WPSML Plotting Support
Chris Hector
Logictran, Inc.
Draft 1.1
September 16, 2005
Introduction
This document provides details on WPSML 2.0 support for plotting.
Revision History
Draft 1.0
Draft 1.1
07/13/2005
09/16/2005


Initial draft
Resolved handling of axis labels that use multiples
of pi or e
Elements
The plotting elements in WPSML are described in this section – and specific examples
are contained in the following Examples section.
Algorithmic Attribute Values
Plotting elements are most often used for algorithmic content, and therefore some
attribute values can be algorithmic in nature. Where this occurs, the attribute values
column will show the attribute type, followed by /CM indicating that this attribute can
contain a Compact Math syntax which must be expanded to obtain the attribute
value.
chart
The chart element is used for all plots. In TestGen exports, the chart element has no
attributes and contains a single "plot-area" element.
plot-area
The plot-area element contains all of the instructions for generating a plot. It has two
attributes, height and width which specify the size of the plot in pixels.
The plot-area must contain one or more axis elements, along with the plot data
(series, series-formula, and composites.) The type of plot (polar, cartesian, line) is
determined by the axis elements contained within the plot-area.
Attribute
Description
Values
Required
height
width
Specifies the height and width in pixels
of the plot-area
floating point
Y
axis
The axis element defines the coordinate system for the plot. In a line plot, there will
be a single axis, in Cartesian there are two (x and y) and in polar there is a single
axis.
Attribute
Description
Values
Required
class
The class attribute determines the axis
type and can contain the values "x" –
x, y, r
Y
specifying the horizontal axis, "y" for
the vertical axis and "r" for the polar
axis.
arrow-start
arrow-end
Indicates whether starting and ending
arrows should be displayed.
yes, no
N, no is
default
visible
Indicates whether the axis should be
displayed.
yes, no
N, yes is
default
minimum
The minimum value for the plot as
displayed
floating point
(CM)
Y
maximum
The maximum value for the plot as
displayed
floating point
(CM)
Y
length
The length of the axis in pixels. This
length only refers to the plottable
portion of the axis (without arrowheads
and other presentational components)
and is used for scaling purposes.
floating point
Y
name
A label for the axis
CDATA
(CM)
N, default
is no label
logscale
Set to "yes" if this axis is log scale.
yes, no
N, no is
default
tick-marks
The tick-marks element defines the ticks that are displayed along the axis. They also
specify any grid lines for the plot. There can be zero or more tick-marks elements
within an axis.
Attribute
Description
Values
Required
units
Specifies the number of units
represented by each tick
floating point
(CM)
Y
position
Indicates the position of a single tick
mark. tick-marks may contain a label
floating point
(CM)
N
sub-element with a specific label.
labels
Specifies the number of units before a
label is displayed. If omitted no labels
are displayed.
floating point
(CM)
N, default
is no label.
type
Specifies the tick mark type
inner,
outer,
cross,
N, default
is cross
none
grid-line
Specifies a grid line corresponding to
this tick-mark
none,
continuous,
dashed,
dotted
N, default
is none
series
The series element defines a series of individual points by providing the coordinates
of each point.
Attribute
Description
Values
Required
name
Specifies a name for the series
CDATA
Y
visible
Indicates whether the series should be
displayed.
yes, no
N, yes is
default
series-formula
The series-formula element defines a plotted line by providing a formula.
Attribute
Description
Values
Required
name
Specifies a name for the series-formula
CDATA
N
visible
Indicates whether the series-formula
should be displayed.
yes, no
N, yes is
default
domain-
The minimum valid value for the
floating point
N, negative
min
domain of the function. .
(CM)
infinity is
the default
domainmax
The maximum valid value for the
domain of the function. ..
floating point
(CM)
N, infinity
is the
default
template
Specifies a template for the seriesformula – this is the name of a
predefined template (hyperbola, circle)
CDATA
N, no
default
composite
The composite element allows multiple series-formulas or composites to be AND'ed
together.
Attribute
Description
Values
Required
name
Specifies a name for the composite
CDATA
Y
visible
Indicates whether the composite should
be displayed.
yes, no
N, yes is
default
Values
Required
point
The point element describes a single plot point.
