CHAPTER 7
528
Transparency
TABLE 7.4 Variables used in the source shape and opacity formulas
VARIABLE
MEANING
f
s
f
j
f
m
f
k
q
s
q
j
q
m
q
k
Source shape
Object shape
Mask shape
Constant shape
Source opacity
Object opacity
Mask opacity
Constant opacity
Note:
When an object is painted with a tiling pattern, the object shape and object
opacity for points in the object’s interior are determined by those of corresponding
points in the pattern, rather than being 1.0 everywhere (see Section 7.5.6, “Patterns
Result Shape and Opacity
In addition to a result color, the painting operation also computes an associated
result shape
and
result opacity.
These computations are based on the
union func-
tion
Union
(
b
,
s
) =
1
–
[ (
1
–
b
) × (
1
–
s
) ]
=
b
+
s
–
(
b
×
s
)
where
b
and
s
are the backdrop and source values to be composited. This is a gen-
eralization of the conventional concept of union for opaque shapes, and it can be
thought of as an “inverted multiplication”—a multiplication with the inputs and
outputs complemented. The result tends toward 1.0: if either input is 1.0, the re-
sult is 1.0.