Section 5.1 The <repeat> element
Some diagrams contain a number of components that are similar and differ only in a few attributes. For example, Figure 5.1.1 shows several solutions to a differential equation with different initial values.
Of course, we could simply include a
<plot-de-solution> element for each one, but this could be difficult to maintain if we decide to make some small change. Instead, PreFigure offers a <repeat> element that can streamline this process, as illustrated by the PreFigure source code in Listing 5.1.2.<diagram width="300" height="300" margins="10">
<definition>f(t,y) = t-y</definition>
<coordinates bbox="[-4,-4,4,4]">
<grid at="grid"/>
<axes at="axes" xlabel="t" ylabel="y"/>
<slope-field at="slope-field" function="f"/>
<repeat parameter="k=-4..4">
<plot-de-solution at="solution" function="f" t0="0" y0="k"
domain="[0,4]" stroke="orange" />
<point at="initial-value" p="(0,k)" size="4" fill="orange" />
</repeat>
</coordinates>
<annotations>
<annotation ref="figure"
text="Solutions to the differential equation dy dt = t - y">
<annotation ref="grid" text="The coordinate grid"/>
<annotation ref="axes" text="The coordinate axes"/>
<annotation ref="slope-field" text="The slope field"/>
<annotation ref="solutions" text="A collection of solution curves">
<annotation ref="solution-k=-4"
text="The solution with initial value -4"/>
<annotation ref="solution-k=-3"
text="The solution with initial value -3"/>
<annotation ref="solution-k=-2"
text="The solution with initial value -2"/>
<annotation ref="solution-k=-1"
text="The solution with initial value -1"/>
<annotation ref="solution-k=0"
text="The solution with initial value 0"/>
<annotation ref="solution-k=1"
text="The solution with initial value 1"/>
<annotation ref="solution-k=2"
text="The solution with initial value 2"/>
<annotation ref="solution-k=3"
text="The solution with initial value 3"/>
<annotation ref="solution-k=4"
text="The solution with initial value 4"/>
</annotation>
</annotation>
</annotations>
</diagram>
Line 7 contains a
<repeat> element with the attribute @parameter="k=-4..4". This places the parameter name k into the user namespace with the value of -4 and adds the <plot-de-solution> and <point> elements contained within the <repeat> element. This repeats with the values \(k=-4,-3,-2,\ldots,3,4\text{.}\)
The annotations included in Listing 5.1.2 show how the handles within the
<repeat> element are generated. If an element inside a repeat element has a handle @at="handle", then the graphical component generated when the parameter is, say, param=value is given the handle @at="handle-param=value". For example, when k=2, the solution has the handle @at="solution-k=2". There is not yet a repeat feature for annotations.A second example, given in Figure 5.1.3, shows how labels can be managed within a
<repeat> element.
<diagram width="300" height="300" margins="5">
<definition>
alignments=['ne','ne','ne','nw','nw','sw','se','se']
</definition>
<definition substitution="no">
labels=['1','\omega','i','\omega^3','-1','\omega^5','-i','\omega^7']
</definition>
<definition>f(t)=(cos(pi*t/4),sin(pi*t/4))</definition>
<coordinates bbox="[-1.4,-1.4,1.4,1.4]">
<grid at="grid" />
<axes at="axes" labels="no" />
<circle at="unit-circle" center="(0,0)" radius="1" stroke="blue"/>
<repeat parameter="k=0..7">
<point at="point" p="f(k)" alignment="alignments[k]">
<m>${labels[k]}</m>
</point>
</repeat>
</coordinates>
<annotations>
<annotation id="figure" text="The eighth roots of unity">
<annotation id="axes" text="The coordinate axes" />
<annotation id="grid" text="The coordinate grid" />
<annotation id="unit-circle" text="The unit circle" circular="true">
<annotation id="point-k=0"
text="The primitive eighth root of unity to the power zero"
speech="one"/>
<annotation id="point-k=1"
text="The primitive eighth root of unity"
speech="omega"/>
<annotation id="point-k=2"
text="The primitive eighth root of unity squared"
speech="i"/>
<annotation id="point-k=3"
text="The primitive eighth root of unity cubed"
speech="omega cubed"/>
<annotation id="point-k=4"
text="The primitive eighth root of unity to the fourth"
speech="minus one"/>
<annotation id="point-k=5"
text="The primitive eighth root of unity to the fifth"
speech="omega to the fifth"/>
<annotation id="point-k=6"
text="The primitive eighth root of unity to the sixth"
speech="minus i"/>
<annotation id="point-k=7"
text="The primitive eighth root of unity to the seventh"
speech="omega to the seventh"/>
</annotation>
</annotation>
</annotations>
</diagram>
Lines 5 through 7 define a set of labels, one for each of the eight points. Remember that ^ is usually interpreted as the numerical exponentiation operator. Since we wish to preserve this character for the label, we include the attribute
@substitution="no" to prevent ^ being reinterpreted. Notice that the label is given as ${labels[k]} since anything inside ${...} is evaluated in the user namespace.It is also possible to define the
@parameter attribute so that we iterate over a list. For instance @parameter="point in [[0,0],[3,0],[0,4]]" the elements inside the <repeat> will be visited three times with the value of point being set to each of the points in the list. This is demonstrated in Figure 5.1.5.
<repeat> to iterate over the elements in a list.<diagram dimensions="(300,300)" margins="5">
<coordinates bbox="(0,0,10,10)">
<definition>centers=((2,2),(3,7),(6,4),(8,7))</definition>
<grid-axes decorations="no"/>
<repeat parameter="center in centers">
<circle center="center" radius="1"
fill="springgreen" stroke="black"/>
</repeat>
</coordinates>
</diagram>
We can also nest
<repeat> elements as illustrated in Figure 5.1.7 and PreFigure source Listing 5.1.8.
<repeat> nested inside another.<diagram dimensions="(300,300)" margins="5">
<coordinates bbox="[-1,-1,5,5]">
<grid/>
<repeat parameter="row=0..4">
<repeat parameter="col=0..4">
<rectangle at="rectangle" center="(col, row)"
dimensions="(3/4,3/4)" fill="blue"/>
</repeat>
</repeat>
</coordinates>
</diagram>
A typical handle for one of these rectangles is
@at="rectangle-row=2-col=1".
