asymptote: palette
8.28 'palette'
==============
'Asymptote' can also generate color density images and palettes. The
following palettes are predefined in 'palette.asy':
'pen[] Grayscale(int NColors=256)'
a grayscale palette;
'pen[] Rainbow(int NColors=32766)'
a rainbow spectrum;
'pen[] BWRainbow(int NColors=32761)'
a rainbow spectrum tapering off to black/white at the ends;
'pen[] BWRainbow2(int NColors=32761)'
a double rainbow palette tapering off to black/white at the ends,
with a linearly scaled intensity.
'pen[] Wheel(int NColors=32766)'
a full color wheel palette;
'pen[] Gradient(int NColors=256 ... pen[] p)'
a palette varying linearly over the specified array of pens, using
NColors in each interpolation interval;
The function 'cmyk(pen[] Palette)' may be used to convert any of
these palettes to the CMYK colorspace.
A color density plot using palette 'palette' can be generated from a
function 'f'(x,y) and added to a picture 'pic':
bounds image(picture pic=currentpicture, real f(real, real),
range range=Full, pair initial, pair final,
int nx=ngraph, int ny=nx, pen[] palette, bool antialias=false)
The function 'f' will be sampled at 'nx' and 'ny' evenly spaced
points over a rectangle defined by the points 'initial' and 'final',
respecting the current graphical scaling of 'pic'. The color space is
scaled according to the z axis scaling (
automatic scaling). A
bounds structure for the function values is returned:
struct bounds {
real min;
real max;
// Possible tick intervals:
int[] divisor;
}
This information can be used for generating an optional palette bar.
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(real min, real 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. The example
'imagecontour.asy' illustrates how level sets (contour lines) can be
drawn on a color density plot (contour).
A color density plot can also be generated from an explicit real[][]
array 'data':
bounds image(picture pic=currentpicture, real[][] f, range range=Full,
pair initial, pair final, pen[] palette,
bool transpose=(initial.x < final.x && initial.y < final.y),
bool copy=true, bool antialias=false);
If the initial point is to the left and below the final point, by
default the array indices are interpreted according to the Cartesian
convention (first index: x, second index: y) rather than the usual
matrix convention (first index: -y, second index: x).
To construct an image from an array of irregularly spaced points and
an array of values 'f' at these points, use one of the routines
bounds image(picture pic=currentpicture, pair[] z, real[] f,
range range=Full, pen[] palette)
bounds image(picture pic=currentpicture, real[] x, real[] y, real[] f,
range range=Full, pen[] palette)
An optionally labelled palette bar may be generated with the routine
void palette(picture pic=currentpicture, Label L="", bounds bounds,
pair initial, pair final, axis axis=Right, pen[] palette,
pen p=currentpen, paletteticks ticks=PaletteTicks,
bool copy=true, bool antialias=false);
The color space of 'palette' is taken to be over bounds 'bounds' with
scaling given by the z scaling of 'pic'. The palette orientation is
specified by 'axis', which may be one of 'Right', 'Left', 'Top', or
'Bottom'. The bar is drawn over the rectangle from 'initial' to
ticks::) that takes the following arguments:
paletteticks PaletteTicks(Label format="", ticklabel ticklabel=null,
bool beginlabel=true, bool endlabel=true,
int N=0, int n=0, real Step=0, real step=0,
pen pTick=nullpen, pen ptick=nullpen);
The image and palette bar can be fit to a frame and added and
optionally aligned to a picture at the desired location:
size(12cm,12cm);
import graph;
import palette;
int n=256;
real ninv=2pi/n;
real[][] v=new real[n][n];
for(int i=0; i < n; ++i)
for(int j=0; j < n; ++j)
v[i][j]=sin(i*ninv)*cos(j*ninv);
pen[] Palette=BWRainbow();
picture bar;
bounds range=image(v,(0,0),(1,1),Palette);
palette(bar,"$A$",range,(0,0),(0.5cm,8cm),Right,Palette,
PaletteTicks("$%+#.1f$"));
add(bar.fit(),point(E),30E);
[image]
Here is an example that uses logarithmic scaling of the function
values:
import graph;
import palette;
size(10cm,10cm,IgnoreAspect);
real f(real x, real y) {
return 0.9*pow10(2*sin(x/5+2*y^0.25)) + 0.1*(1+cos(10*log(y)));
}
scale(Linear,Log,Log);
pen[] Palette=BWRainbow();
bounds range=image(f,Automatic,(0,1),(100,100),nx=200,Palette);
xaxis("$x$",BottomTop,LeftTicks,above=true);
yaxis("$y$",LeftRight,RightTicks,above=true);
palette("$f(x,y)$",range,(0,200),(100,250),Top,Palette,
PaletteTicks(ptick=linewidth(0.5*linewidth())));
[logimage]
One can also draw an image directly from a two-dimensional pen array
or a function 'pen f(int, int)':
void image(picture pic=currentpicture, pen[][] data,
pair initial, pair final,
bool transpose=(initial.x < final.x && initial.y < final.y),
bool copy=true, bool antialias=false);
void image(picture pic=currentpicture, pen f(int, int), int width, int height,
pair initial, pair final,
bool transpose=(initial.x < final.x && initial.y < final.y),
bool antialias=false);
as illustrated in the following examples:
size(200);
import palette;
int n=256;
real ninv=2pi/n;
pen[][] v=new pen[n][n];
for(int i=0; i < n; ++i)
for(int j=0; j < n; ++j)
v[i][j]=rgb(0.5*(1+sin(i*ninv)),0.5*(1+cos(j*ninv)),0);
image(v,(0,0),(1,1));
[penimage]
import palette;
size(200);
real fracpart(real x) {return (x-floor(x));}
pair pws(pair z) {
pair w=(z+exp(pi*I/5)/0.9)/(1+z/0.9*exp(-pi*I/5));
return exp(w)*(w^3-0.5*I);
}
int N=512;
pair a=(-1,-1);
pair b=(0.5,0.5);
real dx=(b-a).x/N;
real dy=(b-a).y/N;
pen f(int u, int v) {
pair z=a+(u*dx,v*dy);
pair w=pws(z);
real phase=degrees(w,warn=false);
real modulus=w == 0 ? 0: fracpart(log(abs(w)));
return hsv(phase,1,sqrt(modulus));
}
image(f,N,N,(0,0),(300,300),antialias=true);
[penfunctionimage]
For convenience, the module 'palette' also defines functions that may
be used to construct a pen array from a given function and palette:
pen[] palette(real[] f, pen[] palette);
pen[][] palette(real[][] f, pen[] palette);
Info Catalog
asymptote: graph
asymptote: Base modules
asymptote: three