A new diffusion paper that I was working on heavily during SIGGRAPH Asia in Hong Kong last year paper has been accepted with no additional changes to the Journal of Computational and Theoretical Transport (formerly TTSP). The reader in computer graphics might find this interesting if you’ve ever wondered:
- How are transport theory and the theory of random flights related?
- There is more than one diffusion approximation!? How, why?
- How are the various diffusion approximations (like Grosjean’s modified diffusion) derived, and what are their various tradeoffs?
- How would diffusion approximations change if you considered scattering volumes with partially-correlated scattering particles like that 2007 EGSR paper with a bowl of glass Buddhas (which leads to non-exponential free path distributions)?
- How does diffusion theory change if you consider multiple scattering in spaces with number of dimensions other than 3?
- What is the ‘spectrum’ of the transport operator, what are these ‘singular eigenfunctions’ in Caseology, and how does this all relate to diffusion theory?
Also, I use a cool trick that involves the Taylor series expansion about the single-scattering albedo of some analytic transport quantity to transform an all-orders density into its Neumann series (ie. into separate quantities that correspond to light that has experienced exactly n previous collisions). Using this I compare the accuracy of expressions ‘hidden within’ the classical and Grosjean diffusion approximations for predicting the nth-scattered fluence about a point source.