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The group compositing formulas for a non-isolated, non-knockout group are de ned as follows:
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f g = g = 00 0 0
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For each group element Ei G (i = 1, , n):
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Composite ( C i 1, i 1, E i ) Cs , f j , j = i i i intrinsic color, shape, and ( shape opacity ) of E i fs = fj fm fk i i i i s = j ( fm qm ) ( fk qk ) i i i i i i f g = Union ( f g , f s ) i i 1 i g = Union ( g , s )
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i i 1 i
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if E i is a group otherwise
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i = Union ( 0 , g )
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s s -i C i = 1 ------i C i 1 + ------ ( ( 1 i 1 ) C s + i 1 B i ( C i 1 , C s ) ) i i i i
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0 C = C n + ( C n C 0 ) ------- 0 gn f = fg
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where the variables have the meanings shown in Table 78 (in addition to those in Table 77 above) For an element Ei that is an elementary object, the color, shape, and alpha values C s , f j , and j are intrinsic attributes of the object itself For an element i i i that is itself a group, the group compositing function is applied recursively to the subgroup and the resulting C, f, and values are used for its C s , f j , and j in i i i the calculations for the parent group
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TABLE 78 Variables used in the group compositing formulas
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Element i of the group: a compound variable representing the element s color, shape, opacity, and blend mode Source shape for element Ei Object shape for element Ei
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fs fj
fm fk fg
Mask shape for element Ei Constant shape for element Ei Group shape: the accumulated source shapes of group elements E1 to Ei , excluding the initial backdrop
qm qk
Mask opacity for element Ei Constant opacity for element Ei Source alpha for element Ei Object alpha for element Ei : the product of its object shape and object opacity Group alpha: the accumulated source alphas of group elements E1 to Ei, excluding the initial backdrop Accumulated alpha after compositing element Ei , including the initial backdrop
s j
g i
Cs Ci
Source color for element Ei Accumulated color after compositing element Ei , including the initial backdrop
B i (C i 1, C s )
Blend function for element Ei
Note that the elements of a group are composited onto a backdrop that includes the group s initial backdrop This is done to achieve the correct effects of the blend modes, most of which are dependent on both the backdrop and source colors being blended (This feature is what distinguishes non-isolated groups from isolated groups, discussed in the next section)
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Special attention should be directed to the formulas at the end that compute the nal results, C, f, and , of the group compositing function Essentially, these formulas remove the contribution of the group backdrop from the computed results This ensures that when the group itself is subsequently composited with that backdrop (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 simpli cation of the following formulas, which present this operation more intuitively: ( 1 g ) 0 n b = -------------------------------------Union ( 0 , g )
Cn b C0 C = -----------------------------1 b where b 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 g , accumulate only the shape and alpha of the group elements, excludi i ing the group backdrop; their nal values become the group results returned by the group compositing function The complete alpha, i , 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: