Monte Carlo evaluation of non-linear scattering equations for subsurface reflection

ABSTRACT

We describe a new mathematical framework for solving a wide variety of rendering problems based on a non-linear integral scattering equation. This framework treats the scattering functions of complex aggregate objects as first-class rendering primitives; these scattering functions accurately account for all scattering events inside them. We also describe new techniques for computing scattering functions from the composition of scattering objects. We demonstrate that solution techniques based on this new approach can be more efficient than previous techniques based on radiance transport and the equation of transfer and we apply these techniques to a number of problems in rendering scattering from complex surfaces.

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.7 Three-Dimensional Graphics and Realism
          Subjects: Color, shading, shadowing, and texture

Additional Classification:
  G. Mathematics of Computing
  G.3 PROBABILITY AND STATISTICS
      Subjects: Probabilistic algorithms (including Monte Carlo)

  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
  I.6 SIMULATION AND MODELING
      I.6.8 Types of Simulation
          Subjects: Monte Carlo

General Terms:
Algorithms, Design, Measurement, Performance, Reliability, Theory

Keywords:
Chandrasehkar's equation, Monte Carlo techniques, adding equations, equation of transfer, illumination, invariant imbedding, principles of invariance, reflectance and shading models, rendering, scattering function