structures and algorithms in a fuzzy model
has been done for some problems in the literature, but it is way less
generally used in computational geometry, and CGAL does not support it so far.
And it is hard.

> So that a < b is not 
> true if they are within tolerance. Also, what is the chance that your 
> algorithms encounter something like what you described, where in 
> "mathematical sense" a < b < c and then you think CGAL has a bug because 
> it's not giving you the answer you expect? Instead, if you use a type 
> that is not exact, you would expect algorithms to behave with the same 
> degree of "exactness". I guess that is what users would expect, at least 
> that is what I expect. If they want a more exact predicate, then use an 
> "exact" type.

Depends on your needs.  How do you define this tolerance?
(note that interval arithmetic can be used with CGAL, but this is not double,
this is slower, but this gives guarantees).
Tell us more about your problem.

--
Sylvain Pion
INRIA Sophia-Antipolis
Geometrica Project-Team
CGAL, http://cgal.org/