CGAL users discussion list

[Andreas Fabri <>]

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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