asymptote: graph
8.27 'graph'
============
This package implements two-dimensional linear and logarithmic graphs,
including automatic scale and tick selection (with the ability to
override manually). A graph is a 'guide' (that can be drawn with the
draw command, with an optional legend) constructed with one of the
following routines:
* guide graph(picture pic=currentpicture, real f(real), real a, real b,
int n=ngraph, real T(real)=identity,
interpolate join=operator --);
guide[] graph(picture pic=currentpicture, real f(real), real a, real b,
int n=ngraph, real T(real)=identity, bool3 cond(real),
interpolate join=operator --);
Returns a graph using the scaling information for picture 'pic'
(
automatic scaling) of the function 'f' on the interval
['T'('a'),'T'('b')], sampling at 'n' points evenly spaced in
['a','b'], optionally restricted by the bool3 function 'cond' on
['a','b']. If 'cond' is:
* 'true', the point is added to the existing guide;
* 'default', the point is added to a new guide;
* 'false', the point is omitted and a new guide is begun.
The points are connected using the interpolation specified by
'join':
* 'operator --' (linear interpolation; the abbreviation
'Straight' is also accepted);
* 'operator ..' (piecewise Bezier cubic spline interpolation;
the abbreviation 'Spline' is also accepted);
* 'Hermite' (standard cubic spline interpolation using boundary
condition 'notaknot', 'natural', 'periodic', 'clamped(real
slopea, real slopeb)'), or 'monotonic'. The abbreviation
'Hermite' is equivalent to 'Hermite(notaknot)' for nonperiodic
data and 'Hermite(periodic)' for periodic data).
* guide graph(picture pic=currentpicture, real x(real), real y(real),
real a, real b, int n=ngraph, real T(real)=identity,
interpolate join=operator --);
guide[] graph(picture pic=currentpicture, real x(real), real y(real),
real a, real b, int n=ngraph, real T(real)=identity,
bool3 cond(real), interpolate join=operator --);
Returns a graph using the scaling information for picture 'pic' of
the parametrized function ('x'(t),'y'(t)) for t in the interval
['T'('a'),'T'('b')], sampling at 'n' points evenly spaced in
['a','b'], optionally restricted by the bool3 function 'cond' on
['a','b'], using the given interpolation type.
* guide graph(picture pic=currentpicture, pair z(real), real a, real b,
int n=ngraph, real T(real)=identity,
interpolate join=operator --);
guide[] graph(picture pic=currentpicture, pair z(real), real a, real b,
int n=ngraph, real T(real)=identity, bool3 cond(real),
interpolate join=operator --);
Returns a graph using the scaling information for picture 'pic' of
the parametrized function 'z'(t) for t in the interval
['T'('a'),'T'('b')], sampling at 'n' points evenly spaced in
['a','b'], optionally restricted by the bool3 function 'cond' on
['a','b'], using the given interpolation type.
* guide graph(picture pic=currentpicture, pair[] z,
interpolate join=operator --);
guide[] graph(picture pic=currentpicture, pair[] z, bool3[] cond,
interpolate join=operator --);
Returns a graph using the scaling information for picture 'pic' of
the elements of the array 'z', optionally restricted to those
indices for which the elements of the boolean array 'cond' are
'true', using the given interpolation type.
* guide graph(picture pic=currentpicture, real[] x, real[] y,
interpolate join=operator --);
guide[] graph(picture pic=currentpicture, real[] x, real[] y,
bool3[] cond, interpolate join=operator --);
Returns a graph using the scaling information for picture 'pic' of
the elements of the arrays ('x','y'), optionally restricted to
those indices for which the elements of the boolean array 'cond'
are 'true', using the given interpolation type.
* guide polargraph(picture pic=currentpicture, real f(real), real a,
real b, int n=ngraph, interpolate join=operator --);
Returns a polar-coordinate graph using the scaling information for
picture 'pic' of the function 'f' on the interval ['a','b'],
sampling at 'n' evenly spaced points, with the given interpolation
type.
* guide polargraph(picture pic=currentpicture, real[] r, real[] theta,
interpolate join=operator--);
Returns a polar-coordinate graph using the scaling information for
picture 'pic' of the elements of the arrays ('r','theta'), using
the given interpolation type.
An axis can be drawn on a picture with one of the following commands:
* void xaxis(picture pic=currentpicture, Label L="", axis axis=YZero,
real xmin=-infinity, real xmax=infinity, pen p=currentpen,
ticks ticks=NoTicks, arrowbar arrow=None, bool above=false);
Draw an x axis on picture 'pic' from x='xmin' to x='xmax' using pen
'p', optionally labelling it with Label 'L'. The relative label
location along the axis (a real number from [0,1]) defaults to 1
(Label), so that the label is drawn at the end of the axis.
