CHAPTER 7
526
Transparency
gether in another compositing operation, the color’s contribution is correctly rep-
resented. Note that if
α
r
is zero, the result color is undefined.
The formula shown above is a simplification of the following formula, which pre-
sents the relative contributions of backdrop, source, and blended colors in a more
straightforward way:
α
r
×
C
r
=
[ (
1
–
α
s
) × α
b
×
C
b
]
+
[ (
1
–
α
b
) × α
s
×
C
s
]
+
[ α
b
× α
s
×
B
(
C
b
,
C
s
)
]
(The simplification requires a substitution based on the alpha compositing for-
mula, which is presented in the next section.) Thus, mathematically, the back-
drop and source alphas control the influence of the backdrop and source colors,
respectively, while their product controls the influence of the blend function. An
alpha value of
α
s
=
0.0 or
α
b
=
0.0 results in no blend mode effect; setting
α
s
=
1.0
and
α
b
=
1.0 results in maximum blend mode effect.
7.2.6 Shape and Opacity Computations
As stated earlier, the alpha values that control the compositing process are de-
fined as the product of shape and opacity:
α
b
=
f
b
×
q
b
α
r
=
f
r
×
q
r
α
s
=
f
s
×
q
s
This section examines the various shape and opacity values individually. Once
again, keep in mind that conceptually these values are computed for every point
on the page.
Source Shape and Opacity
Shape and opacity values can come from several sources. The transparency mod-
el provides for three independent sources for each. However, the PDF representa-
tion imposes some limitations on the ability to specify all of these sources
independently (see Section 7.5.3, “Specifying Shape and Opacity”).
•
Object shape.
Elementary objects such as strokes, fills, and text have an intrin-
sic shape, whose value is 1.0 for points inside the object and 0.0 outside. Simi-
larly, an image with an explicit mask (see “Explicit Masking” on page 351) has a