Team Alice

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

Section: Scientific Foundations

Introduction

Figure 1. Top: Computer Graphics in the 1970's: Henri Gouraud's shading algorithm. His algorithm is still used today, 30 years after. To obtain the data, Sylvie Gouraud accepted to be manually digitalized (A), this gave this facetted surface (B) which Henri Gouraud did improve with his celebrated smooth shading algorithm (C). Bottom: Computer Graphics in the 2000's: huge advances were made. However, the basic problems still remain unsolved, i.e. finding common representations for data acquisition (D), modeling (E) and image generation (F) (image (D) and 3D model in (E),(F) courtesy of Stanford Digital Michelangelo Project).
cg_evolution

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, as shown in Figure 1 , despites these advances, fundamental problems still remain open. For instance, a scanned mesh composed of 30 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, in isolation. However, we think that they share a common theoretical basis. For instance, multi-resolution and wavelets were mathematical tools used by both communities [24] . We develop a new approach, that 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. Our long-term research goal is to find a formulation that permits a unified treatment of geometry and illumination over this geometry.


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