An infinite value of 'xmin' or 'xmax' specifies that the
corresponding axis limit will be automatically determined from the
picture limits. The optional 'arrow' argument takes the same
values as in the 'draw' command (arrows). The axis is
drawn before any existing objects in 'pic' unless 'above=true'.
The axis placement is determined by one of the following 'axis'
types:
'YZero(bool extend=true)'
Request an x axis at y=0 (or y=1 on a logarithmic axis)
extending to the full dimensions of the picture, unless
'extend'=false.
'YEquals(real Y, bool extend=true)'
Request an x axis at y='Y' extending to the full dimensions of
the picture, unless 'extend'=false.
'Bottom(bool extend=false)'
Request a bottom axis.
'Top(bool extend=false)'
Request a top axis.
'BottomTop(bool extend=false)'
Request a bottom and top axis.
Custom axis types can be created by following the examples in the
module 'graph.asy'. One can easily override the default values for
the standard axis types:
import graph;
YZero=new axis(bool extend=true) {
return new void(picture pic, axisT axis) {
real y=pic.scale.x.scale.logarithmic ? 1 : 0;
axis.value=I*pic.scale.y.T(y);
axis.position=1;
axis.side=right;
axis.align=2.5E;
axis.value2=Infinity;
axis.extend=extend;
};
};
YZero=YZero();
The default tick option is 'NoTicks'. The options 'LeftTicks',
'RightTicks', or 'Ticks' can be used to draw ticks on the left,
right, or both sides of the path, relative to the direction in
which the path is drawn. These tick routines accept a number of
optional arguments:
ticks LeftTicks(Label format="", ticklabel ticklabel=null,
bool beginlabel=true, bool endlabel=true,
int N=0, int n=0, real Step=0, real step=0,
bool begin=true, bool end=true, tickmodifier modify=None,
real Size=0, real size=0, bool extend=false,
pen pTick=nullpen, pen ptick=nullpen);
If any of these parameters are omitted, reasonable defaults will be
chosen:
'Label format'
override the default tick label format ('defaultformat',
initially "$%.4g$"), rotation, pen, and alignment (for
example, 'LeftSide', 'Center', or 'RightSide') relative to the
axis. To enable 'LaTeX' math mode fonts, the format string
should begin and end with '$' format. If the format
string is 'trailingzero', trailing zeros will be added to the
tick labels; if the format string is '"%"', the tick label
will be suppressed;
'ticklabel'
is a function 'string(real x)' returning the label (by
default, format(format.s,x)) for each major tick value 'x';
'bool beginlabel'
include the first label;
'bool endlabel'
include the last label;
'int N'
when automatic scaling is enabled (the default;
automatic scaling), divide a linear axis evenly into this
many intervals, separated by major ticks; for a logarithmic
axis, this is the number of decades between labelled ticks;
'int n'
divide each interval into this many subintervals, separated by
minor ticks;
'real Step'
the tick value spacing between major ticks (if 'N'='0');
'real step'
the tick value spacing between minor ticks (if 'n'='0');
'bool begin'
include the first major tick;
'bool end'
include the last major tick;
'tickmodifier modify;'
an optional function that takes and returns a 'tickvalue'
structure having real[] members 'major' and 'minor' consisting
of the tick values (to allow modification of the automatically
generated tick values);
'real Size'
the size of the major ticks (in 'PostScript' coordinates);
'real size'
the size of the minor ticks (in 'PostScript' coordinates);
'bool extend;'
extend the ticks between two axes (useful for drawing a grid
on the graph);
'pen pTick'
an optional pen used to draw the major ticks;
'pen ptick'
an optional pen used to draw the minor ticks.
For convenience, the predefined tickmodifiers 'OmitTick(... real[]
x)', 'OmitTickInterval(real a, real b)', and
'OmitTickIntervals(real[] a, real[] b)' can be used to remove
specific auto-generated ticks and their labels. The
'OmitFormat(string s=defaultformat ... real[] x)' ticklabel can be
used to remove specific tick labels but not the corresponding
ticks. The tickmodifier 'NoZero' is an abbreviation for
'OmitTick(0)' and the ticklabel 'NoZeroFormat' is an abbrevation
for 'OmitFormat(0)'.
