Section: Scientific Foundations
Introduction
Computer Graphics is a quickly evolving domain of research. These last few years, both acquisition techniques (e.g., range laser scanners) and computer graphics hardware (the socalled GPU's, for Graphics Processing Units) have made considerable advances. However, as shown in Figure 1 , despite these advances, fundamental problems still remain open. For instance, a scanned mesh composed of hundred million triangles cannot be used directly in realtime visualization or complex numerical simulation. To design efficient solutions for these difficult problems, ALICE studies two fundamental issues in Computer Graphics:

the representation of the objects, i.e., their geometry and physical properties;

the interaction between these objects and light.
Historically, these two issues have been studied by independent research communities. However, we think that they share a common theoretical basis. For instance, multiresolution and wavelets were mathematical tools used by both communities [30] . We develop a new approach, which consists in studying the geometry and lighting from the numerical analysis point of view. In our approach, geometry processing and light simulation are systematically restated as a (possibly nonlinear and/or constrained) functional optimization problem. This type of formulation leads to algorithms that are more efficient. Our longterm research goal is to find a formulation that permits a unified treatment of geometry and illumination over this geometry.