A performance comparison of interval arithmetic and error analysis in geometric predicates (2000) [2 citations — 1 self]
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Abstract:
notwithstanding any copyright annotation thereon. The views and conclusions contained in this document are those of the authors, and should not be interpreted as necessarily representing the ocial policies or endorsements, either expressed or implied, of the Department of Defense or the U.S. Government. Exact arithmetic is used to build robust implementations of geometric algorithms. However, it is slow, and computing to arbitrary precision is unnecessary most of the time. Floatingpoint lters, which are commonly used instead, are fast self-checking computations that fall back on exact arithmetic when the check indicates that the fast calculation is incorrect. The use of interval arithmetic in oating-point lters is attractive because they can be used to build geometric software that does not assume error-free inputs. However, the use of interval arithmetic might impose a penalty on performance. In this report, we study the performance impact of using interval arithmetic based lters in the line-side and in-circle geometric predicates. We report results obtained with implementations of two commonly used geometric algorithms: Delaunay triangulation and convex hull computation, and for a range of point distributions. Our results indicate that interval arithmetic imposes a performance penalty of at most 2 in the worst case, and even improves performance in some cases.
