Graphics Reference
In-Depth Information
the shadow boundaries. However, the wavelet approximation assumes a fixed
view direction
v
, whereas the SH representation handles all viewing directions.
Figure 10.20 illustrates an important distinction often made in rendering. The
very diffuse shadows in the SH image are
plausible
, in the sense that a casual ob-
server would likely believe that the image is accurate. On the other hand, shadows
in the wavelet image on the right are
predictive
in that it is essentially what the
shadows would really look like if the original statue were placed on a Lambertian
surface inside the actual environment. Interestingly, the “plausible” image might
be considered aesthetically superior to the predictive image in this case.
Wavelet approximations do have their own drawbacks compared to other ap-
proximation methods. Haar wavelets are the simplest, but they are piecewise
constant and therefore can only represent step functions. They converge in the
limit, but any finite sum of Haar wavelets has discontinuities. Furthermore, Haar
wavelets do not have the smoothing properties of spherical harmonics. Other
wavelet bases exist that have better properties, but they are more difficult to com-
pute. Another drawback of wavelet representations on the sphere is the lack of
rotational properties exhibited by spherical harmonicss.
For the specific problem of precomputed transfer, the wavelet method de-
scribed in this section works with only one view direction—the matrix
A
has to
be recomputed in order to render the object from another viewpoint. A year after
the publication of their “wavelet lighting” paper, the authors (Ng, Ramamoor-
thi, and Hanrahan) presented a way of solving this problem in a paper entitled
“Triple Product Wavelet Integrals for All-Frequency Relighting” [Ng et al. 04].
The method uses separate wavelet expansions for each of the three different fac-
tors in the reflectance integral: the incident light, the reflectance function, and the
visibility. These expansions are multiplied together and integrated to compute an
outgoing expansion. Shortcuts based on the orthogonality of Haar wavelets are
employed to substantially reduce the computational load. The method handles
radiance transfer with lighting of arbitrary frequency along with changing view
direction. However, the difficulty of rotating the wavelets on the sphere remains,
and because of this it is difficult to adapt arbitrary reflection characteristics. More-
over, when compressing a matrix representing radiance transfer, there is still the
problem of efficiently uncompressing the wavelet expansion at render time. Even
now graphics hardware is not well suited to this.
Progress in the efficiency of PRT, specifically for high-frequency lighting or
reflection having strong directionality, drew a great deal of attention from re-
searchers. A variety of new approaches using different basis functions have
since been presented (e.g., [Liu et al. 04]). The use of wavelets as presented here
focuses on the pioneering use of basis functions other than SH basis functions to
efficiently render scenes that would otherwise be unsuitable for PRT.
