how do I plot different 3D peaks in different locations in single polar plot

In the image shown below I have a peak at center in polar plot. I need like that six peaks surrounding this main peak. Surrounding these six peaks I need nine peaks. To put it simply, in K shell I need 6 peaks, in L shell I need 9 peaks with central peak intact. I need them all in polar plot only.

thanks for help

[dpb]

Please attach the jpg w/ the picture icon instead of as a paperclip download file...

[Rakesh V]

this is polar plot, i need similar six peaks surrounding it in the same plot, but not as total subplots. Meaning the width of the main peak will be reduced. I donot want the peaks in the cartesian coordinates. i need them in polar plots. Even the equation would suffice. Or else even the plotting code also will help me. Thanks once again. feel free to ask more questions to get to clarity.

Answer 1

[Star Strider]

Try this:

N = 500;
rv = linspace(0, 1, N);                                                 % Radius Vector
av = linspace(0, 2*pi, N);                                              % Angle Vector
Ka = linspace(2*pi/12, 2*pi-2*pi/12, 6);                                % ‘K’ Angles
La = linspace(2*pi/18, 2*pi-2*pi/18, 9);                                % ‘L’ Angles
[R,A] = meshgrid(rv, av);
pkf = @(s) exp(-((((-15:15)).^2) + (((-15:15)).^2)')/s);                % Creates Gaussian Peaks
Mf = @(M,r,c) M((-15:15)+r,(-15:15)+c);                                 % Matrix Coordinates Grid For Each Peak

figure
[Xb,Yb,Zb] = pol2cart(A,R,zeros(size(R)));                              % Base Plane
surf(Xb,Yb,Zb)
hold on
surfc(Mf(Xb,16,16), Mf(Yb,16,16), pkf(50)*0.75)                         % Center Peak
for k = 1:numel(La)                                                     % ‘L’ Peaks
    Rrow = 400;
    ix = find(av <= La(k), 1, 'last');
    [X(:,:,k),Y(:,:,k),Z(:,:,k)] = pol2cart(Mf(A,ix,Rrow),Mf(R,ix,Rrow),pkf(2)*0.25);
    surf(X(:,:,k),Y(:,:,k),Z(:,:,k))
end
for k = 1:numel(Ka)                                                     % ‘K’ Peaks
    Rrow = 200;
    ix = find(av <= Ka(k), 1, 'last');
    [X(:,:,k),Y(:,:,k),Z(:,:,k)] = pol2cart(Mf(A,ix,Rrow),Mf(R,ix,Rrow),pkf(5)*0.5);
    surf(X(:,:,k),Y(:,:,k),Z(:,:,k))
end
hold off
shading interp
grid on
axis equal
view(-40,25)

producing:

The grids are defined as (-15:15) for every peak and the coordinate arrays for them. If you change those dimensions, you will need to change them in both the ‘pkf’ and ‘Mf’ functions, as well as in the ‘Center Peak’ plot. The rest of the code should adapt automatically, although within limits.

Experiment to get the result you want.

[dpb]

Nice demo, SS... :)

[Star Strider]

Thank you!

[Rakesh V]

Dear SS,

I am having a problem in the code it seems. The peak function for creating gaussian peaks is giving error for me. More or less the graph is pretty good.

I have done it in cartesian coordinates. please see the attached figure.

Can you solve the error in the function for gaussian peak and include the control for amplitude in each peak and increase the width of the peak if possible.

sorry to ask for too much

[Rakesh V]

Dear SS,

Thank you for the good work for the above code.

[Star Strider]

You did not say what problems you are having. You need to post the code you are using. What version (release) of MATLAB are you using? (My code was written in R2019a.)

I experimented with wider peaks, however that is likely not possible because of the constraints of the peak locations. The ‘s’ parameter of ‘pkf’ controls this to some extent, so you can experiment with that.

You can vary the peak amplitudes simply by multiplying them by whatever constant you want. One way to do that within the function iteslf is to add the amplitude as a parameter (here, ‘a’):

pkf = @(s,a) exp(-((((-15:15)).^2) + (((-15:15)).^2)')/s)*a;            % Creates Gaussian Peaks

A slightly tweaked version of my earlier code that includes that function is:

N = 275;
rv = linspace(0, 1, N);                                                 % Radius Vector
av = linspace(0, 2*pi, N);                                              % Angle Vector
Ka = linspace(2*pi/12, 2*pi-2*pi/12, 6);                                % ‘K’ Angles
La = linspace(2*pi/18, 2*pi-2*pi/18, 9);                                % ‘L’ Angles
[R,A] = meshgrid(rv, av);
pkf = @(s,a) exp(-((((-15:15)).^2) + (((-15:15)).^2)')/s)*a;            % Creates Gaussian Peaks
Mf = @(M,r,c) M((-15:15)+r,(-15:15)+c);                                 % Matrix Coordinates Grid For Each Peak

figure
[Xb,Yb,Zb] = pol2cart(A,R,zeros(size(R)));                              % Base Plane
mesh(Xb,Yb,Zb)
hold on
mesh(Mf(Xb,16,16), Mf(Yb,16,16), pkf(100,0.75))                         % Center Peak
for k = 1:numel(La)                                                     % ‘L’ Peaks
    Rrow = 150;
    ix = find(av <= La(k), 1, 'last');
    [X(:,:,k),Y(:,:,k),Z(:,:,k)] = pol2cart(Mf(A,ix,Rrow),Mf(R,ix,Rrow),pkf(50,0.25));
    mesh(X(:,:,k),Y(:,:,k),Z(:,:,k))
end
for k = 1:numel(Ka)                                                     % ‘K’ Peaks
    Rrow = 75;
    ix = find(av <= Ka(k), 1, 'last');
    [X(:,:,k),Y(:,:,k),Z(:,:,k)] = pol2cart(Mf(A,ix,Rrow),Mf(R,ix,Rrow),pkf(75,0.5));
    mesh(X(:,:,k),Y(:,:,k),Z(:,:,k))
end
hold off
% shading interp
grid on
axis equal
view(-40,25)

producing:

This is the best I can do.

[Star Strider]

Rakesh V’s Answer moved here:

Dear SS,

I am using the same code which you have written to generate polar plot. I am using 2014b which our university provided us. That is the reason why i am unable to use the code.

The error was at this point.

pkf = @(s,a) exp(-((((-15:15)).^2) + (((-15:15)).^2)')/s)*a; % Creates Gaussian Peaks

If I remove the transpose in the above equation it executes.

hence i had the problem it seems.

Anyhow i will work it from here

Thanks and regards for the help.

[Star Strider]

My pleasure.

You did not descirbe the specific problems you are having. There may be ways to solve them if I know what they are.

My code works in 2019a, and does what you describe what you want it to do, following your original post.

If my Answer helped you solve your problem, please Accept it!