Showing papers by "Hans-Peter Lenhof published in 1992"
24 Oct 1992
TL;DR: An algorithm is given that computes the k closest pairs in the set S in O(nlogn+k) time, using O(n-k) space, which is optimal and fits in the algebraic decision tree model.
Abstract: Let S be a set of n points in D-dimensional space, where D is a constant, and let k be an integer between 1 and (/sub 2//sup n/) An algorithm is given that computes the k closest pairs in the set S in O(nlogn+k) time, using O(n+k) space. The algorithm fits in the algebraic decision tree model and is, therefore, optimal. >
28 citations
08 Jul 1992
TL;DR: 3D visibility problems for scenes that consist of n non-intersecting spheres are investigated, and algorithms that compute the visibility graph at the start of the flight, all time parameters t at which the topology of the scene changes, and the corresponding topology changes are described.
Abstract: We investigate 3D visibility problems for scenes that consist of n non-intersecting spheres. The viewing point v moves on a flightpath that is part of a “circle at infinity” given by a plane P and a range of angles {α(t)¦t ∈ [0∶1]} ⊂ [0∶2π], At “time” t, the lines of sight are parallel to the ray r(t) in the plane P, which starts in the origin of P and represents the angle α(t) (orthographic views of the scene). We describe algorithms that compute the visibility graph at the start of the flight, all time parameters t at which the topology of the scene changes, and the corresponding topology changes. We present an algorithm with running time O((nk+p)log n), where n is the number of spheres in the scene; p is the number of transparent topology changes (the number of different scene topologies visible along the flightpath, assuming that all spheres are transparent); and k denotes the number of vertices (conflicts) which are in the (transparent) visibility graph at the start and do not disappear during the flight.
10 citations
01 Jan 1992
TL;DR: In this article, the authors investigated 3D visibility problems for scenes that consist of n non-intersecting spheres, and presented an algorithm with running time O((nk+p)log n), where n is the number of spheres in the scene; p is number of transparent topology changes (the number of different scene topologies visible along the flightpath, assuming that all spheres are transparent); and k denotes the vertices (conflicts) which are in the visibility graph at the start and do not disappear during the flight.
Abstract: We investigate 3D visibility problems for scenes that consist of n non-intersecting spheres. The viewing point v moves on a flightpath that is part of a “circle at infinity” given by a plane P and a range of angles {α(t)¦t ∈ [0∶1]} ⊂ [0∶2π], At “time” t, the lines of sight are parallel to the ray r(t) in the plane P, which starts in the origin of P and represents the angle α(t) (orthographic views of the scene). We describe algorithms that compute the visibility graph at the start of the flight, all time parameters t at which the topology of the scene changes, and the corresponding topology changes. We present an algorithm with running time O((nk+p)log n), where n is the number of spheres in the scene; p is the number of transparent topology changes (the number of different scene topologies visible along the flightpath, assuming that all spheres are transparent); and k denotes the number of vertices (conflicts) which are in the (transparent) visibility graph at the start and do not disappear during the flight.
3 citations