References
- Borovoi, A. 2002. On the extinction of radiation by a homogeneous but spatially correlated random medium: comment. J. Opt. Soc. Am. A Opt. Image Sci. Vis. 19 (12):2517–2520.
- Camminady, T., M. Frank, and E. W. Larsen. 2017. Nonclassical particle transport in heterogeneous materials. In Proceedings M&C2017, Korea, April.
- Cook, R. L. 1986. Stochastic sampling in computer graphics. ACM Trans. Graph 5 (1):51–72.
- Davis, A. B., and A. Marshak. 2004. Photon propagation in heterogeneous optical media with spatial correlations: enhanced mean-free-paths and wider-than-exponential free-path distributions. J. Quant. Spectrosc. Radiat. Transf. 84 (1):3–34.
- Davis, A. B., and M. B. Mineev-Weinstein. 2011. Radiation propagation in random media: From positive to negative correlations in high-frequency fluctuations. J. Quant. Spectrosc. Radiat. Transf. 112 (4):632–645.
- Davis, A. B., and R. Sanchez. 2011. Two truly special sessions at the 2009 international conference on mathematics and computational methods (M&C 2009): Transport… across disciplinary divides. J. Quant. Spectrosc. Radiat. Transf. 112 (4):560–565. 2009 International Conference on Mathematics and Computational Methods (M&C 2009).
- Davis, A. B., and Xu, F. 2014. A generalized linear transport model for spatially correlated stochastic media. J. Comput. Theor. Trans. 43 (1–7):474–514.
- Davis, A. B., Xu, F., and Diner, D. J. 2018. Generalized radiative transfer theory for scattering by particles in an absorbing gas: Addressing both spatial and spectral integration in multi-angle remote sensing of optically thin aerosol layers. J. Quant. Spectrosc. Radiat. Transf. 205:148–162.
- d’Eon, E., and M. M. R. Williams. 2018. Isotropic scattering in a Flatland half-space. J. Comput. Theor. Trans. (in this issue). doi: 10.1080/23324309.2018.1544566.
- d’Eon. E. 2014. Rigorous asymptotic and moment-preserving diffusion approximations for generalized linear Boltzmann transport in arbitrary dimension. Transport Theory Stat. Phys. 42 (6-7):237–297.
- Dupuy, J., E. Heitz, and E. d’Eon. 2016. Additional progress towards the unification of microfacet and microflake theories. In Proceedings of the Eurographics Symposium on Rendering: Experimental Ideas & Implementations, Eurographics Association, 55–63.
- Ebeida, M. S., S. A. Mitchell, A. Patney, A. A. Davidson, and J. D. Owens. 2012. A simple algorithm for maximal poisson-disk sampling in high dimensions. Computer Graphics Forum 31:785–794.
- Frank, M., K. Krycki, E. W. Larsen, and R. Vasques. 2015. The nonclassical Boltzmann equation and diffusion-based approximations to the Boltzmann equation. SIAM J. Appl. Math. 75 (3):1329–1345.
- Golse, F. 2012. Recent results on the Periodic Lorentz Gas. In Nonlinear Partial Differential Equations, 39–99. Basel: Springer.
- Griesheimer, D. P., D. L. Millman, and C. R. Willis. 2011. Analysis of distances between inclusions in finite binary stochastic materials. J. Quant. Spectrosc. Radiat. Transf. 112 (4):577–598.
- Heitz, E., J. Hanika, E. d’Eon, and C. Dachsbacher. 2015. Multiple-scattering microfacet BSDFs with the Smith Model. ACM Trans. Graph 35:58.
- Henderson, D. 2009. Analytic methods for the Percus-Yevick hard sphere correlation functions. Condens. Matter Phys. 12:127–135.
- Jarbo, A., Aliaga, C., and Gutierrez, D. 2018. A radiative transfer framework for spatially-correlated materials.ACM Trans. Graph. 37 (4):14.
- Kostinski, A. B. 2001. On the extinction of radiation by a homogeneous but spatially correlated random medium. J. Opt. Soc. Am. A Opt. Image Sci. Vis. 18 (8):1929–1933.
