An Analytical Solution to Single Scattering in Homogeneous Participating Media

Despite their numerous applications, efficiently rendering participating media remains a challenging task due to the intricacy of the radiative transport equation. As they provide a generic means of solving a wide variety of problems, numerical methods are most often used to solve the air‐light inte...

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Bibliographic Details
Published in:Computer graphics forum 2009-04, Vol.28 (2), p.329-335
Main Authors: Pegoraro, Vincent, Parker, Steven G.
Format: Article
Language:English
Subjects:
and texture
Color
Color, shading, shadowing, and texture
Computer science
Electronics
Federations
I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism
Light
Media
Numerical analysis
shading
shadowing
Studies
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Summary:Despite their numerous applications, efficiently rendering participating media remains a challenging task due to the intricacy of the radiative transport equation. As they provide a generic means of solving a wide variety of problems, numerical methods are most often used to solve the air‐light integral even under simplifying assumptions. In this paper, we present a novel analytical approach to single scattering from isotropic point light sources in homogeneous media. We derive the first closed‐form solution to the air‐light integral in isotropic media and extend this formulation to anisotropic phase functions. The technique relies neither on pre‐computation nor on storage, and we provide a practical implementation allowing for an explicit control on the accuracy of the solutions. Finally, we demonstrate its quantitative and qualitative benefits over both previous numerical and analytical approaches.
ISSN:0167-7055
1467-8659
DOI:10.1111/j.1467-8659.2009.01372.x