CHAPTER 7
518
Transparency
TABLE 7.1 Variables used in the basic compositing formula
VARIABLE
MEANING
C
b
C
s
C
r
Backdrop color
Source color
Result color
Backdrop alpha
Source alpha
Result alpha
Blend function
α
b
α
s
α
r
B
(
C
b
,
C
s
)
This formula is actually a simplified form of the compositing formula in which
the shape and opacity values are combined and represented as a single alpha val-
ue; the more general form is presented later. This function is based on the
over
operation defined in the article “Compositing Digital Images,” by Porter and Duff
(see the Bibliography), extended to include a blend mode in the region of over-
lapping coverage. The following sections elaborate on the meaning and implica-
tions of this formula.
7.2.3 Blending Color Space
The compositing formula shown above is actually a vector function: the colors it
operates on are represented in the form of
n-element
vectors, where
n
is the num-
ber of components required by the color space in which compositing is per-
formed. The
ith
component of the result color
C
r
is obtained by applying the
compositing formula to the
ith
components of the constituent colors
C
b
,
C
s
, and
B
(C
b
,
C
s
). The result of the computation thus depends on the color space in
which the colors are represented. For this reason, the color space used for com-
positing, called the
blending color space,
is explicitly made part of the transparent
imaging model. When necessary, backdrop and source colors are converted to the
blending color space before the compositing computation.