How to manage colormap and colorbar in a matlab multi-curves plot?

Hi to everyone,

I have a plot with 50 curves that are the orbits of 50 periodic orbits, each orbit correspond to a value of a constant called "Jacobi constant" (it is an energy value) , so I have a vector of 50 elements called "jacobi_cst" that stores the followings 50 scalars:

3.000576748353570
3.000583342259840
3.000590018845460
3.000596554947660
3.000603171772120
3.000609870077710
3.000616425935580
3.000623060310100
3.000629657944820
3.000636330415510
3.000642857256680
3.000649560630930
3.000656116141060
3.000662738391370
3.000669315388860
3.000675958537960
3.000682547292110
3.000689196186970
3.000695791284050
3.000702431180730
3.000709016645110
3.000715644446600
3.000722309400740
3.000728906460450
3.000735532899990
3.000742084743060
3.000748750854930
3.000755335851910
3.000761928862980
3.000768609354090
3.000775192199620
3.000781845363950
3.000788475204760
3.000795067776960
3.000801695858850
3.000808265737810
3.000814922863360
3.000821489088600
3.000828099771820
3.000834723697250
3.000841330136040
3.000847948043080
3.000854592397690
3.000861196034850
3.000867791975870
3.000874419173230
3.000881028967010
3.000887643313580
3.000894276927840
3.000900891023230

So we have that to each orbit is associated one of these scalar (in increasing order). Can you show me how to color each orbit by using the "colormap" command and then how to show the colors in a lateral bar by using the command "colorbar"? Can you also indicate as display an accetable number of the scalars (surely, the first one and the last one and for example 10 values in total, by using at least 6 decimal digits) on the lateral colorbar?

Here is the code fragment that I use to plot orbits:

fig = figure;

for k1 = 1:50
    plot([Ly_orb_filt(1).prop(k1).orbits.x],[Ly_orb_filt(1).prop(k1).orbits.y],...
        "Color",my_green); hold on
end

% Info about number of Lyapunov orbits
dim = [.168 .85 .275 .06];
str = '$50 Planar\ Lyapunov\ orbits\ $';
annotation('textbox',dim,'String',str,'Interpreter',"latex",'FitBoxToText','off',...
           'BackgroundColor',[1 1 1],'FontSize',9);
% Plot L1 point
plot(Ly_orb_filt_sys_data(1).x,Ly_orb_filt_sys_data(1).y,'.',...
    'color',[0,0,0],'MarkerFaceColor',my_green,'MarkerSize',10);
text(Ly_orb_filt_sys_data(1).x-0.00015,Ly_orb_filt_sys_data(1).y-0.0008,'L_{1}');

%Primary bodies plots 
plot(AstroData.mu_SEM_sys  -1,0,'.',...
    'color',my_blue,'MarkerFaceColor',my_blue,'MarkerSize',20);
text(AstroData.mu_SEM_sys-1.0028,0-0.001,'$Earth + Moon$','Interpreter',"latex","FontSize",9); 

grid on; hold off
xlabel('$x$','interpreter','latex','fontsize',12);
ylabel('$y$','interpreter','latex','FontSize',12);

Sorry if my example is not reproducible but I avoid to load many data files and code lines.

To reply my question you can use an example with a simple set of 50 random curves by using my vector "jacobi_cst".

As final result, I want to get something like the following image taken on internet (in my case I have only one set of curves and not two as shown in the image below):

I would also add the label on the lateral colorbar and show on it, as I have already said above, 10 values of constants (the first value, the last one and then 8 values evenly spaced) with 6 decimal digits.

Answer 1

[KSSV]

Say you have 30 curves approximately. I will show these with circles.

R = 1:30 ;
th = linspace(0,2*pi) ; 
cmap = jet(30) ;
figure
hold on
for i = 1:30
    x = R(i)*cos(th) ;
    y = R(i)*sin(th) ; 
    plot(x,y,'color',cmap(i,:))
end
colorbar
colormap(cmap)

[Giuseppe]

Thank you @KSSV, can you use the vector "jacobi_cst" shown in my question instead of [0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1] following the indications written in my question?

Thank you again in advance!

P.s. as shown in the example image, the inner orbit is the one with the higher value of Jacobi constant, so I expect that the inner curve correspond to the red color on the colobar.

[DGM]

Alternatively, you can just set the axes 'colororder' and 'colormap' properties to use the same color table.

