CHAPTER 7
532
Transparency
These conventions permit the compositing formulas to be restated as recurrence
relations among the elements of a stack. For instance, the result of the color com-
positing computation for object
i
is denoted by
C
i
(formerly
C
r
). This computa-
tion takes as one of its inputs the immediate backdrop color, which is the result of
the color compositing computation for object
i
−
1; this is denoted by
C
i
−
1
(formerly
C
b
).
The revised formulas for a simple
n-element
stack (not including any groups) are,
for
i
=
1, … ,
n:
f
s
=
f
j
×
f
m
×
f
k
i
i
i
i
q
s
=
q
j
×
q
m
×
q
k
i
i
i
i
α
s
=
f
s
×
q
s
i
i
i
α
i
=
Union
(
α
i
–
1
,
α
s
)
i
f
i
=
Union
(
f
i
–
1
,
f
s
)
i
q
i
= ----
-
f
i
α
i
α
s
⎛
α
s
i
⎞
C
i
=
⎜
1
– ------
⎟
×
C
i
–
1
+ ------
i
× [ (
1
–
α
i
–
1
) ×
C
s
+
α
i
–
1
×
B
i
(
C
i
–
1
,
C
s
)
]
-
-
α
i
⎠
α
i
i
i
⎝
where the variables have the meanings shown in Table 7.6. Compare these
formulas with those shown in Section 7.2.7, “Summary of Basic Compositing
TABLE 7.6 Revised variables for the basic compositing formulas
VARIABLE
MEANING
f
s
f
j
i
Source shape for object
i
Object shape for object
i
Mask shape for object
i
i
f
m
i