In this paper, we reexamine in the framework of robust computation the Bent
ley-Ottmann algorithm for reporting intersecting pairs of segments in the p
lane. This algorithm has been reported as being very sensitive to numerical
errors. Indeed, a simple analysis reveals that it involves predicates of d
egree 5, presumably never evaluated exactly in most implementations. Within
the exact-computation paradigm we introduce two models of computation aime
d at replacing the conventional model of real-number arithmetic. The first
model (predicate arithmetic) assumes the exact evaluation of the signs of a
lgebraic expressions of some degree, and the second model (exact arithmetic
) assumes the exact computation of the value of such (bounded-degree) expre
ssions. We identify the characteristic geometric property enabling the corr
ect report of all intersections by plane sweeps. Verification of this prope
rty involves only predicates of (optimal) degree 2, but its straightforward
implementation appears highly inefficient. We then present algorithmic var
iants that have low degree under these models and achieve the same performa
nce as the original Bentley Ottmann algorithm. The technique is applicable
to a more general case of curved segments.