Global Illumination: Cornell Box, Reconstruction, and Depth of Field

Vocabulary flashcards covering Global Illumination foundations, the Cornell Box, signal reconstruction, anti-aliasing sampling methods, and camera models from Lectures #01 and #02.

Cornell Box

A widely used test scene for global illumination algorithms with precisely measured geometry and reflection characteristics, originally introduced by Goral et al. in Siggraph 1984.

Radiosity

A method introduced by Goral et al. in 1984 ('Modeling the Interaction of Light Between Diffuse Surfaces') to solve the global illumination problem for diffuse surfaces.

Ray-Tracing

The best algorithm for Global Illumination because it can handle non-pinhole cameras and enables numerical integration.

Rasterization

A rendering algorithm that is very badly suited for Global Illumination and struggles even with computing shadows.

WebGI

A very simple framework for global illumination optimized for the Cornell Box that runs on the GPU inside a browser using WebGPU.

Super-Sampled Anti-Aliasing (SSAA)

An anti-aliasing solution that uses multiple samples per pixel and averages their values to approximate the integral of the image function over the pixel area.

Shah-Function

A function represented as a sum of equally distributed Dirac-Peaks $\nu_{W_T}(x) = T \times \frac{1}{\text{sinc}(x)}$ or $\nu_{W_T}(x) = T \times \text{sum}(\text{Dirac})$, where multiplication with the image function in image space corresponds to sampling.

Sinc-Function

A reconstruction function defined as $\text{sinc}(x) = \frac{\text{sin}(x)}{x}$, representing the inverse Fourier transform of a box filter in frequency space.

Lanczos-Kernel

A reconstruction kernel formed by dampening a sinc-function with the central lobe of a larger sinc-function, expressed as k(x) = \text{sinc}\begin{pmatrix}\frac{x}{\tau}\right) \times \text{sinc}(x) for $|x| < r$.

Uniform Grid Sampling

A pixel sampling strategy lacking randomness or irregularity, which results in structured aliasing.

Random Sampling

A sampling technique using $n$ random samples per pixel that converts structured aliasing into visually pleasing noise, though performing numerically worse than uniform sampling.

Stratified Sampling

A sampling method where pixels are subdivided into sub-cells and one random sample is generated per sub-cell to produce an even sample distribution.

n-Rooks Sampling

Also known as Latin Hypercube Sampling, a method where $n$ samples are selected on the diagonal of an $n \times n$ grid of sub-cells and their rows and columns are randomly permuted.

Poisson Disk Sampling

A reference sampling algorithm where new random samples are iteratively generated until the distance to all previous samples is above a threshold radius $r$.

Halton Sequences

Deterministic pseudo-random number sequences $H_b(i)$ constructed by representing an index $i$ in a prime basis $b$ and mirroring its digits across the radix point.

Pinhole Camera Model

A simple graphics camera model where all eye rays pass through an infinitely small point, creating a simple 3D-to-2D projective mapping without lens distortion, vignetting, or depth of field.

Circle of Confusion

The area over which eye rays cover the film plane for object points located in front of or behind the focus plane, causing blurring.

Thin Lens Model

An optical model defined by focal length $f$, where parallel incident rays converge and rays from distance $z$ converge at depth $z'$ according to $\frac{1}{z'} - \frac{1}{z} = \frac{1}{f}$.

Thick Lens Model

A realistic camera model representing a system of multiple lenses, where 4D-sampled eye rays receive weights that account for effects like vignetting and lens distortion.

Vignetting

An optical effect in realistic multi-lens camera models where peripheral eye rays are darkened, causing the image borders to appear darker.