## Section: Research Program

### 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 so-called GPU's, for Graphics
Processing Units) have made considerable advances.
However, despite these advances, fundamental problems still remain open.
For instance, a scanned mesh composed of hundred millions of triangles cannot
be used directly in real-time visualization or complex
numerical simulation. To design efficient solutions for these
difficult problems, ALICE studies two fundamental issues in Computer
Graphics:

Historically, these two issues have been studied by independent
research communities. However, we think that they share
a common theoretical basis. For instance, multi-resolution and
wavelets were mathematical tools used by both communities [31].
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 non-linear and/or constrained) functional
optimization problem. This type of formulation leads to algorithms
that are more efficient. Our long-term research goal is
to find a formulation that permits a unified treatment
of geometry and illumination over this geometry.