Graphics Reference
In-Depth Information
a bounding box hierarchy, the result is the same as was described in the previ-
ous paragraph. However, with this generality we can consider arbitrary bounding
structures, such as a 4D BSP tree or bounding sphere hierarchy, which may pro-
vide tighter (if less intuitive) bounds.
α
)
A single geometric primitive may be used as a proxy for more complex geometry,
for example, representing a window screen or a maple leaf as single rectangle.
In this case, the small-scale coverage can be stored as a material property. By
convention this property is represented by the variable
α
. Alpha is explicit cover-
age:
α
=
0 is no coverage (e.g., areas outside of the leaf's silhouette),
α
=
1is
total coverage (e.g., areas inside the leaf's silhouette), and 0
<α<
1 is partial
coverage (e.g., the entire window screen may be represented with
α
=
0. 5).
Inline Exercise 36.8:
Under what circumstances (e.g., position of the object
relative to other objects or the camera) might the use of coverage-as-material-
property lead to substantial errors in an image?
value is insufficient to represent colored translucency. A
red wall viewed through a green wine bottle should appear black. Yet, if we model
a bottle with a green surface as
Note that a single
α
=
0. 5, we will observe a brown wall through the
bottle, whose color is 50% red and 50% green. This is a common artifact in real-
time rendering. Offline rendering tends to model this situation more accurately
with one coverage value per frequency of light simulated, or by sampling the light
passing through the bottle as scattered rather than composited. This can also be
done efficiently for real-time rendering by trading spatial precision for coverage
precision [ME11].
An explicit coverage
α
must still be injected into the coverage resolution
scheme for the entire framebuffer. Two common approaches are analytic and
stochastic coverage. For the analytic approach, one simply renders in back-to-
front order (with all of the limitations this implies) and explicitly composites each
fragment as it is rendered, or injects the fragments into an A-buffer for it to process
in that manner during resolution.
Stochastic approaches randomly set the fraction of coverage mask bits approx-
imately equal to
α
and then allow another scheme such as MSAA to drive the
shading and resolve operations. It is essential to ensure that the choice of which
coverage bits are set is statistically independent for each fragment [ESSL10]
because this is an underlying assumption of the compositing operations [PD84]
implicit in the resolve filter.
Recent work shows that the quality of the resolve operation for stochastic
antialiasing methods can be improved by filters more sophisticated than the typical
box filter, although it has yet to be shown that the cost of complex resolve opera-
tions is less than the cost of simply increasing the number of samples [SAC
+
11].
α
The classic paper “A characterization of ten hidden-surface algorithms” by Suther-
land and Sproul [SSS74] surveys the state of the art for visibility in 1974, when the
