Interactive hair rendering under environment lighting

We present an algorithm for interactive hair rendering with both single and multiple scattering effects under complex environment lighting. The outgoing radiance due to single scattering is determined by the integral of the product of the environment lighting, the scattering function, and the transmittance that accounts for self-shadowing among hair fibers. We approximate the environment light by a set of spherical radial basis functions (SRBFs) and thus convert the outgoing radiance integral into the sum of radiance contributions of all SRBF lights. For each SRBF light, we factor out the effective transmittance to represent the radiance integral as the product of two terms: the transmittance and the convolution of the SRBF light and the scattering function. Observing that the convolution term is independent of the hair geometry, we precompute it for commonly-used scattering models, and reduce the run-time computation to table lookups. We further propose a technique, called the convolution optical depth map, to efficiently approximate the effective transmittance by filtering the optical depth maps generated at the center of the SRBF using a depth-dependent kernel. As for the multiple scattering computation, we handle SRBF lights by using similar factorization and precomputation schemes, and adopt sparse sampling and interpolation to speed up the computation. Compared to off-line algorithms, our algorithm can generate images of comparable quality, but at interactive frame rates.