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The expected number of 3D visibility events is linear
 SIAM J. COMPUTING
, 2002
"... In this paper, we show that, amongst n uniformly distributed unit balls in R³ the expected number of maximal nonoccluded line segments tangent to four balls is linear, considerably improving the previously known upper bound. Using our techniques we show a linear bound on the expected size of the vi ..."
Abstract

Cited by 20 (9 self)
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In this paper, we show that, amongst n uniformly distributed unit balls in R³ the expected number of maximal nonoccluded line segments tangent to four balls is linear, considerably improving the previously known upper bound. Using our techniques we show a linear bound on the expected size of the visibility complex, a data structure encoding the visibility information of a scene, providing evidence that the storage requirement for this data structure is not necessarily prohibitive. Our results
A Linear Bound on the Expected Number of Visibility Events
, 2001
"... In this paper, we show that the expected number of maximal nonoccluded line segments tangent to 4 balls, amongst n uniformly distributed unit balls in R³, is at most linear. This extends the result of Durand [5] who showed that the expected number of lines (possibly occluded) tangent to 4 unit ball ..."
Abstract
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In this paper, we show that the expected number of maximal nonoccluded line segments tangent to 4 balls, amongst n uniformly distributed unit balls in R³, is at most linear. This extends the result of Durand [5] who showed that the expected number of lines (possibly occluded) tangent to 4 unit balls, under the same model, is O(n ). Using our techniques we show a linear bound on the expected size of the visibility complex, providing evidence that the storage requirement for this data structure is not prohibitive.