Graphics Reference
In-Depth Information
the object select the appropriate level of detail. In expressive rendering (see Chap-
ter 34), we sometimes elide detail on an object for reasons other than screen size
(e.g., we might draw the details on only one or two faces in a crowd, because they
are the important ones); in such a case, the level-of-detail negotiation between ren-
derer and object may include hints other than the purely geometric ones discussed
here.
While we've described level of detail here as a solution to a resource-allocation
problem, it is more than that: Once we have decided to produce a final image using
a single-sample
z
-buffer technique (or any other approach that uses a small, fixed
number of samples per pixel), we've implicitly settled on a “scale” for which
we can hope to produce correct results. Assuming, for the sake of argument,
one sample per pixel, any geometric feature—a step, a windowsill, a doorknob—
whose projected size is less than two pixels will produce aliasing instead of being
accurately reconstructed. Because of this, we'd like to remove all such features,
in a sense “prefiltering before sampling.” Thus, using a level-of-detail approach
is a matter of
correctness
as well as efficiency. We summarize these ideas in a
principle:
N
W
E
S
L
EVEL OF DETAIL PRINCIPLE
:
Level of detail is important for both effi-
Simplify
ciency
and
correctness.
Figure 25.16: The front wall of a
building, seen from above. Notice
the narrow embossed portion of
the wall in the center. The sides of
this embossment will reflect light
from the east or west, while the
rest of the wall will not.
That being said, the “correctness” provided by level-of-detail simplifications
is not always all that one might wish. Consider the front of a building shown in
Figure 25.16. The natural “simplification” of this wall is to replace it with a single
planar wall.
But now consider the light-reflection properties of these two versions of the
building's front. If we assume that the front of the building is made of a somewhat
glossy material, then in the unsimplified wall, some light from the east will reflect
back toward the east, and some light from the west will reflect back to the west,
while lots of light from the south will reflect back toward the south. The bidirec-
tional reflectance distribution function (BRDF) of the wall as a whole, for three
incoming light directions, is shown in Figure 25.17. The BRDF for the simpli-
fied wall is rather different, since it's everywhere zero for light from the east, for
instance.
v
i
v
i
v
i
We could, as we simplified the wall, still represent the geometry by encoding
it in a normal map. But as we decrease the level of detail on the building further,
the normal map itself will have to be simplified as well, to avoid representing too-
high frequency changes. At that point, we can amalgamate the different reflection
characteristics of the surface at different points into a single BRDF that resembles
the “various facets in the wall look a lot like the microfacets” concept used in the
Torrance-Sparrow and Torrance-Cook models, in the sense that they are geometric
features that are too small (in screen coordinates) for us to detect, and hence we
aggregate their effects into a BRDF.
We saw this sort of thing before, back in Chapter 18: If we're taking samples
from a function in hopes of saying something about it, then our sampling rate
should exceed the Nyquist rate for the signal, or we'll suffer aliasing. In this case,
the “function” could be either “the
x
(or
y
or
z
)-coordinate of the points on the
Figure 25.17: The BRDF of the
wall, drawn for light coming from
the east, south, and west.
