Gap Processing for Adaptive Maximal Poisson-Disk Sampling

In this paper, we study the generation of maximal Poisson-disk sets with varying radii. First, we present a geometric analysis of gaps in such disk sets. This analysis is the basis for maximal and adaptive sampling in Euclidean space and on manifolds. Second, we propose efficient algorithms and data structures to detect gaps and update gaps when disks are inserted, deleted, moved, or have their radius changed. We build on the concepts of the regular triangulation and the power diagram. Third, we will show how our analysis can make a contribution to the state-of-the-art in surface remeshing.Comment: 16 pages. ACM Transactions on Graphics, 201

Evolution of galaxies due to self-excitation

These lectures will cover methods for studying the evolution of galaxies since their formation. Because the properties of a galaxy depend on its history, an understanding of galaxy evolution requires that we understand the dynamical interplay between all components. The first part will emphasize n-body simulation methods which minimize sampling noise. These techniques are based on harmonic expansions and scale linearly with the number of bodies, similar to Fourier transform solutions used in cosmological simulations. Although fast, until recently they were only efficiently used for small number of geometries and background profiles. These same techniques may be used to study the modes and response of a galaxy to an arbitrary perturbation. In particular, I will describe the modal spectra of stellar systems and role of damped modes which are generic to stellar systems in interactions and appear to play a significant role in determining the common structures that we see. The general development leads indirectly to guidelines for the number of particles necessary to adequately represent the gravitational field such that the modal spectrum is resolvable. I will then apply these same excitation to understanding the importance of noise to galaxy evolution.Comment: 24 pages, 7 figures, using Sussp.sty (included). Lectures presented at the NATO Advanced Study Institute, "The Restless Universe: Applications of Gravitational N-Body Dynamics to Planetary, Stellar and Galactic Systems," Blair Atholl, July 200

A graphical, scalable and intuitive method for the placement and the connection of biological cells

We introduce a graphical method originating from the computer graphics domain that is used for the arbitrary and intuitive placement of cells over a two-dimensional manifold. Using a bitmap image as input, where the color indicates the identity of the different structures and the alpha channel indicates the local cell density, this method guarantees a discrete distribution of cell position respecting the local density function. This method scales to any number of cells, allows to specify several different structures at once with arbitrary shapes and provides a scalable and versatile alternative to the more classical assumption of a uniform non-spatial distribution. Furthermore, several connection schemes can be derived from the paired distances between cells using either an automatic mapping or a user-defined local reference frame, providing new computational properties for the underlying model. The method is illustrated on a discrete homogeneous neural field, on the distribution of cones and rods in the retina and on a coronal view of the basal ganglia.Comment: Corresponding code at https://github.com/rougier/spatial-computatio