Line space gathering for single scattering in large scenes

We present an efficient technique to render single scattering in large scenes with reflective and refractive objects and homogeneous participating media. Efficiency is obtained by evaluating the final radiance along a viewing ray directly from the lighting rays passing near to it, and by rapidly identifying such lighting rays in the scene. To facilitate the search for nearby lighting rays, we convert lighting rays and viewing rays into 6D points and planes according to their Plücker coordinates and coefficients, respectively. In this 6D line space, the problem of closest lines search becomes one of closest points to a plane query, which we significantly accelerate using a spatial hierarchy of the 6D points. This approach to lighting ray gathering supports complex light paths with multiple reflections and refractions, and avoids the use of a volume representation, which is expensive for large-scale scenes. This method also utilizes far fewer lighting rays than the number of photons needed in traditional volumetric photon mapping, and does not discretize viewing rays into numerous steps for ray marching. With this approach, results similar to volumetric photon mapping are obtained efficiently in terms of both storage and computation.