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Asymptote FAQ - Section 6
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Asymptote FAQ - Section 6 <br>
Questions about 2D graphs
</h1>
<ul>
<li><a href="#axisticks" rel=subdocument>Q6.1. How can I draw x axis ticks on the right side, with the tick labels on
the left side (relative to the axis path)?</a>
<li><a href="#axislabel" rel=subdocument>Q6.2. How can I reposition the x axis label to three-quarters along the axis
length?</a>
<li><a href="#axislabeldown" rel=subdocument>Q6.3. How can I move the x axis label down 10bp?</a>
<li><a href="#threeaxispens" rel=subdocument>Q6.4. Can I use different pens for the axis, the axis label, and the tick
labels?</a>
<li><a href="#axislabelfont" rel=subdocument>Q6.5. How can I change the font type of the axes
label?</a>
<li><a href="#axisticklabelfont" rel=subdocument>Q6.6. How can I change the font type of the tick labels on an
axis?</a>
<li><a href="#overlappingticklabels" rel=subdocument>Q6.7. How can I prevent axes tick labels from rendering on top of each
other?</a>
<li><a href="#fixedsizegraphs" rel=subdocument>Q6.8. How do I make the plot region of a graph, ignoring labels and legends,
have a fixed size?</a>
<li><a href="#graphlimits" rel=subdocument>Q6.9. How can I plot a function f(x) within [0,1]x[0,2] without explicitly
calculating the x values for which f(x) hits the
boundary?</a>
<li><a href="#custompalettes" rel=subdocument>Q6.10. Is it possible to define customized palettes?</a>
<li><a href="#factorial" rel=subdocument>Q6.11. Is there an easy way to graph factorial functions
nicely?</a>
<li><a href="#length" rel=subdocument>Q6.12. How do I indicate that a certain length should be exactly the size I
prescribe with no rescaling, within a picture which has its own
size?</a>
<li><a href="#log2" rel=subdocument>Q6.13. How can I make the y axis display base-2 logarithmic
values?</a>
<li><a href="#align" rel=subdocument>Q6.14. How can I align the x axes of two graphs on the same
figure?</a>
<li><a href="#changeaxis" rel=subdocument>Q6.15. How can I change the direction of the y-axis, such that negatives
values are on the upper y-axis?</a>
<li><a href="#functioncolor" rel=subdocument>Q6.16. How can I fill a path with a function that defines the color of each
location?</a>
<li><a href="#nonexplicitfun" rel=subdocument>Q6.17. Is there a way to draw a function that is not explicitly given, such
as (y - 2)^2 = x - 1 ?</a>
<li><a href="#scalesecondaryaxis" rel=subdocument>Q6.18. Is it possible to reverse or stretch an axis?</a>
<li><a href="#emptymarkers" rel=subdocument>Q6.19. Why can't I use the UnFill option to draw graphs with empty
markers?</a>
<li><a href="#paletterange" rel=subdocument>Q6.20. How can I force several images to use the same palette range (e.g. the
entire 0-255 grayscale range)?</a>
</ul><hr>
<h2><A name="axisticks">
Question 6.1. How can I draw x axis ticks on the right side, with the
tick labels on the left side (relative to the axis
path)?
</A></h2>
<pre>
import graph;
size(250,200,IgnoreAspect);
draw(graph(exp,-1,1),red);
xaxis("$x$",RightTicks(Label(align=left)));
yaxis("$y$",RightTicks);
</pre>
<h2><A name="axislabel">
Question 6.2. How can I reposition the x axis label to three-quarters
along the axis length?
</A></h2>
<pre>
import graph;
size(250,200,IgnoreAspect);
draw(graph(exp,-1,1),red);
xaxis(Label("$x$",0.75),LeftTicks);
yaxis("$y$",RightTicks);
</pre>
<h2><A name="axislabeldown">
Question 6.3. How can I move the x axis label down
10bp?
</A></h2>
<pre>
import graph;
size(250,200,IgnoreAspect);
draw(graph(exp,-1,1),red);
xaxis(shift(0,-10)*"$x$",LeftTicks);
yaxis("$y$",RightTicks);
</pre>
<h2><A name="threeaxispens">
Question 6.4. Can I use different pens for the axis, the axis label,
and the tick labels?
</A></h2>
Yes: <pre>
import graph;
size(300,200,IgnoreAspect);
xlimits(-50,50);
ylimits(0,100);
xaxis(Label("$x$",MidPoint,red),Bottom,blue,LeftTicks(green));
yaxis("$y$",Left,RightTicks);
</pre>
<h2><A name="axislabelfont">
Question 6.5. How can I change the font type of the axes
label?
