Hazel Everett

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Motivated by visibility problems in three dimensions, we investigate the complexity and construction of the set of tangent lines in a scene of three-dimensional polyhedra. We prove that the set of lines tangent to four possibly intersecting convex polyhedra in R3 with a total of n edges consists of Θ(n2) connected components in the worst case. In the(More)
In this paper, we show that, amongst n uniformly distributed unit balls in R , the expected number of maximal non-occluded 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(More)
Given a family of k disjoint connected polygonal sites in general position and of total complexity n, we consider the farthest-site Voronoi diagram of these sites, where the distance to a site is the distance to a closest point on it. We show that the complexity of this diagram is O(n), and give an O(n log n) time algorithm to compute it. We also prove a(More)
We completely describe the structure of the connected components of transversals to a collection of n line segments in R. Generically, the set of transversal to four segments consist of zero or two lines. We catalog the non-generic cases and show that n > 3 arbitrary line segments in R admit at most n connected components of line transversals, and that this(More)
Given a set of n points in the plane, we consider the problem of computing the circular ordering of the points about a viewpoint q and efficiently maintaining this ordering information as q moves. In linear space, and after O(n log n) preprocessing time, our solution maintains the view at a cost of O(log n) amortized time (resp. O(log n) worst case time)(More)
In this paper we study various geometric predicates for determining the existence of and categorizing the configurations of lines in 3D that are transversal to lines or segments. We compute the degrees of standard procedures of evaluating these predicates. The degrees of some of these procedures are surprisingly high (up to 168), which may explain why(More)