It is also possible to specify custom tick locations with
'LeftTicks', 'RightTicks', and 'Ticks' by passing explicit real
arrays 'Ticks' and (optionally) 'ticks' containing the locations of
the major and minor ticks, respectively:
ticks LeftTicks(Label format="", ticklabel ticklabel=null,
bool beginlabel=true, bool endlabel=true,
real[] Ticks, real[] ticks=new real[],
real Size=0, real size=0, bool extend=false,
pen pTick=nullpen, pen ptick=nullpen)
* void yaxis(picture pic=currentpicture, Label L="", axis axis=XZero,
real ymin=-infinity, real ymax=infinity, pen p=currentpen,
ticks ticks=NoTicks, arrowbar arrow=None, bool above=false,
bool autorotate=true);
Draw a y axis on picture 'pic' from y='ymin' to y='ymax' using pen
'p', optionally labelling it with a Label 'L' that is autorotated
unless 'autorotate=false'. The relative location of the label (a
real number from [0,1]) defaults to 1 (Label). An infinite
value of 'ymin' or 'ymax' specifies that the corresponding axis
limit will be automatically determined from the picture limits.
The optional 'arrow' argument takes the same values as in the
'draw' command (arrows). The axis is drawn before any
existing objects in 'pic' unless 'above=true'. The tick type is
specified by 'ticks' and the axis placement is determined by one of
the following 'axis' types:
'XZero(bool extend=true)'
Request a y axis at x=0 (or x=1 on a logarithmic axis)
extending to the full dimensions of the picture, unless
'extend'=false.
'XEquals(real X, bool extend=true)'
Request a y axis at x='X' extending to the full dimensions of
the picture, unless 'extend'=false.
'Left(bool extend=false)'
Request a left axis.
'Right(bool extend=false)'
Request a right axis.
'LeftRight(bool extend=false)'
Request a left and right axis.
* For convenience, the functions
void xequals(picture pic=currentpicture, Label L="", real x,
bool extend=false, real ymin=-infinity, real ymax=infinity,
pen p=currentpen, ticks ticks=NoTicks, bool above=true,
arrowbar arrow=None);
and
void yequals(picture pic=currentpicture, Label L="", real y,
bool extend=false, real xmin=-infinity, real xmax=infinity,
pen p=currentpen, ticks ticks=NoTicks, bool above=true,
arrowbar arrow=None);
can be respectively used to call 'yaxis' and 'xaxis' with the
appropriate axis types 'XEquals(x,extend)' and 'YEquals(y,extend)'.
This is the recommended way of drawing vertical or horizontal lines
and axes at arbitrary locations.
* void axes(picture pic=currentpicture, Label xlabel="", Label ylabel="",
bool extend=true,
pair min=(-infinity,-infinity), pair max=(infinity,infinity),
pen p=currentpen, arrowbar arrow=None, bool above=false);
This convenience routine draws both x and y axes on picture 'pic'
from 'min' to 'max', with optional labels 'xlabel' and 'ylabel' and
any arrows specified by 'arrow'. The axes are drawn on top of
existing objects in 'pic' only if 'above=true'.
* void axis(picture pic=currentpicture, Label L="", path g,
pen p=currentpen, ticks ticks, ticklocate locate,
arrowbar arrow=None, int[] divisor=new int[],
bool above=false, bool opposite=false);
This routine can be used to draw on picture 'pic' a general axis
based on an arbitrary path 'g', using pen 'p'. One can optionally
label the axis with Label 'L' and add an arrow 'arrow'. The tick
type is given by 'ticks'. The optional integer array 'divisor'
specifies what tick divisors to try in the attempt to produce
uncrowded tick labels. A 'true' value for the flag 'opposite'
identifies an unlabelled secondary axis (typically drawn opposite a
primary axis). The axis is drawn before any existing objects in
'pic' unless 'above=true'. The tick locator 'ticklocate' is
constructed by the routine
ticklocate ticklocate(real a, real b, autoscaleT S=defaultS,
real tickmin=-infinity, real tickmax=infinity,
real time(real)=null, pair dir(real)=zero);
where 'a' and 'b' specify the respective tick values at
'point(g,0)' and 'point(g,length(g))', 'S' specifies the
autoscaling transformation, the function 'real time(real v)'
returns the time corresponding to the value 'v', and 'pair dir(real
t)' returns the absolute tick direction as a function of 't' (zero
means draw the tick perpendicular to the axis).