</A></h2>
<pre>
import graph;
size(300,200,IgnoreAspect);
xlimits(-50,50);
ylimits(0,100);
xaxis("x",Bottom,Courier("m","n"),LeftTicks);
yaxis("$y$",Left,RightTicks);
</pre>
<h2><A name="axisticklabelfont">
Question 6.6. How can I change the font type of the tick labels on an
axis?
</A></h2>
Tick labels are by default typeset in (TeX) math mode, so to use other
fonts you need to override the default tick format:
<pre>
import graph;
size(300,200,IgnoreAspect);
xlimits(-50,50);
ylimits(0,100);
xaxis("$x$",Bottom,LeftTicks("%.4g",Courier("m","n")+fontsize(12)));
yaxis("$y$",Left,RightTicks);
</pre>
<h2><A name="overlappingticklabels">
Question 6.7. How can I prevent axes tick labels from rendering on
top of each other?
</A></h2>
Either:
<p>
(i) give LeftTicks/RightTicks/Ticks the arguments beginlabel=false
and/or endlabel=false;
<p>
(ii) explicitly remove specific ticks and their labels (drawing them
manually; see <A href="http://www.github.com/vectorgraphics/asymptote/base/graph.asy">http://www.github.com/vectorgraphics/asymptote/base/graph.asy</A> for the definition of NoZero): <pre>
import graph;
size(10cm);
real f(real x) {return x^2;}
draw(graph(f,-2,2));
xaxis(Ticks(NoZero));
yaxis(Ticks(NoZero));
label("$0$",(0,0),SW);
</pre>
(iii) explicitly remove specific tick labels and draw them manually
(see <A href="http://www.github.com/vectorgraphics/asymptote/base/graph.asy">http://www.github.com/vectorgraphics/asymptote/base/graph.asy</A> for the definition of NoZeroFormat): <pre>
import graph;
size(10cm);
real f(real x) {return x^2;}
draw(graph(f,-2,2));
xaxis(Ticks(NoZeroFormat));
yaxis(Ticks(NoZeroFormat));
label("$0$",(0,0),SW);
</pre>
(iv) use the xasy GUI to move overlapping labels;
<p>
(v) change the Label argument of LeftTicks, RightTicks, or Ticks to:
<pre>
Label(currentpen+overwrite(Move))
</pre>
Solution (v) will move labels that might otherwise overwrite a
previous label. Other possible overwrite arguments are Allow (allows
overlapping labels; the default), Suppress (an overlapping label will not be
written at all), SuppressQuiet, and MoveQuiet. The last two achieve the same
result as the non-quiet types, but will not notify you which labels are
overlapping. See: <A href="http://asymptote.sourceforge.net/doc/Pens.html">http://asymptote.sourceforge.net/doc/Pens.html</A>.
<p>
In the case of a user-specified tick array, you can change which
labels get suppressed/moved by changing the order of array entries.
<h2><A name="fixedsizegraphs">
Question 6.8. How do I make the plot region of a graph, ignoring
labels and legends, have a fixed size?
</A></h2>
Either:
<p>
i) Specify an explicit unitsize, which overrides any call to
<code>size</code>: <pre>
unitsize(x=1cm,y=2cm);
</pre>
ii) Explicitly tell Asymptote to map the plot region to a specific
size: <pre>
import graph;
real[] x={0,1,2,3};
real[] y=x^2;
draw(graph(x,y),red);
xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks);
size(5cm,5cm,point(SW),point(NE));
label("$f_\mathrm{T}$",point(N),2N);
</pre>
iii) Specify the points in user coordinates that should correspond to
a given picture size: <pre>
import graph;
size(250,200,IgnoreAspect);
draw(graph(exp,-1,1),red);
xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks);
fixedscaling((-1.5,-0.5),(1.5,3.5));
</pre>
In this example, the user coordinate <code>(-1.5,-0.5)</code> will end up being the lower left corner of the figure and
<code>(1.5,3.5)</code> will be the upper right corner. You can use this option to ensure multiple
figures have the same scaling and same resulting figure size (just ensure the
two coordinates given to <code>fixedscaling()</code> leaves room for any labels).
<p>
See also <A href="http://asymptote.sourceforge.net/doc/Frames-and-pictures.html">http://asymptote.sourceforge.net/doc/Frames-and-pictures.html</A>.
