Modélisation géométrique de surfaces pour des applications photométriques

Keywords :

• Photométrie
• Optique
• Réflecteur
• Géométrie algorithmique
• Transport optimal

The far-field reflector problem consists in building a surface that reflects light from a given source back into a target at infinity with a prescribed intensity distribution. This problem arises in many fields such as art or architecture. In this thesis, we are interested in applications to the car industry. Indeed, this thesis is conducted in partnership with the company Optis that develops lighting and optical simulation software used in the design of car headlights. Surfaces in car headlight reflectors must satisfy several constraints imposed by manufacturers as well as national and international regulatory authorities. These constraints can be objective such as space requirements or compliance with lighting legal standards but can also can be subjective such as the aesthetic aspects of surfaces. Our goal is to provide industrializable tools to solve the reflector problem while taking into account these constraints. First, we focus on the case of point light sources. We rely on the work of Oliker, Glim, Cafarrelli and Wang who show that the reflector problem can be formulated as an optimal transport problem. This formulation of the problem is presented and implemented in a discrete case. In a second step, we take into account some of the constraints imposed by car headlight manufacturers, such as the size and the style of the reflector. The chosen solution consists in using Bezier surfaces defined as the graph of a function parameterized over a planar domain. Bezier surfaces allow to obtain smooth surfaces and the parameterization over a planar domain allows to control the size and style of the reflector. To build the surface, we propose a heuristic based on a fixed-point algorithm. Finally, we take into account extended light sources. We present an approach that iteratively adapts the parameters of the reflector by minimizing the distance between the desired intensity and the reflected intensity. This led us to propose a method that efficiently evaluates the reflection of light on the surface. Methods developed in this thesis were implemented in an industrial setting at our partner company Optis.

Directors:

• Mr Quentin Mérigot (Chargé de Recherche - CNRS )
• Mme Dominique Attali (Directeur de Recherche - CNRS )
• Mr Boris Thibert (Maître de conférence - Université Joseph Fourier )

Raporteurs:

• Mme Raphaëlle Chaine (Professeur - Université Lyon 1 )
• Mr Frédéric Chazal (Directeur de Recherche - Inria Saclay )

Examinators:

• Mr David Coeurjolly (Directeur de recherche - CNRS )