* These routines are useful for manually putting ticks and labels on
axes (if the variable 'Label' is given as the 'Label' argument, the
'format' argument will be used to format a string based on the tick
location):
void xtick(picture pic=currentpicture, Label L="", explicit pair z,
pair dir=N, string format="",
real size=Ticksize, pen p=currentpen);
void xtick(picture pic=currentpicture, Label L="", real x,
pair dir=N, string format="",
real size=Ticksize, pen p=currentpen);
void ytick(picture pic=currentpicture, Label L="", explicit pair z,
pair dir=E, string format="",
real size=Ticksize, pen p=currentpen);
void ytick(picture pic=currentpicture, Label L="", real y,
pair dir=E, string format="",
real size=Ticksize, pen p=currentpen);
void tick(picture pic=currentpicture, pair z,
pair dir, real size=Ticksize, pen p=currentpen);
void labelx(picture pic=currentpicture, Label L="", explicit pair z,
align align=S, string format="", pen p=currentpen);
void labelx(picture pic=currentpicture, Label L="", real x,
align align=S, string format="", pen p=currentpen);
void labelx(picture pic=currentpicture, Label L,
string format="", explicit pen p=currentpen);
void labely(picture pic=currentpicture, Label L="", explicit pair z,
align align=W, string format="", pen p=currentpen);
void labely(picture pic=currentpicture, Label L="", real y,
align align=W, string format="", pen p=currentpen);
void labely(picture pic=currentpicture, Label L,
string format="", explicit pen p=currentpen);
Here are some simple examples of two-dimensional graphs:
1. This example draws a textbook-style graph of y= exp(x), with the y
axis starting at y=0:
import graph;
size(150,0);
real f(real x) {return exp(x);}
pair F(real x) {return (x,f(x));}
xaxis("$x$");
yaxis("$y$",0);
draw(graph(f,-4,2,operator ..),red);
labely(1,E);
label("$e^x$",F(1),SE);
[exp]
2. The next example draws a scientific-style graph with a legend. The
position of the legend can be adjusted either explicitly or by
using the graphical user interface
'<http://asymptote.sourceforge.net/gallery/.pdf>.asy' (
GUI). If an 'UnFill(real xmargin=0, real ymargin=xmargin)' or
'Fill(pen)' option is specified to 'add', the legend will obscure
any underlying objects. Here we illustrate how to clip the portion
of the picture covered by a label:
import graph;
size(400,200,IgnoreAspect);
real Sin(real t) {return sin(2pi*t);}
real Cos(real t) {return cos(2pi*t);}
draw(graph(Sin,0,1),red,"$\sin(2\pi x)$");
draw(graph(Cos,0,1),blue,"$\cos(2\pi x)$");
xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks(trailingzero));
label("LABEL",point(0),UnFill(1mm));
add(legend(),point(E),20E,UnFill);
[lineargraph0]
To specify a fixed size for the graph proper, use 'attach':
import graph;
size(250,200,IgnoreAspect);
real Sin(real t) {return sin(2pi*t);}
real Cos(real t) {return cos(2pi*t);}
draw(graph(Sin,0,1),red,"$\sin(2\pi x)$");
draw(graph(Cos,0,1),blue,"$\cos(2\pi x)$");
xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks(trailingzero));
label("LABEL",point(0),UnFill(1mm));
attach(legend(),truepoint(E),20E,UnFill);
A legend can have multiple entries per line:
import graph;
size(8cm,6cm,IgnoreAspect);
typedef real realfcn(real);
realfcn F(real p) {
return new real(real x) {return sin(p*x);};
};
for(int i=1; i < 5; ++i)
draw(graph(F(i*pi),0,1),Pen(i),
"$\sin("+(i == 1 ? "" : (string) i)+"\pi x)$");
xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks(trailingzero));
attach(legend(2),(point(S).x,truepoint(S).y),10S,UnFill);
[legend]
3. This example draws a graph of one array versus another (both of the
same size) using custom tick locations and a smaller font size for
the tick labels on the y axis.