Attribute
Description
x-coord
The x-coordinate location (line or
cartesian plot) or the r value (polar plot)
CDATA
(CM)
Y
y-coord
The y-coordinate location (line or
cartesian plot) or the theta value (polar
plot)
CDATA
(CM)
N
Examples
Example 1 Simple Cartesian plot
<chart>
<plot-area height="200" width="200">
<axis class="x" arrow-start="yes" arrow-end="yes" visible="yes"
minimum="0" maximum="5" length="160" name="t">
<tick-marks grid-line="dotted fine" units="1" labels="1"/>
</axis>
<axis class="y" arrow-start="yes" arrow-end="yes" visible="yes"
minimum="0" maximum="600" length="162" name="t">
<tick-marks grid-line="dotted fine" units="100" labels="1"/>
</axis>
<series-formula>
<expression>y</expression>
<eq/>
<expression>((v11+(x*v10))-((x^2)*16.085))</expression>
</series-formula>
</plot-area>
</chart>
1. series-formula contains a y=f(x) expression using compact math
representations. The v11, v10 in the expression element would be replaced
with the correct variables for the algorithmic plot.
2. The x axis is labeled "t", and the y axis is labeled "h".
Example 2 Simple Line plot with labeled points
<chart>
<plot-area height="40" width="238">
<axis class="x" arrow-start="yes" arrow-end="yes" visible="yes"
minimum="1980" maximum="1990" length="238">
<tick-marks units="1" labels="2"/>
</axis>
<series name="1">
<point x-coord="1981">
<label><xhtml:div>A</xhtml:div></label>
</point>
<point x-coord="1982">
<label><xhtml:div>B</xhtml:div></label>
</point>
<point x-coord="1984">
<label><xhtml:div>C</xhtml:div></label>
</point>
</series>
</plot-area>
</chart>
Example 3 Axis numbered in multiples of Pi
<chart>
<plot-area height="200" width="200">
<axis class="x" arrow-start="yes" arrow-end="yes" visible="yes"
minimum="0" maximum="6.283" length="200">
<tick-marks position="1.57080"><label><mathml:math>
<mathml:mfrac><mathml:mrow><mathml:mn>Π</mathml:mn></mathml:mrow>
<mathml:mrow><mathml:mn>2</mathml:mn></mathml:mrow>
</mathml:mfrac></mathml:math></label></tick-marks>
<tick-marks position="3.1416"><label>Π</label>
</tick-marks>
<tick-marks position="4.71238"><label><mathml:math>
<mathml:mfrac><mathml:mrow><mathml:mn>3Π</mathml:mn></mathml:mrow>
<mathml:mrow><mathml:mn>2</mathml:mn></mathml:mrow>
</mathml:mfrac></mathml:math></label></tick-marks>
</axis>
<series-formula>
<expression>y</expression>
<eq/>
<expression>v1*cos(pi/2)</expression>
</series-formula>
</plot-area>
</chart>
In problem 1-5, the labels on the axis are expressed in terms of fractions of pi. This
is specified by providing the tick marks and labels explicitly. The position attribute of
tick-marks specifies a location, and the label sub-element provides the corresponding
label.
Example 4 axis with omitted portion
<axis class="y" minimum="450" maximum="600" ...
Notes:
In problem 1-4, the y axis has an omitted section.
The spelling of this is
<axis class="y" minimum="450" maximum="600" ...
Example 5 Composite plot
<composite fill-pattern="horizontal">
<series-formula>
<expression>y</expression>
<geq/>
<expression>1/2*x-1</expression>
</series-formula>
<series-formula>
<expression>y</expression>
<leq/>
<expression>-x</expression>
</series-formula>
</composite>
Notes:
The plotting of a composite contains the AND'ed result of the two inequalities.
Composites can contain other composites.
Example 6 Polar plot
<chart>
<plot-area ...>
<axis class="r" ...> <!-- only one axis, marked as class="r" -->
<tick-marks .../>
</axis>
<series-formula>
<expression>r</expression>
<eq/>
<expression>v1*sin(v2*t)</expression>
theta as variable name -->
</series-formula>
</plot-area>
</chart>
Example 6 Hyperbola plot
<!-- use t rather than
<chart>
<plot-area ...>
<axis class="x" ...>
<tick-marks .../>
</axis>
<axis class="y" ...>
<tick-marks .../>
</axis>
<series-formula template="hyperbola_a">
<expression>1</expression>
<eq/>
<expression>y^2/v3^2-x^2/v4^2</expression>
</series-formula>
</plot-area>
</chart>
Note that the template attribute is only provided as a hint and is not required.