55 research outputs found
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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