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SECTION 4.2 Coordinate Systems
4.2 Coordinate Systems
Coordinate systems define the canvas on which all painting occurs. They deter-
mine the position, orientation, and size of the text, graphics, and images that
appear on a page. This section describes each of the coordinate systems used in
PDF, how they are related, and how transformations among them are specified.
Note: The coordinate systems discussed in this section apply to two-dimensional
graphics. PDF 1.6 introduces the ability to display 3D artwork, in which objects are
described in a three-dimensional coordinate system, as described in Section 9.5.4,
“Coordinate Systems for 3D.”
4.2.1 Coordinate Spaces
Paths and positions are defined in terms of pairs of coordinates on the Cartesian
plane. A coordinate pair is a pair of real numbers x and y that locate a point hori-
zontally and vertically within a two-dimensional coordinate space. A coordinate
space is determined by the following properties with respect to the current page:
• The location of the origin
• The orientation of the x and y axes
• The lengths of the units along each axis
PDF defines several coordinate spaces in which the coordinates specifying graph-
ics objects are interpreted. The following sections describe these spaces and the
relationships among them.
Transformations among coordinate spaces are defined by transformation matri-
ces, which can specify any linear mapping of two-dimensional coordinates, in-
cluding translation, scaling, rotation, reflection, and skewing. Transformation
matrices are discussed in Sections 4.2.2, “Common Transformations,” and 4.2.3,
“Transformation Matrices.”
Device Space
The contents of a page ultimately appear on a raster output device such as a dis-
play or a printer. Such devices vary greatly in the built-in coordinate systems they
use to address pixels within their imageable areas. A particular device’s coordi-
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