<h2><A name="graphlimits">
Question 6.9. How can I plot a function f(x) within [0,1]x[0,2]
without explicitly calculating the x values for which f(x) hits the
boundary?
</A></h2>
Call <code>limits</code> with the <code>Crop</code> option before drawing the graph: <pre>
import graph;
size(250,200,IgnoreAspect);
draw(graph(exp,-1,1),red);
limits((0,0),(1,2),Crop);
xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks);
</pre>
See also <A href="http://asymptote.sourceforge.net/doc/graph.html">http://asymptote.sourceforge.net/doc/graph.html</A>.
<h2><A name="custompalettes">
Question 6.10. Is it possible to define customized
palettes?
</A></h2>
Yes, you may generate your own pen[] array. For example:
<pre>
int NColors=32768;
pen[] MyPalette=new pen[NColors];
real step=1/(NColors-1.0);
// Start at black: rgb(0,0,0)
// End at yellow: rgb(1,1,0)
for(int i=0; i < NColors; ++i) {
real rgval=i*step;
MyPalette[i]=rgb(rgval,rgval,0.0);
}
</pre>
<h2><A name="factorial">
Question 6.11. Is there an easy way to graph factorial functions
nicely?
</A></h2>
The example below shows a continuous function and two methods for
placing markers at integer values of x: <pre>
import graph;
size(200,200,IgnoreAspect);
real factorial(real t) {return gamma(t+1);}
scale(Linear,Log);
// Graph the factorial function.
draw(graph(factorial,0,10));
// Method 1: Draw nodes, but hide line
pair F(int t) {return (t,factorial(t));}
// Graph of factorial function from 0 to 10
pair[] z=sequence(F,11);
draw(graph(z),invisible,marker(scale(0.8mm)*unitcircle,blue,Fill));
// Method 2: Nongraphing routines require explicit scaling:
pair dotloc(int t) {return Scale(F(t));}
pair[] dotlocs=sequence(dotloc,11);
dot(dotlocs);
xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks);
</pre>
<h2><A name="length">
Question 6.12. How do I indicate that a certain length should be
exactly the size I prescribe with no rescaling, within a picture which
has its own size?
</A></h2>
Here's an easy way to do this. <pre>
size(12cm,0);
void distance(picture pic=currentpicture, pair A, pair B, Label L="", real n=0,
pen p=currentpen)
{
real d=3mm;
path g=A--B;
transform T=shift(-n*d*unit(B-A)*I);
pic.add(new void(frame f, transform t) {
picture opic;
path G=T*t*g;
draw(opic,Label(L,Center,UnFill(1)),G,p,Arrows(NoFill),Bars,PenMargins);
add(f,opic.fit());
});
pic.addBox(min(g),max(g),T*min(p),T*max(p));
}
pair A=(0,0), B=(3,3);
dot(A);
dot(B);
distance(A,B,"$\ell$",1);
</pre>
<h2><A name="log2">
Question 6.13. How can I make the y axis display base-2 logarithmic
values?
</A></h2>
See the example <A href="http://asymptote.sourceforge.net/gallery/2D graphs/log2graph.asy">http://asymptote.sourceforge.net/gallery/2D
graphs/log2graph.asy</A>.
<h2><A name="align">
Question 6.14. How can I align the x axes of two graphs on the same
figure?
</A></h2>
An easy way to do this, if the axes to be aligned have the same
scaling and size, is illustrated in the example <A href="http://asymptote.sourceforge.net/gallery/2D graphs/alignedaxis.asy">http://asymptote.sourceforge.net/gallery/2D
graphs/alignedaxis.asy</A>.
