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   -> Volume 7, Issue 3


Answer: Wavelets and integral equations in 2 and 3D (WD 5.2 #28)
 
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Peter Schroeder (ps@cs.caltech.edu)
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PostPosted: Mon Mar 16, 1998 7:34 pm    
Subject: Answer: Wavelets and integral equations in 2 and 3D (WD 5.2 #28)
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#16 Answer: Wavelets and integral equations in 2 and 3D (WD 5.2 #28)

Andrew,

Looking over the old WDs I found your question. This may be a bit
late, but you can find examples of fast wavelet techniques for the
integral equations which govern radiative heat transfer and
radiosity. Basically a Fredholm Integral equation of the second kind
with a kernel satisfying the needed Calderon-Zygmund bounds. The
domain is 2 dimensional since the relevant quantities are defined as
functions of surfaces. There are also 4D versions when scattering has
a directional dependence. Wavelet algorithms for radiosity and
radiance have been quite an active research area in computer
graphics. The techniques are very fast indeed and researchers have
reported running multi-million element simulations on workstation
class machines. If you want to learn more about this, search for
``Hierarchical Radiosity" as a key. The book by Cohen and Wallace
(``Radiosity and Realistic Image Synthesis") has a chapter on this
and an extensive bibliography. Other good sources of research on this
are the proceedings from the Eurographics Workshop on Rendering which
are published by Springer (most recent: ``Rendering Techniques 97").

Peter
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