A Rendering Algorithm for Discrete Volume Density Objects

Abstract

We present a new algorithm for simulating the effect of light travelling through volume objects. Such objects (haze, fog, clouds…) are usually modelized by voxel grids which define their density distribution in a discrete tridimensional space. The method we propose is a two‐pass Monte‐Carlo ray‐tracing algorithm that does not make any restrictive assumptions neither about the characteristics of the objects (both arbitrary density distributions and phase functions are allowed) nor about the physical phenomena included in the rendering process (multiple scattering is accounted for). The driving idea of the algorithm is to use the phase function for Monte‐Carlo sampling, in order to modify the direction of the ray during scattering.

Lattice-Based Volumetric Global Illumination

“…In real world phenomena, most practical participating media are isotropic and the phase function f (x, ω, ω ′ ) does not vary upon position x. In our implementation, f (x, ω, ω ′ ) = f (ω · ω ′ ) is described with the Schlick model [1]. The participating medium is represented with an FCC lattice of densities and all the coefficients are calculated by scaling ρ(x).…”

“…The computation of the new direction is performed using importance sampling. In the widely used models such as the Schlick model [1], the probability depends on cos(θ ) = ω · ω ′ only, thus the importance sampling returns the value of cos(θ ). In order to compute ω ′ , a local coordinate system at the scattering position has to be constructed to convert spherical angles to direction vectors, which is computationally expensive.…”

A wavelet-based framework for acquired radiometric quantity representation and accurate physical rendering

“…Nishita et al have reported [48] that the expensive Mie scattering functions may be efficiently approximated for sparse and dense particle densities, called hazy and murky, respectively. More recently, Schlick et al presented an accurate approximation for these three scattering functions [2]. We used these to simulate phase function measurements according to the parameters given in their paper.…”

Efficient Light Propagation for Multiple Anisotropic Volume Scattering

“…I would like to thank Holly Rushmeier, John Howell, Roger Crawfis, and Charles Grant for helpful conversations, Chris Patmore, Steven Zucker, and Neeta Bhate for preprints of [Patm93], [Lang93] and [Bhat93], respectively, and anonymous Siggraph and Eurographics reviewers for suggesting improvements and pointing out references [Blas93], [Sak93], and [Kan90].…”

“…Kaneda et al [Kan90] also simulate anisotropic scattering in clouds and fog, including one case of double scattering: first Raleigh and Mie scattering to determine a fixed sky illumination, and then one more scattering of this illumination within a fog. Related work was also done by [Blas93].…”