Experimental study on acceleration of an exact-arithmetic geometric algorithm

The paper presents a method for accelerating an exact arithmetic geometric algorithm. The exact arithmetic is one of the most promising approaches for making numerically robust geometric algorithms, because it enables us to always judge the topological structures of objects correctly and thus makes us free from inconsistency. However, exact arithmetic costs much more time than floating point arithmetic. In order to decrease this cost, the paper studies a hybrid method using both exact and floating point arithmetic. For each judgement in the algorithm, floating point arithmetic is first applied, and exact arithmetic is used only when the floating point computation is not reliable. This idea is applied to the construction of three dimensional convex hulls, and experiments show that 80~95% of the computational cost can be saved