Resumen de Reflector shape design from radiance distributions. Cad for luminaries
Gustavo Patow 
This thesis presents techniques for the design of reflector shapes from prescribed optical properties (far-field radiance distribution), geometrical constraints and, if available, a user-given initial guess, The reflector shape to be found is just a part of a set of pieces of what is known in lighting engineering as an optical set, and is composed of a lamp (light source), a reflector, a holding case and a glass that protects the system from dust and other environmental phenomena. Thus, we aim at the design and development of a system capable of generating a reflector shape in a way such that the optical set emits a given, user-defined, far-field radiance distribution. This problem can be put in the mathematical context of inverse problems, which refer to all the problems where, contrary to what happens with traditional direct problems, several aspects of the scene are unknown. Then, the algorithm is allowed to work backwards to establish the missing parameters.
Inverse rendering problems usually represent extremely complex and costly processes, but their importance in many research areas is well known. In particular, they are of extreme importance in lighting engineering, where potentially costly mistakes usually make it unfeasible to test design decisions on a model. In this thesis we present the main ideas behind these kinds of problems, characterize them, and summarize work developed in the area, revealing problems that remain unsolved and possible areas of further research.
We make a special emphasis on surface design problems like the reflector design problem we are focusing in this thesis.
In order to compute a reflector shape from a prescribed set of optical properties and geometrical constraints, light propagation inside and outside the optical set must be computed and the resulting radiance distribution compared to the desired one. Finally, constraints on the shape imposed by industry needs must be taken into account, boundin
