Coordinate Systems

Using appropriate plt options, you can place labels anywhere in a plot, and you can place plots anywhere on a page. These plt options use four coordinate systems to specify position.

First is the data coordinate system: the coordinates defined by your plot's axes. The ranges of the data coordinates depend on the ranges of $x$ and $y$ values, or on the ranges you specify using the -xa and -ya (or -X and -Y) options. The lower left corner of the data coordinate system is $(x_{min},y_{min})$, and the upper right corner is $(x_{max},y_{max})$.

Second is the window coordinate system. Window coordinates, $(xw,yw)$, always range from $(0,0)$ to $(1,1)$. The window coordinates $(0,0)$ correspond to the data coordinates $(x_{min},y_{min})$, and the window coordinates $(1,1)$ map to the data coordinates $(x_{max},y_{max})$.

Third is the page coordinate system. Page coordinates, $(xp,yp)$, always range from $(0,0)$, at the lower left corner of the page, to $(1,1)$ at the upper right corner. Using the -W option described later on, you can specify a rectangle in page coordinates in which the plot is to be drawn; this option thus allows you to draw multiple plots in any desired layout on a page. When you make a screen plot, the ``page'' may be the entire screen, or it may be an X window. When you make a printable plot, the ``page'' may be the entire sheet of paper, or the printable area (generally less than the full sheet), or it may represent a PostScript bounding box for a plot that can be incorporated into another document such as this book.

Figure 4.1: Data, window, and page coordinates

Figure 4.1 illustrates the relationships among data, window, and page coordinates. Note that it is always possible to refer to data, window, or page coordinates outside of the ranges of these coordinate systems. Depending on the plt options you have chosen, and in some cases on the output device (screen or printer), out-of-bounds elements may or may not appear in the output.

A fourth coordinate system, called text box coordinates, is used by plt to allow fine control over the positioning of text on plots.

plt places an imaginary text box around each string it prints. Descenders (the lower portions of ``g'', ``j'', ``p'', ``q'', ``y'', and ``,'') fall outside of the box, but each text box includes extra space above the top of the characters (30% to 40% of the basic height of the text) for any descenders from the line above. Text box coordinates are symbolic and discrete rather than numeric and continuous. Each text box has twelve points defined as shown in figure 4.2. Thus point CT is at the center of the top side of the text box, RB is the lower right corner, etc.

When you tell plt to print a string at $(x,y)$, plt usually places text box point CC at $(x,y)$, thus centering the string on $(x,y)$. By naming the appropriate text box point as an argument to any of the options described in chapter 8, Labelling Your Plot, you can choose instead to place any of the four corners, the center of any side, or any of the other defined points of the text box at $(x,y)$.

Figure 4.2: Text box coordinates.Note that text box coordinates are always oriented left-right and top-bottom with respect to the text, and not necessarily with respect to the page. At lower left is an example of how to form subscripts using plt's -L option (see chapter 8). As shown, the right bottom (RB) point of the X and the left center (LC) of the subscript n are both placed at the same window coordinates (.1,.25) to achieve the desired alignment.