import graph;
size(200,150,IgnoreAspect);
real[] x={0,1,2,3};
real[] y=x^2;
draw(graph(x,y),red);
xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,
RightTicks(Label(fontsize(8pt)),new real[]{0,4,9}));
[datagraph]
4. This example shows how to graph columns of data read from a file.
import graph;
size(200,150,IgnoreAspect);
file in=input("filegraph.dat").line();
real[][] a=in;
a=transpose(a);
real[] x=a[0];
real[] y=a[1];
draw(graph(x,y),red);
xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks);
[filegraph]
5. The next example draws two graphs of an array of coordinate pairs,
using frame alignment and data markers. In the left-hand graph,
the markers, constructed with
marker marker(path g, markroutine markroutine=marknodes,
pen p=currentpen, filltype filltype=NoFill,
bool above=true);
using the path 'unitcircle' (filltype), are drawn below
each node. Any frame can be converted to a marker, using
marker marker(frame f, markroutine markroutine=marknodes,
bool above=true);
In the right-hand graph, the unit n-sided regular polygon
'polygon(int n)' and the unit n-point cyclic cross 'cross(int n,
bool round=true, real r=0)' (where 'r' is an optional "inner"
radius) are used to build a custom marker frame. Here
'markuniform(bool centered=false, int n, bool rotated=false)' adds
this frame at 'n' uniformly spaced points along the arclength of
the path, optionally rotated by the angle of the local tangent to
the path (if centered is true, the frames will be centered within
'n' evenly spaced arclength intervals). Alternatively, one can use
markroutine 'marknodes' to request that the marks be placed at each
Bezier node of the path, or markroutine 'markuniform(pair z(real
t), real a, real b, int n)' to place marks at points 'z(t)' for n
evenly spaced values of 't' in '[a,b]'.
These markers are predefined:
marker[] Mark={
marker(scale(circlescale)*unitcircle),
marker(polygon(3)),marker(polygon(4)),
marker(polygon(5)),marker(invert*polygon(3)),
marker(cross(4)),marker(cross(6))
};
marker[] MarkFill={
marker(scale(circlescale)*unitcircle,Fill),marker(polygon(3),Fill),
marker(polygon(4),Fill),marker(polygon(5),Fill),
marker(invert*polygon(3),Fill)
};
The example also illustrates the 'errorbar' routines:
void errorbars(picture pic=currentpicture, pair[] z, pair[] dp,
pair[] dm={}, bool[] cond={}, pen p=currentpen,
real size=0);
void errorbars(picture pic=currentpicture, real[] x, real[] y,
real[] dpx, real[] dpy, real[] dmx={}, real[] dmy={},
bool[] cond={}, pen p=currentpen, real size=0);
Here, the positive and negative extents of the error are given by
the absolute values of the elements of the pair array 'dp' and the
optional pair array 'dm'. If 'dm' is not specified, the positive
and negative extents of the error are assumed to be equal.
import graph;
picture pic;
real xsize=200, ysize=140;
size(pic,xsize,ysize,IgnoreAspect);
pair[] f={(5,5),(50,20),(90,90)};
pair[] df={(0,0),(5,7),(0,5)};
errorbars(pic,f,df,red);
draw(pic,graph(pic,f),"legend",
marker(scale(0.8mm)*unitcircle,red,FillDraw(blue),above=false));
scale(pic,true);
xaxis(pic,"$x$",BottomTop,LeftTicks);
yaxis(pic,"$y$",LeftRight,RightTicks);
add(pic,legend(pic),point(pic,NW),20SE,UnFill);
picture pic2;
size(pic2,xsize,ysize,IgnoreAspect);
frame mark;
filldraw(mark,scale(0.8mm)*polygon(6),green,green);
draw(mark,scale(0.8mm)*cross(6),blue);
draw(pic2,graph(pic2,f),marker(mark,markuniform(5)));
scale(pic2,true);
xaxis(pic2,"$x$",BottomTop,LeftTicks);
yaxis(pic2,"$y$",LeftRight,RightTicks);
yequals(pic2,55.0,red+Dotted);
xequals(pic2,70.0,red+Dotted);
// Fit pic to W of origin:
add(pic.fit(),(0,0),W);
// Fit pic2 to E of (5mm,0):
add(pic2.fit(),(5mm,0),E);
[errorbars]
6. A custom mark routine can be also be specified:
import graph;
size(200,100,IgnoreAspect);
markroutine marks() {
return new void(picture pic=currentpicture, frame f, path g) {
path p=scale(1mm)*unitcircle;
for(int i=0; i <= length(g); ++i) {
pair z=point(g,i);
frame f;
if(i % 4 == 0) {
fill(f,p);
add(pic,f,z);
} else {
if(z.y > 50) {
pic.add(new void(frame F, transform t) {
path q=shift(t*z)*p;
unfill(F,q);
draw(F,q);
});
} else {
draw(f,p);
add(pic,f,z);
}
}
}
};
}
pair[] f={(5,5),(40,20),(55,51),(90,30)};
draw(graph(f),marker(marks()));
scale(true);
xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks);
[graphmarkers]
