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                                                          536
CHAPTER 7                                                                                       Transparency



              fs = fj × fm × fk
                i    i    i     i
             αs = αj × ( fm × qm ) × ( fk × qk )
                i      i    i     i      i    i
          f g = Union ( f g , f s )
             i             i–1   i
         α g = Union ( α g , α s )
               i                  i–1       i
             α i = Union ( α 0 , α g )
                                        i


                   ⎛ α si ⎞                  αs
             C i = ⎜1 – ------ ⎟ × C i – 1 + ------i × ( ( 1 – α i – 1 ) × C s + α i – 1 × B i ( C i – 1 , C s ) )
                             -                    -
                   ⎝     αi ⎠                 αi                              i                               i


• Result:
                                   ⎛ α0           ⎞
         C = C n + ( C n – C 0 ) × ⎜ ------- – α 0⎟
                                           -
                                   ⎝ αgn          ⎠
          f = fg
                     n
         α = αg
                n


where the variables have the meanings shown in Table 7.8 (in addition to those in
Table 7.7 above).

For an element Ei that is an elementary object, the color, shape, and alpha
values C s , f j , and α j are intrinsic attributes of the object. For an element that is
          i     i         i
a group, the group compositing function is applied recursively to the subgroup
and the resulting C, f, and α values are used for its C s , f j , and α j in the calcula-
                                                            i  i         i
tions for the parent group.

                         TABLE 7.8 Variables used in the group compositing formulas
VARIABLE                          MEANING

Ei                                Element i of the group: a compound variable representing the ele-
                                  ment’s color, shape, opacity, and blend mode

fs                                Source shape for element Ei
     i

fj                                Object shape for element Ei
     i


fm                                Mask shape for element Ei
         i

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