Section: Overall Objectives

Introduction

Overall objectives

ALICE is one of the six teams in the Algorithms, Computation, Geometry and Image group in Inria Nancy Grand-Est.

ALICE is a project-team in Computer Graphics. The fundamental aspects of this domain concern the interaction of light with the geometry of the objects. The lighting problem consists in designing accurate and efficient numerical simulation methods for the light transport equation. The geometrical problem consists in developing new solutions to transform and optimize geometric representations. Our original approach to both issues is to restate the problems in terms of numerical optimization. We try to develop solutions that are provably correct, numerically stable and scalable.

• By provably correct, we mean that some properties/invariants of the initial object need to be preserved by our solutions.

• By numerically stable, we mean that our solutions need to be resistant to the degeneracies often encountered in industrial data sets.

• By scalable, we mean that our solutions need to be applicable to data sets of industrial size.

To reach these goals, our approach consists in transforming the physical or geometric problem into a numerical optimization problem, studying the properties of the objective function and designing efficient minimization algorithms. To properly construct these discretizations, we use the formalism of finite element modeling, geometry and topology. We are also interested in fundamental concepts that were recently introduced into the geometry processing community, such as discrete exterior calculus, spectral geometry processing and theory of sampling.

The main applications of our results concern scientific visualization. We develop cooperations with researchers and people from the industry, who experiment applications of our general solutions to various domains, comprising CAD, industrial design, oil exploration and plasma physics. Our solutions are distributed in both open-source software (Graphite , OpenNL , CGAL ) and industrial software (Gocad , DVIZ ).