7. This example shows how to label an axis with arbitrary strings.
import graph;
size(400,150,IgnoreAspect);
real[] x=sequence(12);
real[] y=sin(2pi*x/12);
scale(false);
string[] month={"Jan","Feb","Mar","Apr","May","Jun",
"Jul","Aug","Sep","Oct","Nov","Dec"};
draw(graph(x,y),red,MarkFill[0]);
xaxis(BottomTop,LeftTicks(new string(real x) {
return month[round(x % 12)];}));
yaxis("$y$",LeftRight,RightTicks(4));
[monthaxis]
8. The next example draws a graph of a parametrized curve. The calls
to
xlimits(picture pic=currentpicture, real min=-infinity,
real max=infinity, bool crop=NoCrop);
and the analogous function 'ylimits' can be uncommented to set the
respective axes limits for picture 'pic' to the specified 'min' and
'max' values. Alternatively, the function
void limits(picture pic=currentpicture, pair min, pair max, bool crop=NoCrop);
can be used to limit the axes to the box having opposite vertices
at the given pairs). Existing objects in picture 'pic' will be
cropped to lie within the given limits if 'crop'='Crop'. The
function 'crop(picture pic)' can be used to crop a graph to the
current graph limits.
import graph;
size(0,200);
real x(real t) {return cos(2pi*t);}
real y(real t) {return sin(2pi*t);}
draw(graph(x,y,0,1));
//limits((0,-1),(1,0),Crop);
xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks(trailingzero));
[parametricgraph]
The next example illustrates how one can extract a common axis
scaling factor.
import graph;
axiscoverage=0.9;
size(200,IgnoreAspect);
real[] x={-1e-11,1e-11};
real[] y={0,1e6};
real xscale=round(log10(max(x)));
real yscale=round(log10(max(y)))-1;
draw(graph(x*10^(-xscale),y*10^(-yscale)),red);
xaxis("$x/10^{"+(string) xscale+"}$",BottomTop,LeftTicks);
yaxis("$y/10^{"+(string) yscale+"}$",LeftRight,RightTicks(trailingzero));
[scaledgraph]
Axis scaling can be requested and/or automatic selection of the
axis limits can be inhibited with one of these 'scale' routines:
void scale(picture pic=currentpicture, scaleT x, scaleT y);
void scale(picture pic=currentpicture, bool xautoscale=true,
bool yautoscale=xautoscale, bool zautoscale=yautoscale);
This sets the scalings for picture 'pic'. The 'graph' routines
accept an optional 'picture' argument for determining the
appropriate scalings to use; if none is given, it uses those set
for 'currentpicture'.
Two frequently used scaling routines 'Linear' and 'Log' are
predefined in 'graph'.
All picture coordinates (including those in paths and those given
to the 'label' and 'limits' functions) are always treated as linear
(post-scaled) coordinates. Use
pair Scale(picture pic=currentpicture, pair z);
to convert a graph coordinate into a scaled picture coordinate.
The x and y components can be individually scaled using the
analogous routines
real ScaleX(picture pic=currentpicture, real x);
real ScaleY(picture pic=currentpicture, real y);
The predefined scaling routines can be given two optional boolean
arguments: 'automin=false' and 'automax=automin'. These default to
'false' but can be respectively set to 'true' to enable automatic
selection of "nice" axis minimum and maximum values. The 'Linear'
scaling can also take as optional final arguments a multiplicative
scaling factor and intercept (e.g. for a depth axis, 'Linear(-1)'
requests axis reversal).
