Patent ID: 8190403

Claim:
A method for rendering an inhomogeneous scattering medium in a volume space, the inhomogeneous scattering medium having a density field which is at least approximately represented by a radial basis function (RBF) model density field comprising a weighted sum of a set of RBFs each having a RBF center, the density field further comprising a residual density field in addition to the RBF model density field, performed by one or more processors configured with computer-executable instructions, the method comprising: computing a value of a source radiance at each RBF center c l , the source radiance including at least a single scattering term represented by a spherical harmonic product and a convolution term [(L in * {tilde over (τ)}(c l ))★p], L in being a vector representing a spherical harmonic projection of an incident radiance L in the incident radiance L in comprising an environmental lighting, {tilde over (τ)}(c l ) being a transmittance vector associated with RBF center c l , and p being a vector representing a spherical harmonic projection of a phase function p; approximating values of the source radiance at other points in the volume space by interpolating from the values of the source radiance at the RBF centers; computing an effective exitant radiance at a point x in the volume space at least partially based on the source radiance, the computing the effective exitant radiance comprising: computing a base component by integrating the approximate source radiance along a view ray in the approximate model density field; and computing a compensation component by integrating the approximate source radiance along the view ray in the residual density field; and rendering an image of the inhomogeneous scattering medium based on the effective exitant radiance.