Collimated Whole Volume Light Scattering in Homogeneous Finite Media

Crepuscular rays form when light encounters an optically thick or opaque medium which masks out portions of the visible scene. Real-time applications commonly estimate this phenomena by connecting paths between light sources and the camera after a single scattering event. We provide a set of algorithms for solving integration and sampling of single-scattered collimated light in a box-shaped medium and show how they extend to multiple scattering and convex media. First, a method for exactly integrating the unoccluded single scattering in rectilinear box-shaped medium is proposed and paired with a ratio estimator and moment-based approximation. Compared to previous methods, it requires only a single sample in unoccluded areas to compute the whole integral solution and provides greater convergence in the rest of the scene. Second, we derive an importance sampling scheme accounting for the entire geometry of the medium. This sampling strategy is then incorporated in an optimized Monte Carlo integration. The resulting integration scheme yields visible noise reduction and it is directly applicable to indoor scene rendering in room-scale interactive experiences. Furthermore, it extends to multiple light sources and achieves superior converge compared to independent sampling with existing algorithms. We validate our techniques against previous methods based on ray marching and distance sampling to prove their superior noise reduction capability.