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)
We propose a new model of realistic input: k-guardable objects. An object is k-guardable if its boundary can be seen by k guards in the interior of the object. In this abstract, we describe a simple algorithm for trian-gulating k-guardable polygons. Our algorithm, which is easily implementable, takes linear time assuming that k is constant.
We study the problem of cutting a set of rods (line segments in &#8477;<sup>3</sup>) into fragments, using a minimum number of cuts, so that the resulting set of fragments admits a depth order. We prove that this problem is NP-complete, even when the rods have only three distinct orientations. We also give a polynomial-time approximation algorithm with no(More)