W. Barth,
"Using Special Arithmetic in Geometric Algorithms", to 
appear in <I>Numerical Methods and Error-Bounds, Proceedings of the  
IMACS-GAMM International Symposium, University of Oldenburg, Germany</I>,
July 1995, Akademie Verlag, Berlin, 1996. 
<P>

The application of interval arithmetic shown in this paper deals with  
geometric algorithms. The purpose for which we use this reliable computation  
is different from the usual one. It is not to find an inclusion for the final  
results, but it is to control the algorithm correctly, i.e., to find
the right branch the algorithm has to follow from the signs of intermediate  
results, this means assuring reliable control. The problem arises when
working  
with the method of Edelsbrunner and M\"ucke for eliminating all special cases  
in geometric algorithms. Of course the sign of an intermediate result  
(arithmetic expression) can only be determined correctly without any
exception  
by exact arithmetic. But it is much more efficient to calculate such an  
expression first with interval arithmetic, and only in the few cases
where the  
resulting interval contains zero the time consuming exact calculation has to  
be performed.

 <P> W. Barth