How do I plot a multivariate distribution?

I have the efficiency map of an electric drive, in wich I plottet the operating points (torque at rpm) during a driving cycle.

Now I somehow want to display in wich areas the system is operating the most. So a multivariate distributional plot with peaks at the areas where the density of points is higher would be my wish.

Please find the attached file as an example (x-Axis is rpm, y-Axis is torque)

Thanks in advance -Fabian

[Fabian Gock]

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Answer 1

[Pawel Jastrzebski]

Consider the following example:

NoOfPoints = 1000;

    % Generate 'x' and 'y'
    x = rand(NoOfPoints,1);
    y = rand(NoOfPoints,1);

% 2d plot of the data

hFig(1) = figure;
hAx(1)  = gca();
p(1) = scatter(...
    hAx(1),...
    x,...
    y,...
    'ro');

grid on

% generate histogram of the data
% this will give you the density of the points
hFig(2) = figure;
hAx(2)  = gca();

NoOfBins = 10;

p(2) = histogram2(hAx(2),...
    x,...
    y,...
    NoOfBins);

% extract peak value of every bin as well as it's
% 'x' and 'y' location
BinCenterX = p(2).XBinEdges(1:end-1) + diff(p(2).XBinEdges)/2;
BinCenterY = p(2).YBinEdges(1:end-1) + diff(p(2).YBinEdges)/2;
BinPeaks   = p(2).Values;

% plot values from histogram as surface plot

hFig(3) = figure;
hAx(3)  = gca();

p(3) = surface(hAx(3),...
    BinCenterX,...
    BinCenterY,...
    BinPeaks,...
    'EdgeAlpha',0.3,...
    'FaceAlpha',0.4);

hold on

p(3) = scatter3(...
    hAx(3),...
    x,...
    y,...
    zeros(size(x)),...
    'ro');

colorbar;

view(3)
grid on;

% use interpolation function to make the surface
% plot smoother
[meshX, meshY] = meshgrid(linspace(0,1,50));

BinPeaksInterp = interp2(...
    BinCenterX,...
    BinCenterY,...
    BinPeaks,...
    meshX,meshY,...
    'cubic');

hFig(4) = figure;
hAx(4)  = gca();

p(4) = surface(hAx(4) ,...
    meshX,...
    meshY,...
    BinPeaksInterp,...
    'EdgeAlpha',0.3,...
    'FaceAlpha',0.4);

hold on

p(5) = scatter3(hAx(4),...
    x,...
    y,...
    zeros(size(x)),...
    'ro');

colorbar;

view(3)
grid on;