CGAL users discussion list

[Alejandro Aragon <>]

I see your point but as soon as you start using double precision, the  
"mathematical sense" is out of question, right? 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.

Alejandro M. Aragón

On Jul 23, 2008, at 11:25 AM, Andreas Fabri wrote:

> tolerant algorithms are difficult to implement correctly.
> Imagine you do 1D geometry, and decide that points (numbers)
> are equal if they only differ on the 15th digit.
>
> Imagine a < b < c  in the mathematical sense, and  positioned
> in a way that a ~ b and b ~ c, but  a !~ c then  your algorithms
> on top of the  equality test of points must be written with
> the assumption that your equality test is not transitive.
>
>
> andreas
>
> Alejandro Aragon wrote:
> > Thanks for replying, I actually read the FAQ before posting my  
> > message and I understand that the double type is inexact. However,  
> > I don't see why the need of using an "exact" number type when  
> > algorithms can be modified such that they give exact results within  
> > tolerance. If a double precision type is exact up to the 15th  
> > digit, then algorithms should take that into account so when I try  
> > to intersect that point with the line, the point is supposed to lie  
> > over the line within let's say tol = 10e-14.
> > Why would I use an exact number type? I don't want to do that, it  
> > will slow down a program that I'm actually trying to speed up by  
> > doing some profiling.
> > Alejandro M. Aragón
> > On Jul 23, 2008, at 10:42 AM, Olivier Devillers wrote:
> > > Alejandro Aragon a écrit :
> > > > typedef CGAL::Cartesian<double> KernelType;
> > >
> > > If you compute with double, rounding errors make your points non  
> > > collinear
> > > (e.g. during the decimal to binary conversion if your input is  
> > > given by
> > > floating point number in decimal notation)
> > >
> > > http://www.cgal.org/FAQ.html#inexact_NT
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