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it also includes local illumination effects such as interreflections, subsurface scat-
tering, and shadowing. Incorporating BTFs in rendering can assist in efficient
photorealistic rendering of complex materials.
The use of BTFs in production rendering is still in its early stages. However,
since 2008, the use of physically based BRDF models along with physically based
rendering techniques such as global illumination and ray tracing have become
more prevalent, even in movie production. As previously mentioned, BTFs are
considered useful in combination with physically based BRDF models and in
other image-based approaches. BTFs are expected to play an important role in
future rendering techniques. This chapter introduces the basic concept of BTFs
and provides background on the progress of rendering techniques that use them.
9.1 Origin of BTFs
The idea of a bidirectional texture function originated in the paper entitled “Re-
flectance and Texture of Real-World Surfaces” by Kristin J. Dana, Bram van Gin-
neken, Shree K. Nayar and Jan J. Koenderink [Dana et al. 99]. This paper in-
troduced the BTF as a new representation for surface reflectance that reproduced
surface appearance more realistically than existing methods. Figure 9.1 illustrates
the effect of changing the view or lighting direction on the appearance of a sur-
face. The small pits and bumps on the surface exhibit shadowing and interreflec-
tion, which changes with the direction of the light. The local mesostructure also
causes the appearance to change with viewing direction, as shown in Figure 9.2.
A bidirectional texture function is defined as a function of the lighting direc-
tion, the viewing direction, and the surface position. The BTF is thus a function of
six variables: if
θ
i ,
φ
i , represent the light direction in the local surface coordinate
system,
θ
r ,
φ
r represent the viewing direction, and x , y represent the position on
V
z
L 1
L 0
y
x
L 0
L 1
Figure 9.1
Variation of the appearance of a small area with changing light source direction. (From
[Tong et al. 02] c
2002 ACM, Inc. Included here by permission.)
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