Analytic transformations of everywhere dense point sets

Motion Tracking of Dense Feature Point Sets

Dense point sets have sparse Delaunay triangulations

The spread of a finite set of points is the ratio between the longest and shortest pairwise distances. We prove that the Delaunay triangulation of any set of n points in R3 with spread ∆ has complexity O(∆3). This bound is tight in the worst case for all ∆ = O( √ n). In particular, the Delaunay triangulation of any dense point set has linear complexity. We also generalize this upper bound to re...

Dense point sets with many halving lines

We construct a dense point set of n points in the plane with ne( √ logn) halving lines. This improves the bound O(n log n) of Edelsbrunner, Valtr and Welzl from 1997. We also observe that the upper bound on the maximum number of halving lines of dense point set can be improved to O(n). Our construction can be generalized to higher dimensions, for any d we construct a dense point set of n points...

Open Sets of Diffeomorphisms Having Two Attractors, Each with an Everywhere Dense Basin

We announce the discovery of a diffeomorphism of a three-dimensional manifold with boundary which has two disjoint attractors. Each attractor attracts a set of positive 3-dimensional Lebesgue measure whose points of Lebesgue density are dense in the whole manifold. This situation is stable under small perturbations.

Generic Model Transformations: Write Once, Reuse Everywhere

Model transformation is one of the core techniques in Model Driven Engineering. Many transformation languages exist nowadays, but few offer mechanisms directed to the reuse of whole transformations or transformation fragments in different contexts. Taking inspiration from generic programming, in this paper we define model transformation templates. These templates are defined over metamodel conc...