Interactive Rendering with Arbitrary BRDFs using Separable Approximations

  • Jan Kautz
  • Michael D. McCool
Part of the Eurographics book series (EUROGRAPH)


A separable decomposition of bidirectional reflectance distributions (BRDFs) is used to implement arbitrary reflectances from point sources on existing graphics hardware. Two-dimensional texture mapping and compositing operations are used to reconstruct samples of the BRDF at every pixel at interactive rates.

A change of variables, the Gram-Schmidt halfangle/difference vector parameterization, improves separability. Two decomposition algorithms are also presented. The singular value decomposition (SVD) minimizes RMS error. The normalized decomposition is fast and simple, using no more space than what is required for the final representation.


Singular Value Decomposition Graphic Hardware Bidirectional Reflectance Distribution Function Reflectance Model Reflectance Function 
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Copyright information

© Springer-Verlag/Wien 1999

Authors and Affiliations

  • Jan Kautz
    • 1
  • Michael D. McCool
    • 1
  1. 1.Computer Graphics Laboratory; Department of Computer ScienceUniversity of Waterloo WaterlooOntarioCanada

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