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(In actual practice, they are often obtained from auxiliary sources rather than being intrinsic to the object itself) Both shape and opacity vary from 00 (no contribution) to 10 (maximum contribution) At any point where either the shape or the opacity of an object is 00, its color is unde ned At points where the shape is 00, the opacity is also unde ned The shape and opacity are themselves subject to compositing rules, so that the stack as a whole also has a shape and opacity at each point An object s opacity, in combination with the backdrop s opacity, determines the relative contributions of the backdrop color, the object s color, and the blended color to the resulting composite color The object s shape then determines the degree to which the composite color replaces the backdrop color Shape values of 00 and 10 identify points that lie outside and inside a conventional sharpedged object; intermediate values are useful in de ning soft-edged objects Shape and opacity are conceptually very similar In fact, they can usually be combined into a single value, called alpha, which controls both the color compositing computation and the fading between an object and its backdrop However, there are a few situations in which they must be treated separately; see Section 735, Knockout Groups Moreover, raster-based implementations must maintain a separate shape parameter in order to do anti-aliasing properly; it is therefore convenient to have it be an explicit part of the model One or more consecutive objects in a stack can be collected together into a transparency group (often referred to hereafter simply as a group) The group as a whole can have various properties that modify the compositing behavior of objects within the group and their interactions with its backdrop An additional blend mode, shape, and opacity can also be associated with the group as a whole and used when compositing it with its backdrop Groups can be nested within other groups, forming a tree-structured hierarchy Note: The concept of a transparency group is independent of existing notions of group or layer in applications such as Adobe Illustrator Those groupings re ect logical relationships among objects that are meaningful when editing those objects, but they are not part of the imaging model Plate 16 illustrates the effects of transparency grouping In the upper two gures, three colored circles are painted as independent objects, with no grouping At the upper left, the three objects are painted opaquely (opacity = 10); each object
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completely replaces its backdrop (including previously painted objects) with its own color At the upper right, the same three independent objects are painted with an opacity of 05, causing them to composite with each other and with the gray and white backdrop In the lower two gures, the three objects are combined as a transparency group At the lower left, the individual objects have an opacity of 10 within the group, but the group as a whole is painted in the Normal blend mode with an opacity of 05 The objects thus completely overwrite each other within the group, but the resulting group then composites transparently with the gray and white backdrop At the lower right, the objects have an opacity of 05 within the group and thus composite with each other; the group as a whole is painted against the backdrop with an opacity of 10, but in a different blend mode (HardLight), producing a different visual effect The color result of compositing a group can be converted to a single-component luminosity value and treated as a soft mask Such a mask can then be used as an additional source of shape or opacity values for subsequent compositing operations When the mask is used as a shape, this technique is known as soft clipping; it is a generalization of the current clipping path in the opaque imaging model (see Section 443, Clipping Path Operators ) The notion of current page is generalized to refer to a transparency group consisting of the entire stack of objects placed on the page, composited with a backdrop that is pure white and fully opaque Logically, this entire stack is then rasterized to determine the actual pixel values to be transmitted to the output device Note: In contexts where a PDF page is treated as a piece of artwork to be placed on some other page such as an Illustrator artboard or an Encapsulated PostScript (EPS) le it is treated not as a page but as a group, whose backdrop may be de ned differently from that of a page
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