A 2D circle divided into 10 sectors in the 3D plot.

Hello, for the visualization of my research results, I would like to create a 3D chart with a circle split in sectors, similar to the one attached. But I need a circle divided into 10 sectors, and I would like to assign concentrations for each sector, for example like in the chart where circle is separated in squares. How can I do it?

Answer 1

[Star Strider]

I am not exactly certain what you want.

One approach —

r = 7.5;
ac = linspace(0, 2*pi, 500).';
xc = r*cos(ac);
yc = r*sin(ac);
zc = zeros(size(ac));
as = linspace(0, 2*pi, 11).';
xs = r*cos(as);
ys = r*sin(as);
zs = zeros(size(as));
data = rand(50,3).*[2*pi r 150];                            % 'Data': [Angle, Radius, Z-Value]

[X,Y,Z] = pol2cart(data(:,1), data(:,2), data(:,3));        % Convert To Cartesian For Plot

figure
plot3(xc, yc, zc, '-k');
hold on
plot3([zs xs].', [zs ys].', [zs zs].', '-k');
scatter3(X, Y, Z, 25, Z, 'filled')
hold off
grid on
colormap(turbo)
daspect([1 1 15])                                           % Sets Axes Aspect Ratio

figure
plot3(xc, yc, zc, '-k');
hold on
plot3([zs xs].', [zs ys].', [zs zs].', '-k');
plot3(xc, yc, zc+150, '-k');
plot3([zs xs].', [zs ys].', [zs zs].'+150, '-k');
scatter3(X, Y, Z, 25, Z, 'filled')
hold off
grid on
colormap(turbo)
daspect([1 1 15])

To assign them to specific segments in the plot, consider using stem3 as well, with 'Marker','none'. This will connect each data point to the ‘Z’ surface with a line, and can make the plot easier to understand.

.

[Dmitriy]

Thank You so much, this is exactly what I needed!

[Star Strider]

As always, my pleasure!

[Dmitriy]

Hello, I was trying to do it for my data and got a bit lost because in Your example as I understand You create random coordinates for 50 pieces of data and Im strugguling a bit in my tryes to assign a concentration to a particular sector one after another, for example for this set of data:

Sector A - 2597.08 Sector B - 2345.07 Sector C - 2556.82 Sector D - 2547.45 Sector E - 2733.64 Sector F - 2802.18 Sector G - 2748.18 Sector H - 2625.41 Sector I - 2717.81 Sector J - 2650.86

and also I was trying to understand which part of the code is for creating sectors, so for example if I decide to create 12 sectors how can I do it in the code?

Thanks a lot for your help in advance!

[Star Strider]

You need to define the sectors in terms of radian angles in my code.

This extracts the sector designations and values, then converts the sector designations into angles. It arbitratily assigns a constant radius value, and uses the associated value in the array as the Z-value.

Try this —

V = {'Sector A - 2597.08 Sector B - 2345.07 Sector C - 2556.82 Sector D - 2547.45 Sector E - 2733.64 Sector F - 2802.18 Sector G - 2748.18 Sector H - 2625.41 Sector I - 2717.81 Sector J - 2650.86'};
val = cell2mat(cellfun(@(x)str2double(regexp(x, '\d*\.\d*', 'match')), V, 'Unif',0)).';         % Sector Numerical Values
sec = regexp(V,'(?<=Sector )\w', 'match');                                                      % Sector Alphabetical Values

SectorValues = table(sec{:}.', val, 'VariableNames',{'Sector','Value'})                         % Create Table

SectorValues = 10x2 table
    Sector    Value 
    ______    ______

    {'A'}     2597.1
    {'B'}     2345.1
    {'C'}     2556.8
    {'D'}     2547.4
    {'E'}     2733.6
    {'F'}     2802.2
    {'G'}     2748.2
    {'H'}     2625.4
    {'I'}     2717.8
    {'J'}     2650.9

secvals = cellfun(@(x)double(x)-double('A')+1, SectorValues.Sector);                            % Numerical Values Of Sector Alphabetical Designations
angvals = 2*pi*(secvals/10 + 0.5/10);                                                           % Radian Angle Values Of Sector Alphabetical Values

r = 7.5;
ac = linspace(0, 2*pi, 500).';
xc = r*cos(ac);
yc = r*sin(ac);
zc = zeros(size(ac));
as = linspace(0, 2*pi, 11).';
xs = r*cos(as);
ys = r*sin(as);
zs = zeros(size(as));
% data = rand(50,3).*[2*pi r 150];                            % 'Data': [Angle, Radius, Z-Value]

data = [angvals 0.8*ones(size(angvals))*r SectorValues.Value]

data = 10x3

1.0e+03 * 0.0009 0.0060 2.5971 0.0016 0.0060 2.3451 0.0022 0.0060 2.5568 0.0028 0.0060 2.5474 0.0035 0.0060 2.7336 0.0041 0.0060 2.8022 0.0047 0.0060 2.7482 0.0053 0.0060 2.6254 0.0060 0.0060 2.7178 0.0066 0.0060 2.6509

[X,Y,Z] = pol2cart(data(:,1), data(:,2), data(:,3));        % Convert To Cartesian For Plot

figure
plot3(xc, yc, zc, '-k');
hold on
plot3([zs xs].', [zs ys].', [zs zs].', '-k');
scatter3(X, Y, Z, 50, Z, 'filled')
hold off
grid on

txtangl = linspace(0, 2*pi, 11);
txtangl = txtangl(1:10)+2*pi/20;
text(1.1*r*cos(txtangl), 1.1*r*sin(txtangl),  zeros(size(txtangl)), compose('%c', 'A':'J'))
colormap(turbo)
daspect([1 1 300])                                           % Sets Axes Aspect Ratio

This should work with any number of cextor assignments, regardless of the order in which they are provided.

