import graph; size(250,200,IgnoreAspect); draw(graph(exp,-1,1),red); xaxis("$x$",RightTicks(Label(align=left))); yaxis("$y$",RightTicks);
import graph; size(250,200,IgnoreAspect); draw(graph(exp,-1,1),red); xaxis(Label("$x$",0.75),LeftTicks); yaxis("$y$",RightTicks);
import graph; size(250,200,IgnoreAspect); draw(graph(exp,-1,1),red); xaxis(shift(0,-10)*"$x$",LeftTicks); yaxis("$y$",RightTicks);
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);
import graph; size(300,200,IgnoreAspect); xlimits(-50,50); ylimits(0,100); xaxis("x",Bottom,Courier("m","n"),LeftTicks); yaxis("$y$",Left,RightTicks);
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);
(i) give LeftTicks/RightTicks/Ticks the arguments beginlabel=false and/or endlabel=false;
(ii) explicitly remove specific tick labels and draw them manually:
import graph; size(10cm); draw(graph(new real(real x) {return x^2-2;},-2,2)); ticklabel NoZero(string s=defaultformat) { return new string(real x) { return (x != 0) ? format(s,x) : ""; }; } xaxis(Ticks(NoZero()),Arrow); yaxis(Ticks(NoZero()),Arrow); label("$0$",(0,0),SW);(iii) use the xasy GUI to move overlapping labels;
(iv) change the Label argument of LeftTicks, RightTicks, or Ticks to:
Label(currentpen+overwrite(Move))Solution (iv) 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: http://asymptote.sourceforge.net/doc/Pens.html.
In the case of a user-specified tick array, you can change which labels get suppressed/moved by changing the order of array entries.
Further examples of graphs are available at http://home.tele2.fr/phivaldi/asymptote/graph/index.html.
i) Specify an explicit unitsize, which overrides any call to
See also http://asymptote.sourceforge.net/doc/Frames-and-pictures.html.
An approximate solution for now would be to superimpose a fine grid
and specify colors to latticeshade depending on position as a single
pen[][] lattice. Or use Gouraud shading.
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).
size}:
unitsize(x=1cm,y=2cm);
ii) Specify the points in user coordinates that should correspond to a
given picture size:
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));
In this example, the user coordinate (-1.5,-0.5)
will end up being the lower left corner of the figure and
(1.5,3.5)
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 fixedscaling()
leaves room for any labels).
Question 6.9. How can I plot a function f(x) within [0,1]x[0,1]
without explicitly calculating the x values for which f(x) hits the
boundary?
Call limits
with the Crop
option after drawing the graph:
import graph;
size(250,200,IgnoreAspect);
draw(graph(exp,-1,1),red);
xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks);
limits((0,0),(1,1),Crop);
See also http://asymptote.sourceforge.net/doc/graph.html.
Question 6.10. Is it possible to define customized
palettes?
Yes, you may generate your own pen[] array. For example:
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);
}
Question 6.11. Is there an easy way to graph factorial functions
nicely?
The example below shows a continuous function and two methods for
placing markers at integer values of x:
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,Below));
// 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);
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?
Here's an easy way to do this.
size(12cm,0);
void distance(picture pic=currentpicture, pair A, pair B, Label L="", real n=0,
pen p=currentpen)
{
real d=3mm;
guide g=A--B;
transform T=shift(-n*d*unit(B-A)*I);
pic.add(new void(frame f, transform t) {
picture opic;
guide 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);
Question 6.13. How can I make the y axis display base-2 logarithmic
values?
See the example http://asymptote.sourceforge.net/gallery/2D
graphs/log2graph.asy.
Question 6.14. How can I align the x axes of two graphs on the same
figure?
Here is solution that fits the second picture to a frame based on the
horizontal scaling for the first picture:
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=framepoint(N).y-framepoint(S).y;
add(shift(0,-height)*(shift(shift)*pic2).fit(T));
Question 6.15. How can I change the direction of the y-axis, such
that negatives values are on the upper y-axis?
Here is a simple example (see also the example
http://asymptote.sourceforge.net/gallery/2D
graphs/diatom.asy or the discussion of Linear(-1) in the documentation):
import graph;
size(250,200,IgnoreAspect);
scale(Linear,Linear(-1));
draw(graph(log,0.1,10),red);
xaxis("$x$",LeftTicks);
yaxis("$y$",RightTicks);
Question 6.16. How can I fill a path with a function that defines the
color of each location?
General function shading is only supported by PDF, not PostScript, so
this will have to wait until we produce PDF code directly.
Question 6.17. Is there a way to draw a function that is not
explicitly given, such as (y - 2)^2 = x - 1
?
Yes, use the parametric form
y=t
x=(t-2)^2+1
See the example http://asymptote.sourceforge.net/gallery/2D
graphs/parametricgraph.asy.
Question 6.18. Is it possible to reverse or stretch an
axis?
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.
Question 6.19. Why can't I use the UnFill option to draw graphs with
empty markers?
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):
import graph;
size(10cm,0);
pair[] z={(0,0),(0.5,0.5),(1,1)};
guide g=graph(z);
draw(shift(0,.5)*g,marker(scale(5)*unitcircle,FillDraw(white)));
xaxis(BottomTop,LeftTicks);
yaxis(LeftRight,RightTicks);
Question 6.20. How can I force several images to use the same palette
range (e.g. the entire 0-255 grayscale range)?
The palette color space corresponds to a range of values specified by
the argument range, which can be Full
, Automatic
or an explicit range Range(pair min, pair max)
. Here Full} specifies a range varying from the minimum to maximum values of the
function over the sampling interval, while
Automatic
selects "nice" limits.
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