Graphics Reference
In-Depth Information
Rendering with the eigen-BRDFs is straightforward. For a given point on
the object surface, the relative location in the local surface neighborhood is de-
termined, as is the PCA cluster to which it belongs. The actual response vector
is constructed by interpolating the basis vector coefficients as a function of the
lighting/viewing direction, and the appropriate pixel value is extracted from the
interpolated response vector.
9.3.6 General Approximation of Signals
The term
response vector
has been used to describe the collection of radiance
values reflected from a surface point as a function of varying lighting/viewing di-
rections. In general, a response vector represents the response of a system due
to a stimulus known as a
signal
. In the context of BTFs, a signal is a particu-
lar lighting/viewing direction. Like response vectors, signals are usually high-
dimensional vectors, and also like response vectors, they require a vast amount of
storage space. Consequently, various methods for compressing and approximat-
ing signals have been conceived. Some typical methods for doing so are consid-
ered next. These methods employ techniques that have been frequently used in
this topic.
VQ (vector quantization).
In computer graphics,
vector quantization
(VQ)
is a general term for any method of representing a collection of vectors by a single
vector, e.g., by the vector mean. For example, an input signal on a surface might
consist of a set of directions over the surface (
Figure 9.17
). These directions
may be
quantized
to a few representative vectors; each actual signal vector is
=M
p
Mc
p
M
p
: Signal at point
p
M
cp
: Cluster center vector of the cluster
C
p
C
p
: Cluster to which the signal at point
p
is assigned
Figure 9.17
Vector quantization (VQ) of a signal on a surface. The actual signal (not shown) varies
over the surface. A set of representative vectors for the signal is chosen by a clustering
method (three, in this example) and these are used in place of the actual signal vectors.
(Courtesy of Peter-Pike Sloan.)
