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      CHAPTER 7                                                                   Transparency




                      TABLE 7.1 Variables used in the basic compositing formula
      VARIABLE               MEANING

      Cb                     Backdrop color

      Cs                     Source color

      Cr                     Result color

      αb                     Backdrop alpha

      αs                     Source alpha

      αr                     Result alpha

      B ( Cb , Cs )          Blend function


      This formula is actually a simplified form of the compositing formula in which
      the shape and opacity values are combined and represented as a single alpha val-
      ue; the more general form is presented later. This function is based on the over
      operation defined in the article “Compositing Digital Images,” by Porter and Duff
      (see the Bibliography), extended to include a blend mode in the region of over-
      lapping coverage. The following sections elaborate on the meaning and implica-
      tions of this formula.

7.2.3 Blending Color Space

      The compositing formula shown above is actually a vector function: the colors it
      operates on are represented in the form of n-element vectors, where n is the num-
      ber of components required by the color space in which compositing is per-
      formed. The ith component of the result color Cr is obtained by applying the
      compositing formula to the ith components of the constituent colors Cb , Cs , and
      B (Cb , Cs ). The result of the computation thus depends on the color space in
      which the colors are represented. For this reason, the color space used for com-
      positing, called the blending color space, is explicitly made part of the transparent
      imaging model. When necessary, backdrop and source colors are converted to the
      blending color space before the compositing computation.

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