Inverse Lighting Problem in Radiosity

Abstract

There is a need for tools to help a user to illuminate 3D scenes. This non-trivial task consists in setting lighting parameters and rendering the scene to visualize the effect generated by the lighting configuration. A large number of tries is needed to obtain the desired effect. We propose a new method that allows a user to define a target effect in a scene with fixed geometry, discretized with lambertian patches of known reflectances. Our method provides a lighting configuration to satisfy two types of constraints defined by the user: radiosities and forbiddings. Radiosities represent the illumination that we must generate with a lighting configuration. All the patches of the scene are possible light sources except those with known radiosities and those forbidden by the user. We form a system of equations which is solved by means of a pseudo-inverse. The resulting mathematical solution globally satisfies the target effect but has too many light sources and may contain negative values. We use it as a starting point to propose a new configuration with positive self-exitances, which minimizes the number of sources and generates an illumination which is as near as possible to the desired illumination.

Keywords:

• Inverse Lighting
• Global Illumination
• Radiosity
• Least Square Solution
• Pseudo-inverse