The rendering equation is similar to the linear Boltzmann equation which has been widely studied in physics and nuclear engineering. Consequently, many of the powerful techniques which have been developed in these fields can be applied to problems in image synthesis. In this paper we adapt several statistical techniques commonly used in neutron transport to stochastic ray tracing and, more generally, to Monte Carlo solution of the rendering equation. First, we describe a technique known as Russian roulette which can be used to terminate the recursive tracing of rays without introducing statistical bias. We also examine the practice of creating ray trees in classical ray tracing in the light of a well-known technique in particle transport known as splitting. We show that neither ray trees nor paths as described in [10] constitute an optimal sampling plan in themselves and that a hybrid may be more efficient.

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Particle transport and image synthesis

An historical review and current status of buildup factor calculations and applications

This thesis presents new mathematical and computational tools for the simulation of light transport in realistic image synthesis. New algorithms are presented for exact computation of direct illumination effects related to light emission, shadowing, and first-order scattering from surfaces. New theoretical results are presented for the analysis of global illumination algorithms, which account for all interreflections of light among surfaces of an environment.
First, a closed-form expression is derived for the irradiance Jacobian, which is the derivative of a vector field representing radiant energy flux. The expression holds for diffuse polygonal scenes and correctly accounts for shadowing, or partial occlusion. Three applications of the irradiance Jacobian are demonstrated: locating local irradiance extrema, direct computation of isolux contours, and surface mesh generation.
Next, the concept of irradiance is generalized to tensors of arbitrary order. A recurrence relation for irradiance tensors is derived that extends a widely used formula published by Lambert in 1760. Several formulas with applications in computer graphics are derived from this recurrence relation and are independently verified using a new Monte Carlo method for sampling spherical triangles. The formulas extend the range of non-diffuse effects that can be computed in closed form to include illumination from directional area light sources and reflections from and transmissions through glossy surfaces.
Finally, new analysis for global illumination is presented, which includes both direct illumination and indirect illumination due to multiple interreflections of light. A novel operator equation is proposed that clarifies existing deterministic algorithms for simulating global illumination and facilitates error analysis. Basic properties of the operators and solutions are identified which are not evident from previous formulations. A taxonomy of errors that arise in simulating global illumination is presented; these include perturbations of the boundary data, discretization error, and computational error. A priori bounds are derived for each category using properties of the proposed operators.

Analytic methods for simulated light transport

Numerical study on annular tube once-through steam generator using compressible flow model

Methods are presented for the calculation of dose-rate conversion factors for external exposure to photon and electron radiation from radioactive decay. A dose-rate conversion factor is defined as the dose-equivalent rate per unit radionuclide concentration. Exposure modes considered are immersion in contaminated air, immersion in contaminated water, and irradiation from a contaminated ground surface. For each radiation type and exposure mode, dose-rate conversion factors are derived for tissue-equivalent material at the body surface of an exposed individual. In addition, photon dose-rate conversion factors are estimated for 22 body organs. The calculations are based on the assumption that the exposure medium is infinite in extent and that the radionuclide concentration is uniform. The dose-rate conversion factors for immersion in contaminated air and water then follow from the requirement that all of the energy emitted in the radioactive decay is absorbed in the infinite medium. Dose-rate conversion factors for ground-surface exposure are calculated at a reference location above a smooth, infinite plane using the point-kernel integration method and known specific absorbed fractions for photons and electrons in air.

Calculation of dose-rate conversion factors for external exposure to photons and electrons

Dynamic modeling of a large once-through steam generator

Calculations were set up to determine the effect of the grazing flux on the surface-crossing flux estimator and the pillbox track-length estimator used in Monte Carlo calculations. It was found tha...

Variance of certain flux estimators used in monte carlo calculations.

Energy and dose buildup factors for various concretes.

Publisher Summary This chapter discusses the methods and data for reactor shield calculations. The principal problem of shield analysis is the penetration of particles to points that are separated from the particles' birthplaces by large amounts of material. The core is dynamic while the shield is passive. Nonlinearity is characteristic of core studies at high power. In core studies, the important particles are born in the core and they spend the rest of their lifetime there or in its immediate neighborhood. In shielding studies, the important particles are those that reach a sensitive region, generally external to the system. Another major difference is gamma radiation. Both gamma rays and neutrons are important in shielding. One other very significant difference between core and shield problems lies in the expected importance of a neutron born in the core. There are three main ways of estimating shield effectiveness. The first is by measurement. The measurements may be on faithfully detailed system mockups; they may be on general-purpose experimental facilities requiring extensive transformation and interpretation of results or they may be on a facility intermediate between these extremes.

Francis H. Clark

Papers

Dynamic modeling of a large once-through steam generator

Variance of certain flux estimators used in monte carlo calculations.

Energy and dose buildup factors for various concretes.

Methods and data for reactor shield calculations.

Fission neutron attenuation and gamma-ray buildup factors for lithium hydride.