Real-time rendering of light-scattering media

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:ncomputing a value of a source radiance at each RBF center cl, the source radiance including at least a single scattering term represented by a spherical harmonic product and a convolution term [(Lin * {tilde over (τ)}(cl))★p], Lin being a vector representing a spherical harmonic projection of an incident radiance Lin the incident radiance Lin comprising an environmental lighting, {tilde over (τ)}(cl) being a transmittance vector associated with RBF center cl, 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:ncomputing a base component by integrating the approximate source radiance along a view ray in the approximate model density field; andcomputing a compensation component by integrating the approximate source radiance along the view ray in the residual density field; andrendering an image of the inhomogeneous scattering medium based on the effective exitant radiance.

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:ncomputing a single scattering term of source radiance at each RBF center cl, the single scattering term being represented by a spherical harmonic product and a convolution term [(Lin * {tilde over (τ)}(cl))★p], Lin being a vector representing a spherical harmonic projection of an incident radiance Lin, the incident radiance Lin comprising an environmental lighting, {tilde over (τ)}(cl) being a transmittance vector associated with RBF center cl, and p being a vector representing a spherical harmonic projection of a phase function p;computing a multiple scattering term of the source radiance at each RBF center cl;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:ncomputing a base component by integrating the approximate source radiance along a view ray in the approximate model density field; andcomputing a compensation component by integrating the approximate source radiance along the view ray in the residual density field; andrendering an image of the inhomogeneous scattering medium based on the effective exitant radiance.

One or more computer readable medium having tangible physical structure and having stored thereupon a plurality of instructions that, when executed by one or more processors, causes the one or more processors to perform a method for rendering an image of an inhomogeneous scattering medium in a volume space, the method comprising:ncomputing a value of a source radiance at a respective radial basis function (RBF) center cl, of each member of a set of RBFs, the source radiance including at least a single scattering term represented by a spherical harmonic product and a convolution term [(Lin * {tilde over (τ)}(cl))★p], Lin being a vector representing a spherical harmonic projection of an incident radiance Lin, the incident radiance Lin comprising an environmental lighting, {tilde over (τ)}(cl) being a transmittance vector associated with RBF center cl, 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; andrendering the image of the inhomogeneous scattering medium based on the effective exitant radiance, the inhomogeneous scattering medium having a density field which includes an RBF model density field over one or more first frequencies, the RBF model density field comprising a weighted sum of the set of RBFs each having the respective RBF center, and a residual density field over one or more second frequencies, the one or more second frequencies being higher than the one or more first frequencies.