CGAL users discussion list

[Alejandro Aragon <>]

Naive???? Try to represent 0.1 exactly using a double precision type!  
Then you'll realize that as soon as you start using an inexact type,  
the strict "mathematical sense" Andreas was talking about really goes  
away...

I write a GFEM library and as you may know, as soon as you don't use  
standard FEM you need heavy computation involving geometry. A library  
should be written in a way that naive users as me (as you pointed out)  
would expect a point (usually represented by double types) to lie on  
top of a line within the same tolerance as the inexact type.

Alejandro M. Aragón

On Jul 23, 2008, at 12:02 PM, Sylvain Pion wrote:

> 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/
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