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A Model for Anisotropic Reflection

Pierre Poulin and Alain Fournier
Proc. SIGGRAPH, August 1990


A reflection and refraction model for anisotropic surfaces is introduced. The anisotropy is simulated by small cylinders (added or subtracted) distributed on the anisotropic surface. Different levels of anisotropy are achieved by varying the distance between each cylinder and/or rising the cylinders more or less from the surface. Multidirectional anisotropy is modelled by orienting groups of cylinders in different direction. The intensity of the reflected light is computed by determining the visible and illuminated portion of the cylinders, taking self-blocking into account. We present two techniques to compute this in practice. In one the intensity is computed by sampling the surface of the cylinders. The other is an analytic solution. In the case of the diffuse component, the solution is exact. In the case of the specular component, an approximation is developed using a Chebyshev polynomial approximation of the specular term, and integrating the polynomial.

This model can be implemented easily within most rendering system, given a suitable mechanism to define and alter surface tangents. The effectiveness of the model and the visual importance of anisotropy are illustrated with some pictures.

BibTeX entry

  author =       "Pierre Poulin and Alain Fournier",
  editor =       "Forest Baskett",
  title =        "A Model for Anisotropic Reflection",
  journal =      "Computer Graphics",
  volume =       "24",
  number =       "4",
  pages =        "273--282",
  month =        aug,
  year =         "1990",
  coden =        "CGRADI, CPGPBZ",
  ISSN =         "0097-8930",
  conference =   "held in Dallas, Texas; 6--10 August 1990",
  keywords =     "shadowing, surface mapping, Chebyshev polynomials,
                 hair rendering, scientific visualization",

Online Version

Postscript available here