Eugene d’Eon | Geoffrey Irving
Weta Digital


We present a new BSSRDF for rendering images of translucent materials. Previous diffusion BSSRDFs are limited by the accuracy of classical diffusion theory. We introduce a modified diffusion theory that is more accurate for highly absorbing materials and near the point of illumination. The new diffusion solution accurately decouples single and multiple scattering. We then derive a novel, analytic, extended-source solution to the multilayer searchlight problem by quantizing the diffusion Green’s function. This allows the application of the diffusion multipole model to material layers several orders of magnitude thinner than previously possible and creates accurate results under high-frequency illumination. Quantized diffusion provides both a new physical foundation and a variable-accuracy construction method for sum-of-Gaussians BSSRDFs, which have many useful properties for efficient rendering and appearance capture. Our BSSRDF maps directly to previous real-time rendering algorithms. For film production rendering, we propose several improvements to previous hierarchical point cloud algorithms by introducing a new radial-binning data structure and a doubly-adaptive traversal strategy.

Octoguy model and textures courtesy of Bradford deCaussin.


  • The first recognition in graphics of the relationship between BSSRDFs and the searchlight problem in transport theory (and related literature).
  • The proposal (following optics) of a notation for volume properties that clearly distinguishes between material cross-sections and material coefficients (since both appear in parametric tissue models, for example).
  • The first formal study in graphics of the limits of diffusion theory for highly absorbing materials and near sources and boundaries.
  • The introduction to graphics of the idea of modified diffusion theory, including the evaluation of many different alternative forms and selection of one (Grosjean’s) that seemed most appropriate for use in computer graphics.
  • The first application of Grosjean’s modified diffusion theory to method-of-images BSSRDFs producing an accurate decoupling of single and multiple-scattered light.
  • The first recognition in graphics that the diffusion boundary conditions being used in diffusion BSSRDF models are not actually satisfied by mirroring negative sources about the extrapolation plane outside the medium (an error inherited from the medical physics literature).
  • The first application in graphics of asymptotically consistent diffusion boundary conditions for reflecting boundaries.
  • The first application in graphics of an exitant-flux calculation consistent with the full form of the diffusion solution at the bounary (Kienle and Patterson’s).
  • The first application in any field of an extended diffusion source model together with Kienle and Patterson’s exitance formulation, which is essential in order for the extended source model to outperform the dipole/multipole models.
  • Introduction of a new analytic BSSRDF model for slabs and multilayer materials using an ‘extended multipole’: a generalization of the multipole model for slabs by mirroring continuous exponential (beam) source distributions about extrapolated boundaries. Additionally, we evaluated the accuracy of this model for quite thin material layers and included a new reduced-intensity term to the adding-equations method for combining layers.
  • Introduction of a closed-form variable-accuracy quadrature for the extended (beam) source multiple-scattering component of the BSSRDF via temporal quantization of point source diffusion Green’s function. This produces radial profiles that are sums of Gaussians, providing a new physical foundation to a previous popular expansion of BSSRDFs for real-time rendering (and thereby avoiding the necessity for any non-linear fitting procedures to find such Gaussian expansions).
  • A new efficient, stable and energy-conserving method for convolving two layer profiles when the inputs are expressed as sums of Gaussians.
  • Introduction of a missing normalization term in the angular/spatial-factored expression of diffusion BSSRDFs.
  • A new ‘radial binning’ acceleration method for exploiting the radial symmetry for the [Jensen Buhler 2002] algorithm.
  • A new doubly-adaptive acceleration method for reusing similar far contributions for the [Jensen Buhler 2002] algorithm.

PDF (free download from ACM)

Errata, Discussion and Reviews

We include additional information about stable numerical evaluation of the model here:
Publon 2802

Original Score

Music composed for the Fast Forward program at SIGGRAPH 2011, Vancouver:

Related Patent

US Patent 8,064,726, 2011