Efficient exact arithmetic for computational geometry

Abstract

We experiment with exact integer arithmetic to implement primitives for geometric algorithms. Naive use of exact arithmetic - either modular or multiprecision integer - increases execution time dramatically over the use of floating-point arithmetic. By combining tuned multiprecision integer arithmetic and a floating-point filter based on interval analysis, we can obtain the effect of exact integer arithmetic at a cost close to that of floating-point arithmetic. We describe an experimental expression compiler that conveniently packages our techniques.