This topic concerns the structure of geometric objects, in order to allow their representation, characterization, and the description of their evolution either during their modeling or during an animation. Our works belongs particularly to different topological models, like the combinatoric cards, and are done in collaboration with some French laboratories, e.g. iCube (Strasbourg) and Liris (Lyon), with which we regularly publish together.
We also study the links between the physical and topological models for simulation and animation, for instance in the ANR project Dynamé with the laboratory ICA (Grenoble). We also work on fluid simulation with the SIR team (hierarchical simulation, rendering of fluids, physical phenomena simulation like waves or thermal blending).
Last but not least, since some years ago we follow an original approach, without any equivalent in France or in any international team: we propose robust geometric modeling tools, relying on formal methods using graph transformation, integrated into a formal language in our software platform JERBOA.
Concerning the discrete geometry, we are interested in the modeling of object regarding particular space subdivisions. With the perceptual models, this is the topic where the IG and ICONES teams have the more links. Here, the team is the source of numerous works on the analytical models of discrete objects, on the link between the continuous and discrete spaces, and more recently on discrete object fitting.
We have some collaboration with French laboratories like Loria, Liris, and the Gaspard Monge laboratory. At the international level, where our works on the analytical description of structured discrete objects are recognized, we have some collaboration with the NII in Japan, the State University of New York, or the IIT in India.
We study here the physical simulation of the light propagation, for structured objects or environments. Regarding the visualization, the link between perceptual models (studied in ICONES team), the BRDF and the synthesis images is also a specificity of the IG team.
We also work on the visibility representation and usages, focusing on the underlying algorithms, for instance by using the geometric algebra. In collaboration with the SIR team, we thus have proposed different visibility’s application, for instance hard and soft shadows.
At last, the optical propagation simulation is also studied in IG team, by using robust mathematical models (Monte-Carlos, Metropolis, etc.) for defining some innovative simulation algorithms, both robust and fast. These works are done partly in collaboration with the SIR and RESYST team, and IRISA.