There is a whole hierarchy of coordinate systems associated with
any PLplot graph. At the lowest level a device provides a view surface
(coordinates in mm's) which can be a terminal screen or a sheet of paper
in the output device. plinit or plstar (or plstart) makes that
device view surface accessible as a page or divided up into sub-pages
(see plssub) which are accessed with pladv. Before a graph can be
drawn for a subpage, the program must call appropriate routines in
PLplot to define the viewport for the subpage and a window for the
viewport. A viewport is a rectangular region of the
subpage which is specified in normalized subpage
coordinates or millimetres. A window is a rectangular region of
world-coordinate space which is mapped directly to its viewport. (When
drawing a graph, the programmer usually wishes to specify the
coordinates of the points to be plotted in terms of the values of the
variables involved. These coordinates are called world
coordinates, and may have any floating-point value
representable by the computer.)
Although the usual choice is to have one viewport per subpage, and one window per viewport, each subpage can have more than one (possibly overlapping) viewport defined, and each viewport can have more than one window (more than one set of world coordinates) defined.
After defining the view surface and subpage with the appropriate
call to plinit or plstar (or plstart) and a call to pladv it
is necessary to define the portion of this subpage which is to be used
for plotting the graph (the viewport). All lines and symbols (except
for labels drawn by plbox, plmtex and pllab) are clipped at the
viewport boundaries.
Viewports are created within the current subpage. If the
division of the output device into equally sized subpages is
inappropriate, it is best to specify only a single subpage which
occupies the entire output device (by using plinit or by setting
nx = 1 and ny = 1 in plstar
or plstart), and use one of the viewport specification subroutines
below to place the plot in the desired position on the page.
There are four methods for specifying the viewport size, using the
subroutines plvpor, plsvpa, plvasp, and plvpas which are
called like this:
plvpor(xmin, xmax, ymin, ymax); plsvpa(xmin, xmax, ymin, ymax); plvasp(aspect); plvpas(xmin, xmax, ymin, ymax, aspect); |
where in the case of plvpor and plvpas, the arguments are given
in normalized subpage coordinates which are
defined to run from 0.0 to 1.0 along each edge of the subpage. Thus
for example,
plvpor(0.0, 0.5, 0.5, 1.0); |
uses the top left quarter of the current subpage.
In order to get a graph of known physical size, the routine plsvpa
defines the viewport in terms of absolute coordinates (millimeters)
measured from the bottom left-hand corner of the current subpage.
This routine should only be used when the size of the view surface is
known, and a definite scaling is required.
The routine plvasp gives the largest viewport with the given aspect
ratio that fits in the current subpage (i.e. the ratio of the length
of the y axis to that of the x axis is equal to
aspect). It also allocates space on the left and
top of the viewport for labels.
The routine plvpas gives the largest viewport with the given aspect
ratio that fits in the specified region (specified with normalized
subpage coordinates, as with plvpor). This routine is functionally
equivalent to plvpor when a "natural" aspect ratio is
chosen (done by setting aspect to 0.0). Unlike
plvasp, this routine reserves no extra space at the edges for
labels.
To help the user call plsvpa correctly, the routine plgspa is
provided which returns the positions of the extremities of the
current subpage measured in millimeters from the bottom left-hand
corner of the device. Thus, if to set up a viewport with a 10.0 mm
margin around it within the current subpage, the following sequence
of calls may be used:
plgspa(xmin, xmax, ymin, ymax); plsvpa(10.0, xmax-xmin-10.0, 10.0, ymax-ymin-10.0); |
A further routine plvsta is available which sets up a standard
viewport within the current subpage with suitable margins on each
side of the viewport. This may be used for simple graphs, as it
leaves enough room for axis labels and a title. This standard
viewport is that used by plenv (See the Section called Setting up a Standard Window).
Another way to get a specified aspect ratio is via the routine
plsasp [not!.. fix this], which sets the global
aspect ratio and must be called prior to plstar. An aspect ratio
of 0.0 corresponds to "natural" dimensions (i.e. fill
the page); any positive value will give the specified aspect ratio.
This scaling of plots is actually done in the driver, and so may not
work for all output devices (note that plrender
is capable of scaled aspect ratio plots to any device whether that
device supports scaling or not). In such scaled plots, absolute
plotting is done in the scaled coordinate system.
The window must be defined after the viewport in order to map the
world coordinate rectangle into the viewport rectangle. The routine
plwind is used to specify the rectangle in world-coordinate space.
