Transfer Equations in Global Illumination

The purpose of these notes is to describe some of the physical and mathematical properties of the equations occurring in global illumination. We rst examine the physical assumptions that make the particle model of light an appropriate paradigm for computer graphics and then derive a balance equation for photons. In doing this we establish connections with the eld of radiative transfer and its more abstract counterpart, transport theory. The resulting balance equation, known as the equation of transfer, accounts for large-scale interaction of light with participating media as well as complex reeecting surfaces. Under various simplifying assumptions the equation of transfer reduces to more conventional equations encountered in global illumination.

[1]  E. Richard Cohen,et al.  Neutron Transport Theory , 1959 .

[2]  Stephen H. Westin,et al.  Predicting reflectance functions from complex surfaces , 1992, SIGGRAPH.

[3]  M. Kline,et al.  Electromagnetic theory and geometrical optics , 1965 .

[4]  James Arvo,et al.  Particle transport and image synthesis , 1990, SIGGRAPH.

[5]  T. Teichmann,et al.  Radiative Transfer on Discrete Spaces , 1966 .

[6]  S. Glasstone,et al.  Nuclear Reactor Engineering , 1955 .

[7]  G. C. Pomraning,et al.  Linear Transport Theory , 1967 .

[8]  David Salesin,et al.  An importance-driven radiosity algorithm , 1992, SIGGRAPH.

[9]  Kenneth E. Torrance,et al.  Extending the radiosity method to include specularly reflecting and translucent materials , 1990, TOGS.

[10]  J R Meyer-Arendt,et al.  Radiometry and photometry: units and conversion factors. , 1968, Applied optics.

[11]  BIBLIOGRAPHY ON NEUTRAL PARTICLE TRANSPORT THEORY. , 1970 .

[12]  R. D. Richtmyer,et al.  Basic Methods in Transfer ProblemsRadiative Equilibrium and Neutron Diffusion , 1953 .

[13]  Kenneth E. Torrance,et al.  The zonal method for calculating light intensities in the presence of a participating medium , 1987, SIGGRAPH.

[14]  Wolfgang Krueger.  Volume rendering and data feature enhancement , 1990, SIGGRAPH 1990.

[15]  E. Lewis,et al.  Computational Methods of Neutron Transport , 1993 .

[16]  R. Myneni,et al.  A review on the theory of photon transport in leaf canopies , 1989 .

[17]  Turner Whitted,et al.  An improved illumination model for shaded display , 1979, SIGGRAPH.

[18]  M. Pinar Mengüç,et al.  Thermal Radiation Heat Transfer , 2020 .

[19]  Donald P. Greenberg,et al.  Modeling the interaction of light between diffuse surfaces , 1984, SIGGRAPH.

[20]  K. Schwarzschild,et al.  On the equilibrium of the Sun's atmosphere , 1906 .

[21]  James T. Kajiya,et al.  Ray tracing volume densities , 1984, SIGGRAPH.

[22]  R. K. Luneburg,et al.  Mathematical Theory of Optics , 1966 .

[23]  James T. Kajiya,et al.  The rendering equation , 1986, SIGGRAPH.

[24]  R. Jones,et al.  Atmospheric transmission: Concepts, symbols, units and nomenclature , 1965 .

[25]  Donald P. Greenberg,et al.  A comprehensive physical model for light reflection , 1991, SIGGRAPH.

[26]  A. Schuster.  Radiation through a foggy atmosphere , 1903 .

[27]  M. M. R. Williams,et al.  Mathematical methods in particle transport theory , 1971 .

[28]  Xiao Dong He,et al.  Physically-based models for the reflection, transmission and subsurface scattering of light by smooth and rough surfaces, with applications to realistic image synthesis , 1993 .

[29]  Stephen H. Westin,et al.  A global illumination solution for general reflectance distributions , 1991, SIGGRAPH.

[30]  Rudolph W. Preisendorfer,et al.  Radiative Transfer Axioms , 1957 .

[31]  Ranga B. Myneni,et al.  Photon-Vegetation Interactions , 1991, Springer Berlin Heidelberg.

[32]  E. Wigner.  Mathematical Problems of Nuclear Reactor Theory , 1992 .

[33]  Parry. Moon,et al.  The scientific basis of illuminating engineering , 1936 .

[34]  H. Grad.  Principles of the Kinetic Theory of Gases , 1958 .

[35]  Claude Puech,et al.  A general two-pass method integrating specular and diffuse reflection , 1989, SIGGRAPH '89.

[36]  Christoph C. Borel,et al.  The radiosity method in optical remote sensing of structured 3-D surfaces , 1991 .

[37]  Richard L. Thompson,et al.  A computer graphics based model for scattering from objects of arbitrary shapes in the optical region , 1991 .

[38]  D. Menzel,et al.  Selected papers on the transfer of radiation , 1966 .

[39]  J. Lenoble.  Radiative transfer in scattering and absorbing atmospheres: Standard computational procedures , 1985 .

[40]  Rudolph W. Preisendorfer,et al.  A Mathematical Foundation for Radiative Transfer Theory , 1957 .

[41]  Tomoyuki Nishita,et al.  Continuous tone representation of three-dimensional objects taking account of shadows and interreflection , 1985, SIGGRAPH '85.

[42]  Eugene P. Wigner,et al.  The Physical Theory of Neutron Chain Reactors , 1958 .

[43]  R. R. Coveyou.  Monte Carlo Principles and Neutron Transport Problems , 1971 .

[44]  Chris Buckalew,et al.  Fast Illumination Networks: Realistic Rendering with General Reflectance Functions , 1989 .