NURBS-based Inverse Reflector Design

Commonly used direct rendering techniques simulate light transport for a complete scene, specified in terms of light sources, geometry, materials, participating media, etc. On the other hand, inverse rendering problems take as input a desired light distribution and try to find the unknown parts of the scene needed to get such light field. The latter kind, where inverse reflector design is included, is traditionally solved by simulation optimization methods, due to the high complexity of the inverse problem. In this paper we present an inverse reflector design method which handles surfaces as NURBS and simulates accurately the light transport by means of a modified photon mapping algorithm. The proposed method is based on an optimization method, called pattern search, in order to compute the reflector needed to generate a target near light field. Some assumptions are determined in order to reduce the complexity of the problem, such as a rotationally symmetric reflector or its perfectly specular reflective behavior. The optimization method specifies the reflector shape by handling a NURBS curve as a generatrix, sequentially modifying the position and weights of its control points in order to obtain the reflector solution. Areas of applications of inverse reflector design span from architectural lighting design to car headlamps design.