Improved Incremental Randomized Delaunay Triangulation

We propose a new data structure to compute the Delaunay triangulation of a set of points in the plane. It combines good worst case complexity, fast behavior on real data, and small memory occupation. The location structure is organized into several levels. The lowest level just consists of the triangulation, then each level contains the triangulation of a small sample of the levels below. Point location is done by marching in a triangulation to determine the nearest neighbor of the query at that level, then the march restarts from that neighbor at the level below. Using a small sample (3%) allows a small memory occupation; the march and the use of the nearest neighbor to change levels quickly locate the query.Comment: 19 pages, 7 figures Proc. 14th Annu. ACM Sympos. Comput. Geom., 106--115, 199

Geometric Compression for Interactive Transmission

The compression of geometric structures is a relatively new #eld of data compression. Since about 1995, several articles have dealt with the coding of meshes, using for most of them the following approach: the vertices of the mesh are coded in an order that partially contains the topology of the mesh. In the same time, some simple rules attempt to predict the position of each vertex from the positions of its neighbors that have been previously coded

Dog Bites Postman: Point Location in the Moving Voronoi Diagram and Related Problems

In this paper, we discuss two variations of the two-dimensional post-office problem that arise when the post-offices are n postmen moving with constant velocities. The first variation addresses the question: given a point q 0 and time t 0 who is the nearest postman to q 0 at time t 0 ? We present a randomized incremental data structure that answers the query in expected O(log 2 n) time. The second variation views a query point as a dog searching for a postman to bite and finds the postman that a dog running with speed v d could reach first. We show that if the dog is quicker than all of the postmen then the data structure developed for the first problem permits us to solve this one in O(log 2 n) time as well. The proposed structure is semi-dynamic, that is the set of postmen can be modified by inserting new postmen. A fully dynamic structure supporting also deletions can be obtained, but in that case the query time becomes O(log 3 n)

et calcul symbolique

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