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

Triangulating the Real Projective Plane

We consider the problem of computing a triangulation of the real projective plane P2, given a finite point set S={p1, p2,..., pn} as input. We prove that a triangulation of P2 always exists if at least six points in S are in general position, i.e., no three of them are collinear. We also design an algorithm for triangulating P2 if this necessary condition holds. As far as we know, this is the first computational result on the real projective plane

Rational Approximation Of Transfer Functions In The Hyperion Software

The objective of this paper is to explain how rational approximation is performed within the hyperion software. This work is divided into three parts. In the first part, we explain the theory underlying the algorithm: given some Fourier coe#cients, find a rational transfer function of McMillan degree n of best approximation in the l -sense to the corresponding Fourier series. This gives a certain number of equations for stationary points and we detail in the second part how they can be e#ciently solved numerically, using techniques of automatic di#erentiation. In the last part, we further discuss the complexity of the implementation thus obtained

On The Number Of Cylindrical Shells

Given a set P of n points in three dimensions, a cylindrical shell or zone cylinder is formed bytwo cylindrical cylinders with the same axis such that all points of P are between the two cylinders. We prove that the number of cylindrical shells enclosing P passing through combinatorially di#erent subsets of P has size# # and O#n # #previous known bound was O#n ##

et calcul symbolique

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