.

[Dmitriy]

I got it! Now I understand, have succesfully made charts for my work, thank You very much for your help!

[Star Strider]

As always, my pleasure!

Answer 2

[Adam Danz]

Creating a polar heatmap within Cartesian coordinates

The basic idea is to create a polar grid centered under the data, plotted as a surface. The color in the surface is defined by the density of points that fall within each sector of the polar grid. To compute density, the 3D points are convered to 2D polar coordinates, ignoring z-coordinates. Then, each point is assigned to a section of the grid using logical conditions. Then the polar grid is converted back to Cartesian units and centered under the data.

Important caveat: The polar grid cells do not have the same area. This means that larger cells will contain more data points than smaller cells in a uniform distribution. This biases the interpretation of the colored regions. This could be corrected by normalizing the color values to the area of each segment in which case the colors would not indicate number of points but instead, number of points per unit of area.

Please also see a limitation to this visualization at the end of the answer.

Demo

Create data

data is an nx3 matrix of [x,y,z] coordinates.

rng default
data = pearsrnd(0,1,.6,4,500,3); % requires stats toolbox
% data = randn(200,3).*[1.2,1,1]+[2,-1,0]; % Alternative

Convert data to polar coordinates

% Shift data to be centered on (0,0) and convert to polar
center = mean(data(:,1:2));  % (x,y) center of the data
[xTheta, yRad] = cart2pol(data(:,1)-center(1),data(:,2)-center(2)); 

Create a polar grid

nThetaSectors determines the number of sections around the circle, starting and ending at -pi, pi.

nRadiiSectors determines the number of sections between the center and outer edge of the circle.

% Compute polar grid
nThetaSectors = 10;  % parameter
thetaGrid = linspace(-pi,pi,nThetaSectors+1);

nRadiiSectors = 5; % parameter
maxRadius = max(yRad);
radiiGrid = linspace(0,maxRadius,nRadiiSectors+1);

Compute the density of data points within each polar grid cell

% Assign each point to a grid cell
% This only works when there is a border at -pi and pi
[radiusGroup, ~] = find((yRad(:)>radiiGrid(1:nRadiiSectors) & yRad(:)<=radiiGrid(2:end))');
[thetaGroup, ~] = find((xTheta(:)>thetaGrid(1:nThetaSectors) & xTheta(:)<=thetaGrid(2:end))');

% Create density grid
[gcounts,gvecs] = groupcounts([thetaGroup,radiusGroup]);
gidx = sub2ind([nThetaSectors, nRadiiSectors],gvecs{1},gvecs{2});
density = zeros(nThetaSectors, nRadiiSectors);
density(gidx) = gcounts;

Convert the polar grid to Cartesian coordinates

Here, we also shift the polar grid to the center of the data.

The grid is located under the data along the z-axis by finding the minimum z value and shifting downward by 5 % of the range of z-data.

% Create the polar grid in cartesian coordinates
[tg,rg] = ndgrid(thetaGrid,radiiGrid);  % meshgrid requires transpose
[px, py] = pol2cart(tg,rg);
px = px + center(1); 
py = py + center(2); 
[minZ,maxZ] = bounds(data(:,3));
pFloor = minZ*(0.05*(maxZ-minZ));
pz = zeros(size(px)) + pFloor; 

Plot the 3D scatter points

scatter3(data(:,1),data(:,2),data(:,3),'ko')
grid on
axis equal

Add the polar density surface

zlim([pFloor,inf])
hold on
h = surf(px,py,pz,density,'FaceAlpha',.5,'EdgeAlpha',.3);
cb = colorbar();
cb.Label.String = 'Density';

axis vis3d

View from the bottom

view(0,-90)

Limitations

Points are assigned to the segments assuming the segments are circular. The segments aren't plotted circularly, they are plotted as trapazoids. This means in some cases a point will appear outside of a segment when it was, in fact, counted as a member of that segment.

This is illustrated in the image below where a yellow segment indicates that it contains 1 data point. The yellow segement on the left counts the point just outside of the segment because it is within the circular zone (dotted line). This could lead to some confusing results.

One way to improve that is to compute density using inpolygon so belongingness is defined by the plotted trapezoidal segments.

Another way to improve this is to plot circular zones instead of trapezoidal zone.

Neither of these improvements would be quick and easy so I'll leave that to the next person.