Graphics Reference
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Sample points
Directional light sources
Matrix representing
ray-traced light
Projected wavelet
basis functions with
small elements
made zero
Shrunken Matrix
with zero elements
removed
Figure 10.19 Radiance transfer using wavelet basis functions.
corresponds to the radiant exitance (radiosity) or irradiance. The rows of A pro-
duce one radiance value at a given surface sample point from a light vector, but
that value is in the direction of the viewpoint. (Another difference of course is
that the PRT transfer vectors contain SH coefficients rather than sample values.)
Because the directional samples
s j correspond to pixels in an environment
map ( Figure 10.19 ), each matrix row i corresponds to all the pixels in the envi-
ronment map at surface sample point p i . The visibility function V
(
,
)
can be
regarded as the silhouette of the local geometry projected from p i onto the en-
vironment map. The matrix elements a ij in row i can thus be regarded as the
silhouette times the cosine-weighted BRDF pixelized in the environment map.
The BRDF usually changes slowly and smoothly, except near a specular peak.
The visibility function is by nature discontinuous, but the discontinuities are lim-
ited to the silhouette edges. The pixelized visibility-BRDF products (which are
the rows of A ) are therefore well suited to wavelet approximation.
The method described in the 2003 “wavelet lighting” paper actually uses a
cube environment map as illustrated in Figure 10.18. A separate matrix A is con-
structed for each face, with the directional samples corresponding to the pixels in
the environment map on the face. A Haar wavelet approximation is then applied
p i
s j
 
 
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