Graphics Reference
In-Depth Information
Figure 8.19
The process of “charting” a nonlinear approximation to BRDF data. Points in linear sub-
spaces are projected onto the Gaussian curve. (From [Matusik et al. 03] c
2003 ACM,
Inc. Included here by permission.)
thors is called
charting
,
11
in which points on an unknown curved subspace are
projected onto a collection of known subspaces, which are Gaussian surfaces in
this case. The projected values are weighted according to their distance from
the unknown subspace. The Gaussian surfaces are then merged to approximate
the unknown subspace. Figure 8.19 illustrates the basic approach in the plane;
in this figure the Gaussian subspaces are shown as straight lines. The size of the
projected points represents the weights. The process is much more complicated
in the 45-dimensional linear BRDF space, and the actual method used by the au-
thors is only sketched in the paper. The difficult part is selecting a minimal set of
Gaussians to cover the subspace.
The authors' experiments indicate that as few as 10 properly chosen Gaussian
surfaces is likely sufficient to represent the physically realizable BRDF subspace.
However, they employ a basis of 15 Gaussian to fit the measured data. They note
that this gives comparable approximation results to the 45 linear basis functions.
While this is a notable reduction, the real advantage of the nonlinear approxima-
tion is that it stays closer to the space of realizable BRDFs. As noted earlier, some
parts of the linear subspace correspond to implausible BRDFs. Figure 8.20 shows
an example: moving away from a point in the linear subspace results in a BRDF
that has a low value at the specular direction, which causes a specular highlight to
have a hole in the middle. In contrast, moving an equal distance on the nonlinear
subspace stays in the domain of plausible BRDFs.
Given the Gaussian basis, the next question is how to determine the weights
in order to represent a particular BRDF. Ultimately the authors wanted to provide
a BRDF designer with a set of intuitive controls, such as its “diffuseness” and
how “metallic” it appears. Ideally these controls should be independent of each
other. Unfortunately, the Gaussian bases are not very intuitive, so the authors de-
11
Charting is described more fully in “Charting a Manifold” by Matthew Brand [Brand 03].
