Section: New Results

Applications

Creating large-scale city models from 3D-point clouds: a robust approach with hybrid representation

Participant : Florent Lafarge.

We present a novel and robust method for modeling cities from 3D-point data. Our algorithm provides a more complete description than existing approaches by reconstructing simultaneously buildings, trees and topologically complex grounds. A major contribution of our work is the original way of modeling buildings which guarantees a high generalization level while having semantized and compact representations. Geometric 3D-primitives such as planes, cylinders, spheres or cones describe regular roof sections, and are combined with mesh-patches that represent irregular roof components. The various urban components interact through a non-convex energy minimization problem in which they are propagated under arrangement constraints over a planimetric map. Our approach is experimentally validated on complex buildings and large urban scenes of millions of points, and is compared to state-of-the-art methods [19] .

The sticky geometry of the cosmic web

Participant : Monique Teillaud.

In collaboration with Johan Hidding, Rien van de Weygaert, Bernard J.T. Jones (Kapteyn Institute, Groningen University) and Gert Vegter (Johan Bernoulli Institute, Groningen University)

We highlight the application of Computational Geometry to our understanding of the formation and dynamics of the Cosmic Web. The emergence of this intricate and pervasive weblike structure of the Universe on Megaparsec scales can be approximated by a well-known equation from fluid mechanics, the Burgers’ equation. The solution to this equation can be obtained from a geometrical formalism. We have extended and improved this method by invoking weighted Delaunay and Voronoi tessellations. The duality between these tessellations finds a remarkable and profound reflection in the description of physical systems in Eulerian and Lagrangian terms [28] .