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      CHAPTER 6                                                                  Rendering



      subtractive device such as a printer. Transfer functions produce color values in
      additive form; see Section 6.3, “Transfer Functions.”


6.4.2 Spot Functions

      A common way of defining a halftone screen is by specifying a frequency, angle,
      and spot function. The frequency is the number of halftone cells per inch; the
      angle indicates the orientation of the grid lines relative to the device coordinate
      system. As a cell’s desired gray level varies from black to white, individual pixels
      within the cell change from black to white in a well-defined sequence: if a partic-
      ular gray level includes certain white pixels, lighter grays will include the same
      white pixels along with some additional ones. The order in which pixels change
      from black to white for increasing gray levels is determined by a spot function,
      which specifies that order in an indirect way that minimizes interactions with the
      screen frequency and angle.

      Consider a halftone cell to have its own coordinate system: the center of the cell is
      the origin and the corners are at coordinates ±1.0 horizontally and vertically.
      Each pixel in the cell is centered at horizontal and vertical coordinates that both
      lie in the range −1.0 to +1.0. For each pixel, the spot function is invoked with the
      pixel’s coordinates as input and must return a single number in the range −1.0 to
      +1.0, defining the pixel’s position in the whitening order.

      The specific values the spot function returns are not significant; all that matters
      are the relative values returned for different pixels. As a cell’s gray level varies
      from black to white, the first pixel whitened is the one for which the spot function
      returns the lowest value, the next pixel is the one with the next higher spot func-
      tion value, and so on. If two pixels have the same spot function value, their rela-
      tive order is chosen arbitrarily.

      PDF provides built-in definitions for many of the most commonly used spot
      functions. A halftone can simply specify any of these predefined spot functions
      by name instead of giving an explicit function definition. For example, the name
      SimpleDot designates a spot function whose value is inversely related to a pixel’s
      distance from the center of the halftone cell. This produces a “dot screen” in
      which the black pixels are clustered within a circle whose area is inversely pro-
      portional to the gray level. The predefined function Line is a spot function whose
      value is the distance from a given pixel to a line through the center of the cell,
      producing a “line screen” in which the white pixels grow away from that line.

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