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      SECTION 7.2                                                   Basic Compositing Computations



      mnemonic subscript indicating which of several color values is being referred to;
      for instance, Cs stands for “source color.” Shape and opacity values are denoted re-
      spectively by the letters f (for “form factor”) and q (for “opaqueness”)—again with
      a mnemonic subscript, such as qs for “source opacity.” The symbol α (alpha)
      stands for a product of shape and opacity values.

      In certain computations, one or more variables may have undefined values; for
      instance, when opacity is zero, the corresponding color is undefined. A quantity
      can also be undefined if it results from division by zero. In any formula that uses
      such an undefined quantity, the quantity has no effect on the ultimate result
      because it is subsequently multiplied by zero or otherwise canceled out. The sig-
      nificant point is that while any arbitrary value can be chosen for such an unde-
      fined quantity, the computation must not malfunction because of exceptions
      caused by overflow or division by zero. It is convenient to adopt the further con-
      vention that 0 ÷ 0 = 0.


7.2.2 Basic Compositing Formula

      The primary change in the imaging model to accommodate transparency is in
      how colors are painted. In the transparent model, the result of painting (the result
      color) is a function of both the color being painted (the source color) and the color
      it is painted over (the backdrop color). Both of these colors may vary as a function
      of position on the page; however, this section focuses on some fixed point on the
      page and assumes a fixed backdrop and source color.

      Other parameters in this computation are the alpha, which controls the relative
      contributions of the backdrop and source colors, and the blend function, which
      specifies how they are combined in the painting operation. The resulting basic
      color compositing formula (or just basic compositing formula for short) determines
      the result color produced by the painting operation:

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

      where the variables have the meanings shown in Table 7.1.

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