Plotting 2D XY values as a 3D radial contour plot

I want to plot XY values, where X represents the values accross a radius (0 is the center of the distrbution) and Y represents the colors of a heatmap (like a Gaussian distribution). I want it to look like the image attached. Can anyone please tell me how to do this? Thanks!

Answer 1

[Mathieu NOE]

hello

my 2 cents suggestion

clc
clearvars
data = importdata('data.txt');

x = data.data(:,1);
n = 200;
r = linspace(min(x),max(x),n);
z = data.data(:,2);
zz = interp1(x,z,r);

figure, hold on
axis square
for ci = 1:200
    theta = rand(n,1)*2*pi;
    XX = r'.*cos(theta);
    YY  = r'.*sin(theta);
    scatter(XX,YY,5,log10(zz),'filled')
end

%   Color maps.
%     parula     - Blue-green-orange-yellow color map
%     hsv        - Hue-saturation-value color map.
%     hot        - Black-red-yellow-white color map.
%     gray       - Linear gray-scale color map.
%     bone       - Gray-scale with tinge of blue color map.
%     copper     - Linear copper-tone color map.
%     pink       - Pastel shades of pink color map.
%     white      - All white color map.
%     flag       - Alternating red, white, blue, and black color map.
%     lines      - Color map with the line colors.
%     colorcube  - Enhanced color-cube color map.
%     vga        - Windows colormap for 16 colors.
%     jet        - Variant of HSV.
%     prism      - Prism color map.
%     cool       - Shades of cyan and magenta color map.
%     autumn     - Shades of red and yellow color map.
%     spring     - Shades of magenta and yellow color map.
%     winter     - Shades of blue and green color map.
%     summer     - Shades of green and yellow color map.
    
colormap('autumn');

[Aero Descerazes]

@Mathieu NOE Thank you very much for your response!

I have two questions:

1. The colorbar doesn't seem to be accurate. At the center (x=0), the y-value is 197 and the lowest y-value is 5. But the colorbar seems to be on a different scale. Is there a way to fix this?
2. I realized you used a scatterplot but the points seem to be scattered leaving white spaces in between. Is there a way to smoothen it in the periphery (like the center)?

Thanks again!

[Mathieu NOE]

hello again

1/ this is due to the fact that I wanted the center peak to be flatten , so I decided to plot the log10 of the data

scatter(XX,YY,5,log10(zz),'filled')

remove the log10 and the colorbar range will be according to your input data

scatter(XX,YY,5,zz,'filled')

2/ I supposed from the picture example that the result should be a scatter plot, with dots a bit random distributed inside the circle ; otherwise we can do a "continuous" surface plot (with surf)

what is your preference ?

[Mathieu NOE]

here an alternative with surf

my "r" correspond to the first column of your data

my "z" correspond to the second column of your data

clc
clearvars
data = importdata('data.txt');

r = data.data(:,1);
z = data.data(:,2);

figure(1), 
n = 50;
for ci = 1:n
    theta = (ci-1)/(n-1)*2*pi;
    XX(:,ci) = r'.*cos(theta);
    YY(:,ci)  = r'.*sin(theta);
    zz(:,ci) = z;
end
s = surf(XX,YY,zz);
view(2); 
%   view(2) sets the default 2-D view, AZ = 0, EL = 90.
%   view(3) sets the default 3-D view, AZ = -37.5, EL = 30.
s.EdgeColor = 'none'; %  hide the edges by setting the EdgeColor property.
axis square

%   Color maps.
%     parula     - Blue-green-orange-yellow color map
%     hsv        - Hue-saturation-value color map.
%     hot        - Black-red-yellow-white color map.
%     gray       - Linear gray-scale color map.
%     bone       - Gray-scale with tinge of blue color map.
%     copper     - Linear copper-tone color map.
%     pink       - Pastel shades of pink color map.
%     white      - All white color map.
%     flag       - Alternating red, white, blue, and black color map.
%     lines      - Color map with the line colors.
%     colorcube  - Enhanced color-cube color map.
%     vga        - Windows colormap for 16 colors.
%     jet        - Variant of HSV.
%     prism      - Prism color map.
%     cool       - Shades of cyan and magenta color map.
%     autumn     - Shades of red and yellow color map.
%     spring     - Shades of magenta and yellow color map.
%     winter     - Shades of blue and green color map.
%     summer     - Shades of green and yellow color map.

colormap('autumn');
colorbar('vert');

[Aero Descerazes]

@Mathieu NOE thank you that is so much better! I like it with surf

Just need your help in one last thing - when I try to plot a different data, the plot is not as smooth (see below). I tried using interp2 to smoothen the surf but it is giving me an error. "Input grid is not a valid MESHGRID."

How do I overcome this? Thanks again.

[Mathieu NOE]

Hello

if your data lack a bit of resolution, you can do some interpolation at the evry beginning (added this in the code below)

clc
clearvars
data = importdata('data.txt');

x = data.data(:,1);
% resample the data (interpolation) for a better resolution
r = linspace(min(x),max(x),100);
z = data.data(:,2);
z = interp1(x,z,r);

figure(1), 
n = 100;
for ci = 1:n
    theta = (ci-1)/(n-1)*2*pi;
    XX(:,ci) = r'.*cos(theta);
    YY(:,ci)  = r'.*sin(theta);
    zz(:,ci) = z(:);
end
s = surf(XX,YY,zz);
view(2); 
%   view(2) sets the default 2-D view, AZ = 0, EL = 90.
%   view(3) sets the default 3-D view, AZ = -37.5, EL = 30.
s.EdgeColor = 'none'; %  hide the edges by setting the EdgeColor property.
axis square

%   Color maps.
%     parula     - Blue-green-orange-yellow color map
%     hsv        - Hue-saturation-value color map.
%     hot        - Black-red-yellow-white color map.
%     gray       - Linear gray-scale color map.
%     bone       - Gray-scale with tinge of blue color map.
%     copper     - Linear copper-tone color map.
%     pink       - Pastel shades of pink color map.
%     white      - All white color map.
%     flag       - Alternating red, white, blue, and black color map.
%     lines      - Color map with the line colors.
%     colorcube  - Enhanced color-cube color map.
%     vga        - Windows colormap for 16 colors.
%     jet        - Variant of HSV.
%     prism      - Prism color map.
%     cool       - Shades of cyan and magenta color map.
%     autumn     - Shades of red and yellow color map.
%     spring     - Shades of magenta and yellow color map.
%     winter     - Shades of blue and green color map.
%     summer     - Shades of green and yellow color map.
    
colormap('autumn');
colorbar('vert');

[Aero Descerazes]

@Mathieu NOE This is perfect! Thank you so much for your help!

[Mathieu NOE]

my pleasure !