For example, to draw a log/log graph of a function, use
'scale(Log,Log)':
import graph;
size(200,200,IgnoreAspect);
real f(real t) {return 1/t;}
scale(Log,Log);
draw(graph(f,0.1,10));
//limits((1,0.1),(10,0.5),Crop);
dot(Label("(3,5)",align=S),Scale((3,5)));
xaxis("$x$",BottomTop,LeftTicks);
yaxis("$y$",LeftRight,RightTicks);
[loggraph]
By extending the ticks, one can easily produce a logarithmic grid:
import graph;
size(200,200,IgnoreAspect);
real f(real t) {return 1/t;}
scale(Log,Log);
draw(graph(f,0.1,10),red);
pen thin=linewidth(0.5*linewidth());
xaxis("$x$",BottomTop,LeftTicks(begin=false,end=false,extend=true,
ptick=thin));
yaxis("$y$",LeftRight,RightTicks(begin=false,end=false,extend=true,
ptick=thin));
[loggrid]
One can also specify custom tick locations and formats for
logarithmic axes:
import graph;
size(300,175,IgnoreAspect);
scale(Log,Log);
draw(graph(identity,5,20));
xlimits(5,20);
ylimits(1,100);
xaxis("$M/M_\odot$",BottomTop,LeftTicks(DefaultFormat,
new real[] {6,10,12,14,16,18}));
yaxis("$\nu_{\rm upp}$ [Hz]",LeftRight,RightTicks(DefaultFormat));
[logticks]
It is easy to draw logarithmic graphs with respect to other bases:
import graph;
size(200,IgnoreAspect);
// Base-2 logarithmic scale on y-axis:
real log2(real x) {static real log2=log(2); return log(x)/log2;}
real pow2(real x) {return 2^x;}
scaleT yscale=scaleT(log2,pow2,logarithmic=true);
scale(Linear,yscale);
real f(real x) {return 1+x^2;}
draw(graph(f,-4,4));
yaxis("$y$",ymin=1,ymax=f(5),RightTicks(Label(Fill(white))),EndArrow);
xaxis("$x$",xmin=-5,xmax=5,LeftTicks,EndArrow);
[log2graph]
Here is an example of "broken" linear x and logarithmic y axes that
omit the segments [3,8] and [100,1000], respectively. In the case
of a logarithmic axis, the break endpoints are automatically
rounded to the nearest integral power of the base.
import graph;
size(200,150,IgnoreAspect);
// Break the x axis at 3; restart at 8:
real a=3, b=8;
// Break the y axis at 100; restart at 1000:
real c=100, d=1000;
scale(Broken(a,b),BrokenLog(c,d));
real[] x={1,2,4,6,10};
real[] y=x^4;
draw(graph(x,y),red,MarkFill[0]);
xaxis("$x$",BottomTop,LeftTicks(Break(a,b)));
yaxis("$y$",LeftRight,RightTicks(Break(c,d)));
label(rotate(90)*Break,(a,point(S).y));
label(rotate(90)*Break,(a,point(N).y));
label(Break,(point(W).x,ScaleY(c)));
label(Break,(point(E).x,ScaleY(c)));
[brokenaxis]
9. 'Asymptote' can draw secondary axes with the routines
picture secondaryX(picture primary=currentpicture, void f(picture));
picture secondaryY(picture primary=currentpicture, void f(picture));
In this example, 'secondaryY' is used to draw a secondary linear y
axis against a primary logarithmic y axis:
import graph;
texpreamble("\def\Arg{\mathop {\rm Arg}\nolimits}");
size(10cm,5cm,IgnoreAspect);
real ampl(real x) {return 2.5/sqrt(1+x^2);}
real phas(real x) {return -atan(x)/pi;}
scale(Log,Log);
draw(graph(ampl,0.01,10));
ylimits(0.001,100);
xaxis("$\omega\tau_0$",BottomTop,LeftTicks);
yaxis("$|G(\omega\tau_0)|$",Left,RightTicks);
picture q=secondaryY(new void(picture pic) {
scale(pic,Log,Linear);
draw(pic,graph(pic,phas,0.01,10),red);
ylimits(pic,-1.0,1.5);
yaxis(pic,"$\Arg G/\pi$",Right,red,
LeftTicks("$% #.1f$",
begin=false,end=false));
yequals(pic,1,Dotted);
});
label(q,"(1,0)",Scale(q,(1,0)),red);
add(q);
[Bode]
A secondary logarithmic y axis can be drawn like this:
import graph;
size(9cm,6cm,IgnoreAspect);
string data="secondaryaxis.csv";
file in=input(data).line().csv();
string[] titlelabel=in;
string[] columnlabel=in;
real[][] a=in;
a=transpose(a);
real[] t=a[0], susceptible=a[1], infectious=a[2], dead=a[3], larvae=a[4];
real[] susceptibleM=a[5], exposed=a[6],infectiousM=a[7];
scale(true);
draw(graph(t,susceptible,t >= 10 & t <= 15));
draw(graph(t,dead,t >= 10 & t <= 15),dashed);
xaxis("Time ($\tau$)",BottomTop,LeftTicks);
yaxis(Left,RightTicks);
picture secondary=secondaryY(new void(picture pic) {
scale(pic,Linear(true),Log(true));
draw(pic,graph(pic,t,infectious,t >= 10 & t <= 15),red);
yaxis(pic,Right,red,LeftTicks(begin=false,end=false));
});
add(secondary);
label(shift(5mm*N)*"Proportion of crows",point(NW),E);
[secondaryaxis]
10. Here is a histogram example, which uses the 'stats' module.
import graph;
import stats;
size(400,200,IgnoreAspect);
int n=10000;
real[] a=new real[n];
for(int i=0; i < n; ++i) a[i]=Gaussrand();
draw(graph(Gaussian,min(a),max(a)),blue);
// Optionally calculate "optimal" number of bins a la Shimazaki and Shinomoto.
