Chris Gray

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We present new results for three problems dealing with a set <i>P</i> of <i>n</i> convex constant-complexity fat polyhedra in 3-space. (i) We describe a data structure for vertical ray shooting in <i>P</i> that has <i>O</i>(log<sup>2</sup> <i>n</i>) query time and uses <i>O</i>(<i>n</i> log<sup>2</sup> <i>n</i>) storage. (ii) We give an algorithm to compute(More)
In this paper we consider imprecise terrains, that is, triangulated terrains with a vertical error interval in the vertices. In particular, we study the problem of removing as many local extrema (minima and maxima) as possible from the terrain. We show that removing only minima or only maxima can be done optimally in O(n log n) time, for a terrain with n(More)
We present a data structure for ray-shooting queries in a set of convex fat polyhedra of total complexity <i>n</i> in <i>R</i><sup>3</sup>. The data structure uses <i>O(n</i><sup>2+&#949;</sup>) storage and preprocessing time, and queries can be answered in <i>O</i>(log<sup>2</sup> <i>n</i>) time. A trade-off between storage and query time is also possible:(More)
his entropy and sense of style, showing me the importance of making software simple and writing concrete, always asking about the why behind the what and how, and his support and inspiration. Two years and some change ago I received an email that lead to what became BPFS. Thank you, Ed Nightingale and Jeremy Condit, for reaching out, for convincing me it(More)
In this paper we study three related problems: (i) Given a fat polygon P , we show how to find a set G of points in P such that every point on the boundary of P sees at least one point of G. The set G is said to guard the boundary of P and its cardinality depends on the shape parameters of P. Fat polygons are often used to model more realistic inputs. (ii)(More)