Graphing with Gnuplot and Xmgr
Three dimensional surfaces can be generated with the splot command, which has syntax almost identical to plot. An additional range specifies the range of the y variable and the set view command lets the user control the orientation of the plot in space. A simple example would be:
splot x*x-y*y title "Hyperbolic Paraboloid"
Gnuplot also supports hiding lines that are behind other lines with the hidden3d parameter: set hidden3d.
Gnuplot can plot “parametric” functions. A parametric function is one in which both the x and y coordinates are functions of a third variable, which in Gnuplot is t. For example:
set parametric plot 2*sin(t), 2*cos(t)
produces a circle of radius 2. The command:
set trange <range>
sets the values of t that are evaluated. Parametric plots are also valid while doing a three-dimensional splot. In this case, the independent variables under gnuplot are u and v.
Gnuplot can also take data points from the standard output of a Unix command specified on gnuplot's command line. This allows the display of points generated from almost any source. The command should be specified like a filename, preceded by a < character.
Xmgr is oriented more towards plotting data created from an external source, as opposed to plotting a given mathematical function. Xmgr normally reads files, but can also take input piped from its standard input. Once data has been read into an xmgr set, it can be displayed, scaled, and manipulated in many ways.
Xmgr also has an on-line help. When the “help” menu is selected, xmgr runs your favorite HTML browser (Mosaic by default) with the xmgr documentation as input. Several sites on the internet have this page on-line. If you don't have a browser, you end up having to read raw html. Having a program's documentation as a hypertext document is quite nice, as you can jump from subject to subject as well as being able to do text searches. A gallery of graphs produced by xmgr is also included with the xmgr distribution, which gives the user a visual look at the wide range of effects possible with xmgr.
The first step in graphing some data is to read the data into xmgr. The “Read Sets...” option under “File” produces a file browser from which a file can be selected. Several types of data can be read in, but the two column “XY” format is the most common. The format of the data is much the same as in gnuplot—individual points on lines by themselves separated by spaces or tabs. Lines beginning with # are also considered comment lines, and lines without numeric data (like a blank line) separate sets. Lines beginning with the @ symbol can control the actions of xmgr separately from the user.
Xmgr data sets are somewhat like registers, in that only a fixed number are available (fixed at compile time), and they are referred to by number. Once the data is in a set, it is displayed immediately. The left hand side of the xmgr window contains a number of buttons that provide shortcuts for various operations.
Most of the shortcut buttons let the user change the appearance of the graph interactively. A set of four arrow buttons scrolls the data in all four directions—tick marks and tick labels are automatically updated. The “Z” and “z” buttons allow uniform zooming in and out. Arbitrary zooms in are accomplished by using the magnifying glass button. This prompts the user for a rectangle that becomes the new limits of the graph. A text line at the top of xmgr's window constantly displays the current position of the mouse, in the coordinates of the graph. A crosshair extending the length and breadth of the window may be toggled to help position the mouse within a pixel of the desired point.
The “autoO” button provides an autoscaling feature. The cursor changes to a crosshair, which when clicked at some point selects the set nearest to the clicked point. The graph is rescaled such that all points in this set are visible. The “autoT” button immediately rescales the tick marks that can get cramped while doing a zoom.
Each data set has several attributes that control how the set is displayed—which symbol is used for points, the color of the symbol, whether the symbols are connected by lines or not, the color and style of the lines, the legend associated with the data set, and more. One rather packed menu controls all these options.
The user has a great deal of control over how the graph is displayed. Major and minor tick marks chosen by xmgr can be overridden. Simple box and line graphics as well as text strings can be drawn at arbitrary locations. All strings can be displayed in a variety of fonts and sizes, with subscripts, superscripts and some special characters available.
To repeat the earlier example using gnuplot, Figure 2 shows the xmgr display immediately after loading the hits file. Figure 3 shows the symbols and legends menu used to control the appearance of the set and the set's legend respectively, while Figure 4 shows the results. Figure 5 shows us getting ready to fix the X-axis by replacing the numbers with month names with the result in Figure 6. Figure 7 is after the final touch-up, adding a title, giving the Y-axis a name, getting rid of the tenths digit in the tick labels and expanding the X-axis to fill the entire bottom of the graph. Figure 8 is the final PostScript output.