Exact Geometric Computation using Cascading
Christoph Burnikel, Stefan Funke, Michael Seel
In this paper we talk about a new efficient numerical approach to
deal with inaccuracy when implementing geometric algorithms. Using
various floating-point filters together with arbitrary precision packages,
we develop an easy-to-use expression compiler called EXPCOMP. EXPCOMP
supports all common operations \( +,-,\cdot ,/,\sqrt{\,} \). Applying a new semi-static filter,
EXPCOMP combines the speed of static filters with the power of dynamic
filters. The filter stages deal with all kinds of floating-point exceptions,
including underflow. The resulting programs show a very good runtime
behaviour.
a preliminary version appeared in Proc.
14th ACM Symposium on Computational Geometry (SoCG) 1998, Minneapolis
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