- Kostinski, A. B. 2002. On the extinction of radiation by a homogeneous but spatially correlated random medium: reply to comment. J. Opt. Soc. Am. A 19 (12):2521–2525.
- Lagae, A., and P. Dutré. 2008. A comparison of methods for generating Poisson disk distributions. Comput. Graph. Forum 27 (1):114–129.
- Larsen, E. W., and R. Vasques. 2011. A generalized linear Boltzmann equation for non-classical particle transport. J. Quant. Spectrosc. Radiat. Transf. 112 (4):619–631.
- Levermore, C., J. Wong, and G. Pomraning. 1988. Renewal theory for transport processes in binary statistical mixtures. J. Math. Phys. 29 (4):995–1004.
- Meng, J., M. Papas, R. Habel, C. Dachsbacher, S. Marschner, M. H. Gross, and W. Jarosz. 2015. Multi-scale modeling and rendering of granular materials. ACM Trans. Graph 34 (4):49–41.
- Metropolis, N., A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller. 1953. Equation of state calculations by fast computing machines. J. Chem. Phys. 21 (6):1087.
- Mishchenko, M. I. 2013. 125 years of radiative transfer: Enduring triumphs and persisting misconceptions. In AIP Conference Proceedings, vol. 1531, 11.
- Moon, J., B. Walter, and S. Marschner. 2007. Rendering discrete random media using precomputed scattering solutions. In Rendering Techniques 2007, 231–242.
- Müller, T., M. Papas, M. H. Gross, W. Jarosz, and J. Novák. 2016. Efficient rendering of heterogeneous polydisperse granular media. ACM Trans. Graph 35 (6):168:1–168:14.
- Myneni, R. B., Marshak, A. L., and Knyazikhin, Y. V. 1991. Transport theory for a leaf canopy of finite-dimensional scattering centers. J. Quant. Spectrosc. Radiat. Transf. 46 (4):259–280.
- Novák, J., I. Georgiev, J. Hanika, and W. Jarosz. 2018. Monte Carlo Methods for Volumetric Light Transport Simulation. Computer Graphics Forum.37:551–576.
- Olson, G. L. 2008. Chord length distributions between hard disks and spheres in regular, semi-regular, and quasi-random structures. Ann. Nucl. Energy 35 (11):2150–2155.
- Pharr, M., and G. Humphreys. 2010. Physically based rendering from theory to implementation. 2nd ed. Burlington, MA: Morgan Kaufmann.
- Pomraning, G. 1998. Radiative transfer and transport phenomena in stochastic media. Int. J. Eng. Sci. 36 (12-14):1595–1621.
- Rukolaine, S. A. 2016. Generalized linear Boltzmann equation, describing non-classical particle transport, and related asymptotic solutions for small mean free paths. Physica A 450:205–216.
- Sanchez, R., and G. Pomraning. 1991. A statistical analysis of the double heterogeneity problem. Ann. Nucl. Energy 18 (7):371–395.
- Smith, W., and D. Henderson. 1970. Analytical representation of the Percus-Yevick hard-sphere radial distribution function. Mol. Phys. 19 (3):411–415.
- Torquato, S., and B. Lu. 1993. Chord-length distribution function for two-phase random media. Phys. Rev. E 47 (4):2950.
- Vasques, R., and E. W. Larsen. 2014a. Non-classical transport with angular-dependent path-length distributions. 1: Theory. Ann. Nucl. Energy. 70:292–300.
- Vasques, R., and E.W. Larsen. 2014b. Non-classical particle transport with angular-dependent path-length distributions. II: Application to pebble bed reactor cores. Ann. Nucl. Energy. 70:301–311.
- Veach, E. 1997. Robust Monte Carlo Methods for Light Transport Simulation. PhD thesis, Stanford University.
- Wrenninge, M., R. Villemin, and C. Hery. 2017. Path traced subsurface scattering using anisotropic phase functions and non-exponential free flights. Pixar Technical Memo #17-07. https://graphics.pixar.com/library/PathTracedSubsurface/ (last accessed Nov 18, 2018).