For example, if we wish to plot a graph showing the collector current
IC as a function of the collector to emitter
voltage VCE for a transistor where 0 ≤
IC ≤ 10.0 mA and 0 ≤
VCE ≤ 12.0 V, we would call the
function plwind as follows:
plwind(0.0, 12.0, 0.0, 10.0); |
Note that each of the arguments is a floating point number, and so
the decimal points are required. If the order of either the X limits
or Y limits is reversed, the corresponding axis will point in the
opposite sense, (i.e., right to left for X and top to bottom for Y).
The window must be defined before any calls to the routines which
actually draw the data points. Note however that plwind may also
be called to change the window at any time. This will affect the
appearance of objects drawn later in the program, and is useful for
drawing two or more graphs with different axes on the same piece of
paper.
The routine plbox is used to specify whether a frame is drawn
around the viewport and to control the positions of the axis
subdivisions and numeric labels. For our simple graph of the
transistor characteristics, we may wish to draw a frame consisting of
lines on all four sides of the viewport, and to place numeric labels
along the bottom and left hand side. We can also tell PLplot to
choose a suitable tick interval and the number of subticks between
the major divisions based upon the data range specified to plwind.
This is done using the following statement
plbox("bcnst", 0.0, 0, "bcnstv", 0.0, 0); |
The lengths of major and minor ticks on the axes are set up by the
routines plsmaj and plsmin.
Another routine pllab provides for text labels for the bottom, left
hand side and top of the viewport. These labels are not clipped,
even though they lie outside the viewport (but they are clipped at
the subpage boundaries). pllab actually calls the more general
routine plmtex which can be used for plotting labels at any point
relative to the viewport. For our example, we may use
pllab("V#dCE#u (Volts)", "I#dC#u (mA)", "TRANSISTOR CHARACTERISTICS"); |
Note that #d and #u are escape sequences (see the Section called Escape sequences in text) which allow subscripts and superscripts to be used in text. They are described more fully later in this chapter.
The appearance of axis labels may be further altered by auxiliary
calls to plprec, plschr, plsxax, plsyax, and plszax. The
routine plprec is used to set the number of decimal places
precision for axis labels, while plschr modifies the heights of
characters used for the axis and graph labels. Routines plsxax,
plsyax, and plszax are used to modify the
digmax setting for each axis, which affects how
floating point labels are formatted.
The digmax variable represents the maximum field width for the numeric labels on an axis (ignored if less than one). If the numeric labels as generated by PLplot exceed this width, then PLplot automatically switches to floating point representation. In this case the exponent will be placed at the top left for a vertical axis on the left, top right for a vertical axis on the right, and bottom right for a horizontal axis.
For example, let's suppose that we have set digmax =
5 via plsyax, and for our plot a label is generated at
y = 0.0000478. In this case the actual field
width is longer than digmax, so PLplot switches to
floating point. In this representation, the label is printed as
simply 4.78 with the 10-5 exponent placed
separately.
The determination of maximum length (i.e. digmax) for fixed point quantities is complicated by the fact that long fixed point representations look much worse than the same sized floating point representation. Further, a fixed point number with magnitude much less than one will actually gain in precision when written as floating point. There is some compensation for this effect built into PLplot, thus the internal representation for number of digits kept (digfix) may not always match the user's specification (via digmax). However, it will always be true that digfix ≤ digmax. The PLplot defaults are set up such that good results are usually obtained without user intervention.
Finally, after the call to plbox, the user may call routines
plgxax, plgyax, or plgzax to obtain information about the
window just drawn. This can be helpful when deciding where to put
captions. For example, a typical usage would be to call plgyax to
get the value of digits, then offset the y axis
caption by that amount (plus a bit more) so that the caption
"floats" just to the outside of the numeric labels.
Note that the digits value for each axis for the
current plot is not correct until after the call
to plbox is complete.
Having to call pladv, plvpor, plwind and plbox is excessively
cumbersome for drawing simple graphs. Subroutine plenv combines
all four of these in one subroutine, using the standard viewport, and
a limited subset of the capabilities of plbox. For example, the
graph described above could be initiated by the call:
plenv(0.0, 12.0, 0.0, 10.0, 0, 0); |
which is equivalent to the following series of calls:
pladv(0);
plvsta();
plwind(0.0, 12.0, 0.0, 10.0);
plbox("bcnst", 0.0, 0, "bcnstv", 0.0, 0); |