Exact Geometric Computation Using Cascading

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 +,−, ·, /,√ . 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.