Abstract

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.

Bibtex Entry

    @PHDTHESIS{ Arvo-Thesis,
        AUTHOR = "James Arvo",
        TITLE  = "Analytic Methods for Simulated Light Transport",
        SCHOOL = "Yale University",
        MONTH  = Dec,
        YEAR   = 1995
        }