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In this paper we show how to traverse a subdivision and to report all cells, edges and vertices, without making use of mark bits in the structure or a stack. We do this by performing a depth-rst search on the subdivision, using local criteria for deciding what is the next cell to visit. Our method is extremely simple and provably correct. The algorithm has(More)
Most of the existing methods for measuring melodic similarity use one-dimensional textual representations of music notation, so that melodic similarity can be measured by calculating editing distances. We view notes as weighted points in a two-dimensional space, with the coordinates of the points reflecting the pitch and onset time of notes and the weights(More)
We consider a competitive facility location problem with two players. Players alternate placing points, one at a time, into the playing arena, until each of them has placed n points. The arena is then subdivided according to the nearest-neighbor rule, and the player whose points control the larger area wins. We present a winning strategy for the second(More)
Casting is a manufacturing process in which molten material is poured into a cast (mould), which is opened after the material has solidified. As in all applications of robotics, we have to deal with imperfect control of the casting machinery. In this paper, we consider directional uncertainty: given a 3-dimensional polyhedral object, is there a polyhedral(More)
We consider a competitive facility location problem with two players. Players alternate placing points, one at a time, into the playing arena, until each of them has placed n points. The arena is then subdivided according to the nearest-neighbor rule, and the player whose points control the larger area wins. We present a winning strategy for the second(More)
In this paper we show that in sorting-based applications of parametric search, Quicksort can replace the parallel sorting algorithms that are usually advocated, and we argue that Cole's optimization of certain parametric-search algorithms may be unnecessary under realistic assumptions about the input. Furthermore, we present a generic, flexible, and(More)
Let P be a simple polygon. We define a witness set W to be a set of points such that if any (prospective) guard set G guards W , then it is guaranteed that G guards P. We show that not all polygons admit a finite witness set. If a finite minimal witness set exists, then it cannot contain any witness in the interior of P ; all witnesses must lie on the(More)
For 2D or 3D meshes that represent the domain of continuous function to the reals, the contours|or isosurfaces|of a speciied value are an important w ay to visualize the function. To nd such contours, a seed set can be used for the starting points from which the traversal of the contours can begin. This paper gives the rst methods to obtain seed sets that(More)
Given a terrain defined as a piecewise-linear function with n triangles, and m point sites on it, we would like to identify the location on the terrain that minimizes the maximum distance to the sites. The distance is measured as the length of the Euclidean shortest path along the terrain. To simplify the problem somewhat, we extend the terrain to (the(More)
A hierarchical decomposition of a simple polygon is introduced. The hierarchy has depth O(log n), linear size, and its regions have at most three neighbors. Using this hierarchy, circular ray shooting queries in a simple polygon can be answered in O(log 2 n) query time and O(n log n) space. If the radius of the circle is xed, the query time can be improved(More)