Section: New Software and Platforms

Mokabajour

Platforms

Following the pioneering work of Caffarelli and Oliker  [42] , Wang  [85] has shown that the inverse problem of freeforming a convex reflector which sends a prescribed source to a target intensity is a particular instance of Optimal Mass Transportation. The method developed in [7] has been used by researchers of TU Eindhoven in collaboration with Philips Lightning Labs to compute reflectors  [81] in a simplified setting. The industrial motivation is the automatic design of reflector given prescribed source and target illuminance. From the mathematical point of view there is a hierarchy of Optimal Mass Transportation reflector and lenses problems and only the simplest "far field" one can be solved with state of the art Monge-Ampère solvers. We will adapt the Monge-Ampère solvers and also attempt to build real optimized reflector prototypes. We plan on investigating the more complicated near field models and design numerical methods. Finally Monge-Ampère based Optimal Mass Transportation solvers will be made available. This could be used for example in Mesh adaptation.

The web site is under construction https://project.inria.fr/mokabajour/ , preliminary results are available.

This ADT (Simon Legrand) on the numerical free forming of specular reflectors started in december. We implement different types of MA solvers in collaboration with Quentin Mérigot (CEREMADE), Boris Thibert (LJK Grenoble) and Vincent Duval. See https://project.inria.fr/mokabajour/ .