<Simulating Multiple Scattering in Hair Using a Photon Mapping Approach>

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Jonathan T. Moon & Stephen R. Marschner
<Simulating Multiple Scattering in Hair Using a Photon Mapping Approach>

Program of Computer Graphics, Cornell University
Appears in ACM Transactions on Graphics 25:3
Proceedings of SIGGRAPH 2006


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The types of non-uniformities that can cause scattering, sometimes known as scatterers or scattering centers, are too numerous to list, but a small sample includes particles, bubbles, droplets, density fluctuations in fluids, defects in crystalline solids, surface roughness, cells in organisms, and textile fibers in clothing.

path tracing

multiple scattering
The main difference between the effects of single and multiple scattering is that single scattering can usually be treated as a random phenomenon and multiple scattering is usually more deterministic.
(Single scattering is therefore often described by probability distributions. With multiple scattering, the randomness of the interaction tends to be averaged out by the large number of scattering events, so that the final path of the radiation appears to be a deterministic distribution of intensity as the radiation is spread out.
The description of scattering and the distinction between single and multiple scattering are often highly involved with wave-particle duality.)

forward scattering
    http://en.wikipedia.org/wiki/Mie_theory
    Light Scattering Codes Library:  http://atol.ucsd.edu/scatlib

photon mapping
    Zack Waters' introduction

Monte Carlo method

density estimation

diffusion process

ray map
ray tracing

2p
Isotropy (the opposite of anisotropy) is the property of being independent of direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented.

Albedo is the ratio of reflected to incident electromagnetic radiation. It is a unitless measure indicative of a surface's or body's diffuse reflectivity.

Azimuth is the horizontal component of a direction (compass direction), measured around the horizon, from the north toward the east (i.e., clockwise) in astronomy and geodesy and from the south toward the west (i.e., clockwise) in surveying. It is usually expressed in degrees.
Azimuth is also terms used in mining for a similar, but slightly different angle: azimuths and meridian angles are used to name any angle measured clockwise from any meridian.

3p
solid angle Ω, that an object subtends at a point is a measure of how big that object appears to an observer at that point. For instance, a small object nearby could subtend the same solid angle as a large object far away. The solid angle is proportional to the surface area, S, of a projection of that object onto a sphere centered at that point, divided by the square of the sphere's radius, R. (Symbolically, Ω = k S/R², where k is the proportionality constant.) A solid angle is related to the surface area of a sphere in the same way an ordinary angle is related to the circumference of a circle.

(the outgoing radiance) = (the scattering function) * (the incident light distribution)

fiber tangent u

(incident light) = (direct light) + (scattered light)

Monte Carlo integration is numerical quadrature using pseudorandom numbers. That is, Monte Carlo integration methods are algorithms for the approximate evaluation of definite integrals, usually multidimensional ones. The usual algorithms evaluate the integrand at a regular grid. Monte Carlo methods, however, randomly choose the points at which the integrand is evaluated.
The traditional Monte Carlo algorithm distributes the evaluation points uniformly over the integration region. Adaptive algorithms such as VEGAS and MISER use importance sampling and stratified sampling techniques to get a better result.

(Random sampling of the region may not uncover all the important features of the function, resulting in an underestimate of the error.)



ref.
<A conceptual model of the dehydration of air due to freeze-drying by optically thin, laminar cirrus rising slowly across the tropical tropopause>
Eric J. Jensen, Leonhard Pfister, Andrew S. Ackerman, and Azadeh Tabazadeh
NASA Ames Research Center, Moffett Field, California
Owen B. Toon
University of Colorado, Laboratory for Atmospheric and Space Physics, Boulder, Colorado  

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Journal of Geophysical Research, Vol. 106, N0. D15, Pages 17,237-17252, August 16, 2001
http://pubs.giss.nasa.gov/abstracts/2001/Jensen_etal.html
http://link.aps.org/abstract/PRA/v63/e052701