CGAL users discussion list

I use the babilonian method, which can approximate a square root in rational
numbers up to a certain precision. The best advantage of this method is that
two identical rational number would produce the same root. The drawback is 
that
it complicates the rational number greatly; For this, I truncate the number to
the precision (i.e., numerator*=10^PRECISION, integer x=div(numerator,
denominator), truncated=x/10^PRECISION).

Amir.

Quoting Fernando Cacciola 
<>:

> Hi Ben,
> Hu Sylvain,
> 
> Sylvain Pion wrote:
> > Ben Supnik wrote:
> >> The docs for make_conforming_Delaunay_2 say that it requires 
> >> ConformingDelaunayTriangulationTraits_2. traits.
> >>
> >> ConformingDelaunayTriangulationTraits_2 is labeled as having "Any 
> >> model of Kernel concept. In particular, all CGAL kernels."
> >>
> >> But...this doesn't seem correct to me - am I right in thinking that 
> >> some CGAL exact pred exact construction kernels do not have sqrt?  The 
> >> one I was using did not, and I get a compile failure due to being 
> >> unable to tkae the sqrt of a number.
> >>
> >> If sqrt is indeed required and not in all kernels, is there a way to 
> >> get an exact predicate/exact construction kernel without one of LEDA 
> >> or GMP?
> > 
> > Known issue (to me at least).
> > 
> > One way to cheat is to define a sqrt() function for the number type
> > that you use, and make it approximate (convert to double, use std::sqrt,
> > and convert back).  It might work for some/most rational number types,
> > and hopefully the algorithms won't break too much...
> > 
> 
> FWIW, the straight skeleton package uses such a cheat.
> 
> If you look at the header:
> 
> CGAL/constructions/Straight_skeleton_cons_ftC2.h
> 
> There is the function:
> 
> inexact_sqrt(num)
> 
> which does what Sylvain said.
> 
> You might wan't to base your version on that one.
> 
> It works for arbitrary number types, it uses CORE::BigFloat instead of 
> double
> if 
> available, and if it uses double, it checks for overflow after the to_double
> 
> conversion, and for Quotient<NT> it avoids the division.
> 
> 
> Best
> 
> Fernando Cacciola
> www.geometryfactory.com
> 
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