Ambient Isotopic Meshing of Implicit Algebraic Surface with Singularities

A complete method is proposed to compute a certified, or ambient isotopic, meshing for an implicit algebraic surface with singularities. By certified, we mean a meshing with correct topology and any given geometric precision. We propose a symbolic-numeric method to compute a certified meshing for the surface inside a box containing singularities and use a modified Plantinga-Vegter marching cube method to compute a certified meshing for the surface inside a box without singularities. Nontrivial examples are given to show the effectiveness of the algorithm. To our knowledge, this is the first method to compute a certified meshing for surfaces with singularities.Comment: 34 pages, 17 Postscript figure

Globally Optimal Spatio-temporal Reconstruction from Cluttered Videos

International audienceWe propose a method for multi-view reconstruction from videos adapted to dynamic cluttered scenes under uncontrolled imaging conditions. Taking visibility into account, and being based on a global optimization of a true spatio-temporal energy, it oilers several desirable properties: no need for silhouettes, robustness to noise, independent from any initialization, no heuristic force, reduced flickering results, etc. Results on real-world data proves the potential of what is, to our knowledge, the only globally optimal spatio-temporal multi-view reconstruction method

On the spine of a PDE surface

yesThe spine of an object is an entity that can characterise the object¿s topology and describes the object by a lower dimension. It has an intuitive appeal for supporting geometric modelling operations. The aim of this paper is to show how a spine for a PDE surface can be generated. For the purpose of the work presented here an analytic solution form for the chosen PDE is utilised. It is shown that the spine of the PDE surface is then computed as a by-product of this analytic solution. This paper also discusses how the of a PDE surface can be used to manipulate the shape. The solution technique adopted here caters for periodic surfaces with general boundary conditions allowing the possibility of the spine based shape manipulation for a wide variety of free-form PDE surface shapes

Geometric Structures for Three-Dimensional Shape Representation

Different geometric structures are investigated in the context of discrete surface representation. It is shown that minimal representations (i.e., polyhedra) can be provided by a surface-based method using nearest neighbors structures or by a volume-based method using the Delaunay triangulation. Both approaches are compared with respect to various criteria, such as space requirements, computation time, constraints on the distribution of the points, facilities for further calculations, and agreement with the actual shape of the objec

2D-Structure Drawings of Similar Molecules

A common strategy in drug design and pharmacophore identification consists of evaluating large sets of molecular structures by comparing their 2D structure drawings. To simplify the chemists' task, the drawings should reveal similarities and differences between drugs. Given a family of molecules all containing a common template, we present an algorithm to compute standardised 2D structure drawings. The molecules being represented as a graph, we compute a structure called supertree in which all molecules can be embedded. Using the correspondences between atoms provided by the supertree, we are able to coordinate the drawings performed by a breadth-first traversal of the molecular graphs. Both parts of the problem are NP-hard. We propose algorithms of heuristic nature