R = 1:30 ;
th = linspace(0,2*pi) ; 
cmap = jet(30) ;
figure
hold on
for i = 1:30
    x = R(i)*cos(th) ;
    y = R(i)*sin(th) ; 
    plot(x,y)
end
colorbar
set(gca,'colororder',cmap,'colormap',cmap)

The result is the same.

Either way, if you want to map red to the lowest values, then just change this:

cmap = jet(30) ;

to this:

cmap = flipud(jet(30)) ;

[Giuseppe]

Thank you @DGM, please can you solve the doubt I've written in the comment to KSSV's answer?

How to change colorbar scale by using elements of vector "jacobi_cst"vector?

[DGM]

Working with the same example:

% this is a linear series
jc = [3.00057674835357;3.00058334225984;3.00059001884546;3.00059655494766;3.00060317177212;
    3.00060987007771;3.00061642593558;3.0006230603101;3.00062965794482;3.00063633041551;
    3.00064285725668;3.00064956063093;3.00065611614106;3.00066273839137;3.00066931538886;
    3.00067595853796;3.00068254729211;3.00068919618697;3.00069579128405;3.00070243118073;
    3.00070901664511;3.0007156444466;3.00072230940074;3.00072890646045;3.00073553289999;
    3.00074208474306;3.00074875085493;3.00075533585191;3.00076192886298;3.00076860935409;
    3.00077519219962;3.00078184536395;3.00078847520476;3.00079506777696;3.00080169585885;
    3.00080826573781;3.00081492286336;3.0008214890886;3.00082809977182;3.00083472369725;
    3.00084133013604;3.00084794804308;3.00085459239769;3.00086119603485;3.00086779197587;
    3.00087441917323;3.00088102896701;3.00088764331358;3.00089427692784;3.00090089102323];

R = 1:numel(jc);
th = linspace(0,2*pi); 
cmap = flipud(jet(numel(jc))); % flip the CT

hold on
for i = numel(R):-1:1 % flip this for sake of visual similarity
    x = R(i)*cos(th) ;
    y = R(i)*sin(th) ; 
    plot(x,y)
end
colorbar

% i just copypasted this.  KSSV's original method works fine too
set(gca,'colororder',cmap,'colormap',cmap)

% since jc is linear, it should suffice to just use caxis
% if it's not linear, everything will be more complicated
caxis([min(jc) max(jc)])

[Giuseppe]

Thanks DGM! Can you also show as to increase the number of decimal digits in colorbar numbers and how to add the label "jacobi constant " above it?

[DGM]

% this is a linear series
jc = [3.00057674835357;3.00058334225984;3.00059001884546;3.00059655494766;3.00060317177212;
    3.00060987007771;3.00061642593558;3.0006230603101;3.00062965794482;3.00063633041551;
    3.00064285725668;3.00064956063093;3.00065611614106;3.00066273839137;3.00066931538886;
    3.00067595853796;3.00068254729211;3.00068919618697;3.00069579128405;3.00070243118073;
    3.00070901664511;3.0007156444466;3.00072230940074;3.00072890646045;3.00073553289999;
    3.00074208474306;3.00074875085493;3.00075533585191;3.00076192886298;3.00076860935409;
    3.00077519219962;3.00078184536395;3.00078847520476;3.00079506777696;3.00080169585885;
    3.00080826573781;3.00081492286336;3.0008214890886;3.00082809977182;3.00083472369725;
    3.00084133013604;3.00084794804308;3.00085459239769;3.00086119603485;3.00086779197587;
    3.00087441917323;3.00088102896701;3.00088764331358;3.00089427692784;3.00090089102323];

R = 1:numel(jc);
th = linspace(0,2*pi); 
cmap = flipud(jet(numel(jc))); % flip the CT

hold on
for i = 1:numel(R)
    x = R(i)*cos(th) ;
    y = R(i)*sin(th) ; 
    plot(x,y)
end
hcb = colorbar;

% this is one method.  the other method works fine too
set(gca,'colororder',cmap,'colormap',cmap)

% since jc is linear, it should suffice to just use caxis
% if it's not linear, everything will be more complicated
caxis([min(jc) max(jc)])

% set ticklabel length
tl = split(sprintf('%.6f\n',hcb.Ticks));
hcb.TickLabels = tl(1:end-1);

% set cb title
title(hcb,'aklsdjflakjf')

Note that the ticklabels are not sampled from jc. They're a conveniently selected linear series with at most 5 decimal places. If you want them to be something else, you'd have to also set hcb.Ticks. Similarly, if you want the full 15 decimal places, you'll likely have to adjust axes position properties, otherwise the numbers will all get cut off.