Lines Classification in the Conformal Space R^(n+1,1)

International audienceLines classification is the central tool for visibility calculation in dimension $n\ge 2$. It has been previously expressed in Grassmann Algebra, allowing to work with any couple of 2-vectors, which may represent two real lines or not. This article discusses about the nature of lines in the conformal model, searching if such a classification is still valid in R^(n+1,1). First, it shows that the projective classification can be expressed in terms of a {meet} operator. Then, given two real lines, the classification still works in the conformal model, but also allowing us to propound some techniques to identify lines and circles among general 3-vectors

Visualisation interactive de grands bâtiments

Best paper awardNational audienceLes performances des algorithmes de lancer de rayons sont directement liées à la structure accélératrice utilisée. En ce qui concerne les environnements architecturaux, plusieurs travaux ont précédemment démontré que la structure accélératrice la plus efficace est la structure cellules-et-passages. Dans cet article, nous proposons une nouvelle structure accélératrice qui consiste en une extension des structures cellules-et-passages classiques par une description topologique complète de la scène. La structure de données est décrite par un graphe dont le parcours, utilisant l'ensemble des propriétés topologiques de notre modèle, est particulièrement simple et rapide. Nous montrons dans cet article que notre structure permet un rendu interactif même pour de grands bâtiments composés de plusieurs centaines de pièces meublées en prenant en compte l'éclairage direct de plusieurs milliers de sources lumineuses ponctuelles

Modélisation et simulation efficaces du canal de propagation optique sans fil en environnement réel.

National audienceCe papier présente nos travaux concernant la simulation du canal optique sans fil. Cel le-ci repose sur l'utilisation d'un lancé de rayons 3D associé à des méthodes de Monte-Carlo visant à résoudre efficacement, en environnement réel, l'équation d'il lumination globale modélisant la propagation de la lumière

Topological Space Partition for Fast Ray Tracing in Architectural Models

International audienceFast ray-tracing requires an efficient acceleration structure. For architectural environment, the most famous is the cells-and-portals one. Many previous works attempt to automatically construct a good cells-and-portals. We propose a new acceleration structure which extends the classical cells-and-portals. It is automatically extracted from the topological model of a given building. It contains a low number of large volumes, all of them linked into a graph model. The scan of our structure is particularly simple and rapid, using all the topological information available from the topological model. The scan can be done for a single ray, or a wide ray packet. We show in this paper that our structure allows an interactive rendering even for large building models, with direct lighting from some thousands of point lights

Expressing Discrete Geometry using the Conformal Model

International audiencePrimitives and transformations in discrete geometry, such as lines, circles, hyperspheres, hyperplanes, have been defined with classical linear algebra in dimension 2 and 3, leading to different expressions and algorithms. This paper explores the use of the conformal algebra to express these discrete primitives in arbitrary dimensions with a minimum of expressions and then algorithms. Starting with hyperspheres and hyperplanes, a generalization to $k$-sphere is then proposed. This gives one simple and compact formula, valid for all geometric conformal elements in R^n, from the circle to the hypersphere, and the line to the hyperplane

Efficient 2D ray-tracing method for narrow and wide-band channel characterization in micro-cellular configurations

International audienceChannel characterization is an essential step to the development of outdoor or indoor wireless networks. Indeed, for multimedia applications, new radio mobile systems must accurately take into account channel behavior. In this paper, we propose an efficient 2D ray-tracing method to characterize the narrow and wide-band radio channels for a very large number of receivers in micro-cellular configurations. It is based on a quick pre-calculation of an exact 2D visibility graph. The proposed method follows an ITU recommendation, which advocates, for wide-band characterization, only considering the paths included in a 18 dB dynamic range of power impulse response. Contrary to the classical approach, which consists in thresholding the complete impulse response in a post-treatment, our method only computes the significant paths. The interest of the proposed method resides in its significant computation time reduction factor, in comparison with the classical approach and this without any significant loss in accuracy. Received power and wide-band parameter maps are computed for about 40,000 receivers, in a dense urban environment, and are provided with an approximate reduction factor of 4 and 80% of null estimation error in comparison to a classical approach

A Framework for n-dimension Visibility Calculation

4 pagesVisibility computation is a fundamental task in computer graphics, as in many other scientific domains. While it is well understood in two dimensions, this does not remain true in high dimensional spaces. Using Grassmann Algebra, we propose a framework for solving visibility problems in any n-dimensional spaces, for n ≥ 2. Our presentation recalls the problem statement, in two and three dimensions. Then, we formalize the space of n-dimensional lines. Finally, we show how this leads to a global framework for visibility computations, giving an example of use with exact soft shadows

Une optimisation en temps de calcul pour la prédiction de zones de couverture radioélectriques

International audienceThis article presents a method which optimises the computation time for the prediction of a radio coverage, whatever the propagation model used. The principle consists in reducing the number of ap- plication points of the propagation model in relation to a classical technique. The proposed method is based on a multi resolution analysis of measured signals carried out around 2 GHz, and on an electroma- gnetic analysis of the propagation environment. The performances of the method are evaluated in term of reduction in computation time and of accuracy, in comparaison with the classical technique

Lazy visibility evaluation for exact soft shadows

Présentation invitée de l'article du même nom publié en 2012 dans la revue Computer Graphics Forum.International audienceThis paper presents a novel approach to compute high quality and noise-free soft shadows using exact visibility computations. This work relies on a theoretical framework allowing to group lines according to the geometry they intersect. From this study, we derive a new algorithm encoding lazily the visibility from a polygon. Contrary to previous works on from-polygon visibility, our approach is very robust and straightforward to implement. We apply this algorithm to solve exactly and efficiently the visibility of an area light source from any point in a scene. As a consequence, results are not sensitive to noise, contrary to soft shadows methods based on area light source sampling. We demonstrate the reliability of our approach on different scenes and configurations

Cartes de photons et visibilité

Les méthodes de simulation d'éclairage par tracé de photons sont souvent utilisées pour leur simplicité et leur versatilité. Les deux étapes classiques de ces approches sont : (i) les calculs d'inter-réflexions lumineuses, indépendantes du point de vue, correspondant à des suivis de chemins lumineux dont les impacts sur les surfaces de la scène sont stockés sous forme de cartes de photons ; (ii) l'exploitation des cartes de photons pour produire une ou plusieurs images de l'environnement virtuel. La première phase repose exclusivement sur des méthodes de Monte-Carlo ; la seconde requiert au moins une estimation de densité pour le calcul d'éclairement. Malheureusement, le tracé de photons est également connu pour les différents biais produits lors de l'estimation de densité des photons pour le calcul de l'éclairement en un point. Ce rapport montre pourquoi la visibilité est un élément fondamental lors de l'estimation de densité ; nous proposons de la prendre en compte de manière précise pour réduire ou supprimer certains biais. Nos résultats mettent en évidence l'importance de la visibilité dans la qualité des images produites