<p>
Here is a more general solution to the problem of aligning two
arbitrary axes. One fits the second picture to a frame based on the horizontal scaling
for the first picture: <pre>
import graph;
real width=15cm;
real aspect=0.3;
picture pic1,pic2;
size(pic1,width,aspect*width,IgnoreAspect);
size(pic2,width,aspect*width,IgnoreAspect);
scale(pic1,false);
scale(pic2,false);
real xmin1=6;
real xmax1=9;
real xmin2=8;
real xmax2=16;
real a1=1;
real a2=0.001;
real f1(real x) {return a1*sin(x/2*pi);}
real f2(real x) {return a2*sin(x/4*pi);}
draw(pic1,graph(pic1,f1,xmin1,xmax1));
draw(pic2,graph(pic2,f2,xmin2,xmax2));
xaxis(pic1,Bottom,LeftTicks());
yaxis(pic1,"$f_1(x)$",Left,RightTicks);
xaxis(pic2,"$x$",Bottom,LeftTicks(Step=4));
yaxis(pic2,"$f_2(x)$",Left,RightTicks);
yequals(pic1,0,Dotted);
yequals(pic2,0,Dotted);
pair min1=point(pic1,SW);
pair max1=point(pic1,NE);
pair min2=point(pic2,SW);
pair max2=point(pic2,NE);
real scale=(max1.x-min1.x)/(max2.x-min2.x);
real shift=min1.x/scale-min2.x;
transform t1=pic1.calculateTransform();
transform t2=pic2.calculateTransform();
transform T=xscale(scale*t1.xx)*yscale(t2.yy);
add(pic1.fit());
real height=truepoint(N,user=false).y-truepoint(S,user=false).y;
add(shift(0,-height)*(shift(shift)*pic2).fit(T));
</pre>
<h2><A name="changeaxis">
Question 6.15. How can I change the direction of the y-axis, such
that negatives values are on the upper y-axis?
</A></h2>
Here is a simple example (see also the example
<A href="http://asymptote.sourceforge.net/gallery/2D graphs/diatom.asy">http://asymptote.sourceforge.net/gallery/2D
graphs/diatom.asy</A> or the discussion of Linear(-1) in the documentation): <pre>
import graph;
size(250,200,IgnoreAspect);
scale(Linear,Linear(-1));
draw(graph(log,0.1,10),red);
xaxis("$x$",LeftTicks);
yaxis("$y$",RightTicks);
</pre>
<h2><A name="functioncolor">
Question 6.16. How can I fill a path with a function that defines the
color of each location?
</A></h2>
Use <code>functionshade</code> with a PDF tex engine, as illustrated by the example {functionshading.asy}.
<p>
If you want to produce PostScript output, an approximate solution for
now would be to superimpose a fine grid and specify colors to
<code>latticeshade</code> that depend on position as a single pen[][]
lattice. Alternatively, it may be more efficient to use
<code>tensorshade}.
<h2><A name="nonexplicitfun">
Question 6.17. Is there a way to draw a function that is not
explicitly given, such as (y - 2)^2 = x - 1
?
</A></h2>
Yes, use the parametric form <pre>
y=t
x=(t-2)^2+1
</pre>
See the example <A href="http://asymptote.sourceforge.net/gallery/2D graphs/parametricgraph.asy">http://asymptote.sourceforge.net/gallery/2D
graphs/parametricgraph.asy</A>.
<h2><A name="scalesecondaryaxis">
Question 6.18. Is it possible to reverse or stretch an
axis?
</A></h2>
The real scaling argument to Linear is used to stretch (or reverse)
the axis. To see the effect of axis stretching, be sure not to specify
IgnoreAspect in the picture size command.
<p>
A secondary axis has the same length as the primary axis, so
stretching cannot have any effect. But one can still reverse the axis, with Linear(-1).
<h2><A name="emptymarkers">
Question 6.19. Why can't I use the UnFill option to draw graphs with
empty markers?
</A></h2>
UnFill won't work here because it only affects the local frame the
markers are initially drawn on, before being added to currentpicture.
Here is a way of achieving the desired effect (assuming a white
background): <pre>
import graph;
size(10cm,0);
pair[] z={(0,0),(0.5,0.5),(1,1)};
path g=graph(z);
draw(shift(0,.5)*g,marker(scale(5)*unitcircle,FillDraw(white)));
xaxis(BottomTop,LeftTicks);
yaxis(LeftRight,RightTicks);
</pre>
<h2><A name="paletterange">
Question 6.20. How can I force several images to use the same palette
range (e.g. the entire 0-255 grayscale range)?
</A></h2>
The palette color space corresponds to a range of values specified by
the argument range, which can be <code>Full</code>, <code>Automatic</code> or an explicit range <code>Range(pair min, pair max)</code>. Here <code>Full} specifies a range varying from the minimum to maximum values of the
function over the sampling interval, while
<code>Automatic</code> selects "nice" limits. <hr>
Next: <a href="section7.html" rel=precedes>Questions about programming</a>.<br>
Back: <a href="section5.html" rev=precedes>Questions about arrows</a>.<br>
<a href="index.html" rev=subdocument>Return to contents</a>.<p>
<address>
<A href="http://asymptote.sourceforge.net">Asymptote</A>
- 21 April 2019
</address><br>
Extracted from Asymptote Frequently Asked Questions,
Copyright © 2019 .
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