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                                                     538
      CHAPTER 7                                                              Transparency



      (possibly with additional shape or opacity inputs or a different blend mode), the
      backdrop’s contribution is included only once.

      For color, the backdrop removal is accomplished by an explicit calculation, whose
      effect is essentially the reverse of compositing with the Normal blend mode. The
      formula is a simplification of the following formulas, which present this opera-
      tion more intuitively:

              ( 1 – αg ) × α0
      φ b = --------------------------------------
                                n
                                                 -
            Union ( α 0 , α g )
                                              n
           Cn – φb × C0
                                        -
       C = ------------------------------
                   1 – φb

      where φb is the backdrop fraction, the relative contribution of the backdrop color
      to the overall color.

      For shape and alpha, backdrop removal is accomplished by maintaining two sets
      of variables to hold the accumulated values. The group shape and alpha,
      f g and α g , accumulate only the shape and alpha of the group elements, exclud-
         i       i
      ing the group backdrop. Their final values become the group results returned by
      the group compositing function. The complete alpha, αi , includes the backdrop
      contribution as well; its value is used in the color compositing computations.
      (There is never any need to compute the corresponding complete shape, fi , that
      includes the backdrop contribution.)

      As a result of these corrections, the effect of compositing objects as a group is the
      same as that of compositing them separately (without grouping) if the following
      conditions hold:

      • The group is non-isolated and has the same knockout attribute as its parent
         group (see Sections 7.3.4, “Isolated Groups,” and 7.3.5, “Knockout Groups”).
      • When compositing the group’s results with the group backdrop, the          Normal
         blend mode is used, and the shape and opacity inputs are always 1.0.


7.3.4 Isolated Groups

      An isolated group is one whose elements are composited onto a fully transparent
      initial backdrop rather than onto the group’s backdrop. The resulting source

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