Directional Dipole Model for Subsurface Scattering

Jeppe Revall Frisvad, Toshiya Hachisuka, Thomas Kim Kjeldsen

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Rendering translucent materials using Monte Carlo ray tracing is computationally expensive due to a large number of subsurface scattering events. Faster approaches are based on analytical models derived from diffusion theory. While such analytical models are efficient, they miss out on some translucency effects in the rendered result. We present an improved analytical model for subsurface scattering that captures translucency effects present in the reference solutions but remaining absent with existing models. The key difference is that our model is based on ray source diffusion, rather than point source diffusion. A ray source corresponds better to the light that refracts through the surface of a translucent material. Using this ray source, we are able to take the direction of the incident light ray and the direction toward the point of emergence into account. We use a dipole construction similar to that of the standard dipole model, but we now have positive and negative ray sources with a mirrored pair of directions. Our model is as computationally efficient as existing models while it includes single scattering without relying on a separate Monte Carlo simulation, and the rendered images are significantly closer to the references. Unlike some previous work, our model is fully analytic and requires no precomputation.
Original languageEnglish
Article number5
JournalA C M Transactions on Graphics
Issue number1
Number of pages12
Publication statusPublished - 2014


  • Rendering
  • diffusion dipole
  • radiative transfer
  • subsurface scattering
  • translucent materials
  • turbid media


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