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                                                       530
     CHAPTER 7                                                                           Transparency



7.2.7 Summary of Basic Compositing Computations

     Below is a summary of all the computations presented in this section. They are
     given in an order such that no variable is used before it is computed; also, some of
     the formulas have been rearranged to simplify them. See Tables 7.1, 7.4, and 7.5
     above for the meanings of the variables used in these formulas.

      Union ( b, s ) = 1 – [ ( 1 – b ) × ( 1 – s ) ]
                     = b + s – (b × s)

       fs = fj × fm × fk
       qs = qj × qm × qk
                      ·
       f r = Union ( f b , f s )


      αb = fb × qb
      αs = fs × qs
      α r = Union ( α b , α s )

              αr
       q r = -----
              fr

            ⎛ αs ⎞               αs
      C r = ⎜1 – ----- ⎟ × C b + ----- × [ ( 1 – α b ) × C s + α b × B ( C b , C s ) ]
            ⎝ αr ⎠               αr


 7.3 Transparency Groups

     A transparency group is a sequence of consecutive objects in a transparency stack
     that are collected together and composited to produce a single color, shape, and
     opacity at each point. The result is then treated as if it were a single object for sub-
     sequent compositing operations. This facilitates creating independent pieces of
     artwork, each composed of multiple objects, and then combining them, possibly
     with additional transparency effects applied during the combination. Groups can
     be nested within other groups to form a tree-structured group hierarchy.

     The objects contained within a group are treated as a separate transparency stack
     called the group stack. The objects in the stack are composited against some initial
     backdrop (discussed later), producing a composite color, shape, and opacity for
     the group as a whole. The result is an object whose shape is the union of the

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