Team Alice

Members
Overall Objectives
Scientific Foundations
Application Domains
Software
New Results
Contracts and Grants with Industry
Other Grants and Activities
Dissemination
Bibliography

Section: Overall Objectives

Overall Objectives

History

ALICE is one of the three INRIA projects proposed by former ISA members. This section summarizes the scientific evolution of the research groups within ISA that yielded those three project proposals. More specifically, since VEGAS and ALICE both do research in geometry, this section explains the two different visions of geometry developed by these two project proposals.

One of the principal research orientations of the ISA project was computer vision and augmented reality. A clearly identified group headed by Marie-Odile Berger developed this approach, so it was natural for them to propose the creation of the MAGRITE project.

The other principal research orientation of the ISA project was physically-based light simulation. The main challenges of this domain are both geometrical (visibility complex, surface intersections) and computational (numerical resolution of an integral equation). To deal with the geometrical problems, a 'geometry research group' was created within ISA. The missions of this group were the following three ones:

  1. To generate the surfacic geometry of the scene from volumic Constructive Solid Geometry descriptions, design new intersection algorithms . More precisely, given the equation of two surfaces, the goal is to obtain a parameterization of the intersection;

  2. Find ways of attaching photometric properties to the geometric objects in the scene. For the numerical simulation of light (i.e., energy transfers), it is necessary to find parameterizations with a constant Jacobian (i.e., energy-preserving parameterizations);

  3. Optimize point-to-point visibility requests (they are massively issued by light simulation algorithms).

To make the scope of this research as general as possible, the two main classes of surfacic representations were considered, i.e., algebraic surfaces and meshed models. When using algebraic surfaces, to represent complex objects, piecewise defined surfaces are used. The geometric continuity between the charts is the main challenge of the Geometric Design domain of research. In other words, Geometric Design is concerned with Gk continuity (Geometric Continuity), defined as follows: a surface of class Gk is a surface for which a parameterization of class Ck exists. To construct a G1 -continuous object with a set of parametric polynomial surfaces defined over triangles, it was proved that at least degree 4 is required [22] . We considered the main class of algebraic surfaces used to represent geometry in the Geometric Design community, i.e., rational fractions called NURBS (Non-Uniform Rational B-Splines). However, it quickly appeared to us that the solution of the mathematical problems expressed with NURBS (surface intersection and energy-preserving parameterization) do not have a closed form in general. As a consequence, two complementary approaches were developed in parallel by ISA:

Overall objectives

ALICE is a new project 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 .

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.

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 ) and industrial software ( Gocad ).


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