Séminaires de l'année 2003

• Orateur: Gert Vegter, Groningen University, The Netherlands
• Titre : "COMPUTING CONTOURS OF EVOLVING IMPLICIT SURFACES"
• Résumé :
  The contour generator of a smooth surface in three-space, under parallel or perspective projection, locally separates backward and forward facing regions on the surface. It consists of those points on the surface where the normal is perpendicular to the direction of projection. The apparent contour is the projection of the contour generator onto the image plane.
  
  The apparent contour and the contour generator are important visibility features of a smooth surface, e.g., in connection with visualization and non-photorealistic rendering. In computer vision, techniques have been developed for partial reconstruction of a surface from a sequence of apparent contours corresponding to a discrete set of nearby projection directions.
  
  Generically, the contour generator is a smooth curve consisting of several components. These components may merge or split when the projection direction changes. In this talk we describe generic evolutions of the apparent contour under varying directions of projection, and we present an algorithm for reliable computation of the contour generator of implicit surfaces.

• Oratrice: Ileana Streinu, Computer Science, Smith College, USA
• Titre : "GRAPH REALIZATIONS WITH PARTIAL ORIENTED MATROID CONSTRAINTS"
• Résumé :
  From Mnev's celebrated universality theorem, it follows that realizing graphs with oriented matroid constraints is as hard as the existential theory of the reals. But if we only impose some partial oriented matroid constraints, how far can we go? We investigate this problem and some of its connections with rigidity theory. In particular, we show that every planar minimally rigid graph has a realization as a pseudo-triangulation.

• Orateur: Ciprian Borcea, Rider University, USA
• Titre : SYSTÈMES ARTICULÉS ET GÉOMÉTRIE ALGÉBRIQUE
• Résumé :
  On étudie des variétés algébriques qui décrivent l'espace des configurations de systèmes articulés, en partant des polygones plans dont les côtés ont des longueurs données.
  
  Certaines considérations remontent aux travaux de Darboux [D] et Bricard [B], mais se rattachent aussi à des questions récentes de symmétrie mirroir (variétés de Calabi-Yau) et conformations moléculaires.
  
  [B] Bricard, Raoul: Leçons de cinématique, 1926-7, Gauthier-Villars, Paris.
  [D] Darboux, Gaston: De l'emploi des fonctions elliptiques dans la théorie du quadrilatère plan, Bull. Sci. Math. (1879), 109-128.

• Orateur: Jack Snoeyink, Computer Science, UNC Chapel Hill, USA
• Titre : "ALMOST-DELAUNAY TETRAHEDRA FOR ANALYZING PROTEIN STRUCTURE"
• Résumé :
  Delaunay tessellations and Voronoi diagrams capture proximity relationships among sets of points. When applied to points representing protein atoms or residue positions, they are used to compute molecular surfaces and protein volumes, to define cavities and pockets, to analyze and score packing interactions, and to find structural motifs. Since atom and residue coordinates are known imprecisely, we explore the effect of coordinate perturbation on Delaunay-based scoring and motif finding.
  
  We define and compute the almost-Delaunay tetrahedra, which are tetrahedra that can become part of a Delaunay tessellation if the point coordinates are perturbed by some epsilon. Analysis of these tetrahedra indicates that Delaunay four-body potential functions are robust and leads to new methods to detect structural motifs.
  
  Fortunately for the audience, many of these long words can be associated with simple pictures. For a preview, see: http://www.cs.unc.edu/~debug/papers/AlmDel. This is joint work with Deepak Bandyopadhyay (UNC CS) and Alex Tropsha (UNC Pharmacy).

• Orateur: André Rassat (Dépt. Chimie, ENS, UMR CNRS 8640)
• Titre : "CHIMIE, GRAPHES ET POLYÈDRES"
• Résumé :
  Dans cet exposé, je voudrais présenter quelques considérations liées à la chiralité des molécules ou des objets de l'espace ordinaire. J'espère grâce à ce séminaire obtenir de l'aide sur des problèmes de ce type, et en particulier, sur la distance de Hausdorff entre deux molécules.[1]
  Dans une première partie, je donnerai des constructions qui pour tout groupe de symétrie «ponctuel» donné, permettent d'obtenir des polyèdres (ou pour les molécules, des «sphéroarènes») appartenant à ce groupe.[2]
  Dans une deuxième partie, je rappellerai comment on obtient les coordonnées topologiques [3] d'un polyèdre trivalent à partir de son graphe plan. J'essaierai de montrer comment la corrélation liée à l'abaissement de symétrie entre la sphère et le polyèdre, ainsi que le mouvement d'un électron dans un parallélépipède rectangle suggèrent la forme de ces coordonnées.
  Enfin, après un rappel sur la méthode généralement utilisée pour décrire de façon univoque un des deux énantiomères d'une molécule par un «descripteur de chiralité», je présenterai des méthodes qui permettent d'attribuer un tel descripteur à un polyèdre chiral et même à un graphe plan.
  
  [1] A. Rassat."Un critère de classement des systèmes chiraux de points à partir de la distance au sens de Haussdorf".C.R. Académie des Sciences, 1984, 299, série II, n° 2. 53-55, .
  [2] A. Rassat. "Chirality and Symmetry Aspects of Spheroarenes Including Fullerenes" Chirality 2001, 13, 395-402
  [3] D. E. Manolopoulos, P. W. Fowler, "Topological co-ordinates for fullerenes"J. Chem. Phys. 1992, 96, 7603-7614.

• Orateur: Pierre Alliez (INRIA-Sophia)
• Titre : "INTERACTIVE SURFACE REMESHING"
• Résumé : As 3D geometry becomes a prevalent media, a proliferation of meshes are readily available, coming from a variety of sources including 3D scanners, modeling software, and output from computer vision algorithms. Although these meshes capture geometry accurately, their sampling quality is usually far from ideal for subsequent applications. For instance, these (sometimes highly) irregular meshes are not appropriate for computations using Finite Elements, or for rapid, textured display on low-end computers. Instead, meshes with nearly-equilateral triangles, a smooth gradation of sample density depending on curvatures, or even uniform sampling are preferable inputs to most existing geometry processing algorithms. Remeshing, i.e., modifying the sampling and connectivity of a geometry to generate a new mesh, is therefore a fundamental step for efficient mesh processing.
  
  In this talk we propose a precise, interactive, and flexible remeshing technique for arbitrary geometry. Unlike previous techniques, we offer a high level of control over the sampling quality of the output mesh, as well as an unprecedented speed of execution. We will show that our remeshing engine can interactively and accurately generate meshes with any tailored sampling, allowing the user to easily design a resampled geometry conforming to her requirements.