int N=bins(a);
histogram(a,min(a),max(a),N,normalize=true,low=0,lightred,black,bars=false);
xaxis("$x$",BottomTop,LeftTicks);
yaxis("$dP/dx$",LeftRight,RightTicks(trailingzero));
[histogram]
11. Here is an example of reading column data in from a file and a
least-squares fit, using the 'stats' module.
size(400,200,IgnoreAspect);
import graph;
import stats;
file fin=input("leastsquares.dat").line();
real[][] a=fin;
a=transpose(a);
real[] t=a[0], rho=a[1];
// Read in parameters from the keyboard:
//real first=getreal("first");
//real step=getreal("step");
//real last=getreal("last");
real first=100;
real step=50;
real last=700;
// Remove negative or zero values of rho:
t=rho > 0 ? t : null;
rho=rho > 0 ? rho : null;
scale(Log(true),Linear(true));
int n=step > 0 ? ceil((last-first)/step) : 0;
real[] T,xi,dxi;
for(int i=0; i <= n; ++i) {
real first=first+i*step;
real[] logrho=(t >= first & t <= last) ? log(rho) : null;
real[] logt=(t >= first & t <= last) ? -log(t) : null;
if(logt.length < 2) break;
// Fit to the line logt=L.m*logrho+L.b:
linefit L=leastsquares(logt,logrho);
T.push(first);
xi.push(L.m);
dxi.push(L.dm);
}
draw(graph(T,xi),blue);
errorbars(T,xi,dxi,red);
crop();
ylimits(0);
xaxis("$T$",BottomTop,LeftTicks);
yaxis("$\xi$",LeftRight,RightTicks);
[leastsquares]
12. Here is an example that illustrates the general 'axis' routine.
import graph;
size(0,100);
path g=ellipse((0,0),1,2);
scale(true);
axis(Label("C",align=10W),g,LeftTicks(endlabel=false,8,end=false),
ticklocate(0,360,new real(real v) {
path h=(0,0)--max(abs(max(g)),abs(min(g)))*dir(v);
return intersect(g,h)[0];}));
[generalaxis]
13. To draw a vector field of 'n' arrows evenly spaced along the
arclength of a path, use the routine
picture vectorfield(path vector(real), path g, int n, bool truesize=false,
pen p=currentpen, arrowbar arrow=Arrow);
as illustrated in this simple example of a flow field:
import graph;
defaultpen(1.0);
size(0,150,IgnoreAspect);
real arrowsize=4mm;
real arrowlength=2arrowsize;
typedef path vector(real);
// Return a vector interpolated linearly between a and b.
vector vector(pair a, pair b) {
return new path(real x) {
return (0,0)--arrowlength*interp(a,b,x);
};
}
real f(real x) {return 1/x;}
real epsilon=0.5;
path g=graph(f,epsilon,1/epsilon);
int n=3;
draw(g);
xaxis("$x$");
yaxis("$y$");
add(vectorfield(vector(W,W),g,n,true));
add(vectorfield(vector(NE,NW),(0,0)--(point(E).x,0),n,true));
add(vectorfield(vector(NE,NE),(0,0)--(0,point(N).y),n,true));
[flow]
14. To draw a vector field of 'nx'\times'ny' arrows in 'box(a,b)', use
the routine
picture vectorfield(path vector(pair), pair a, pair b,
int nx=nmesh, int ny=nx, bool truesize=false,
real maxlength=truesize ? 0 : maxlength(a,b,nx,ny),
bool cond(pair z)=null, pen p=currentpen,
arrowbar arrow=Arrow, margin margin=PenMargin)
as illustrated in this example:
import graph;
size(100);
pair a=(0,0);
pair b=(2pi,2pi);
path vector(pair z) {return (0,0)--(sin(z.x),cos(z.y));}
add(vectorfield(vector,a,b));
[vectorfield]
15. The following scientific graphs, which illustrate many features of
'Asymptote''s graphics routines, were generated from the examples
'diatom.asy' and 'westnile.asy', using the comma-separated data in
'diatom.csv' and 'westnile.csv'.
[diatom]
[westnile]
Info Catalog
asymptote: CAD
asymptote: Base modules
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