How to generate a colourmap for a 2D denisty map?

Hi, I am using MATLAB R2020a with a MacOS. I am currently trying to generate a colourmap to represent the density of points on the following plot:

I have used this function by Malcolm McLean to generate a density:

function [ dmap ] = dataDensity(x, y, width, height, limits, fudge)
    if(nargin == 4)
        limits(1) = min(x);
        limits(2) = max(x);
        limits(3) = min(y);
        limits(4) = max(y);
    end
    deltax = (limits(2) - limits(1)) / width;
    deltay = (limits(4) - limits(3)) / height;
    if(nargin < 6)
        fudge = sqrt(deltax^2 + deltay^2);
    end
    dmap = zeros(height, width);
    for ii = 0: height - 1
        yi = limits(3) + ii * deltay + deltay/2;
        for jj = 0 : width - 1
            xi = limits(1) + jj * deltax + deltax/2;
            dd = 0;
            for kk = 1: length(x)
                dist2 = (x(kk) - xi)^2 + (y(kk) - yi)^2;
                dd = dd + 1 / ( dist2 + fudge); 
            end
            dmap(ii+1,jj+1) = dd;
        end
    end
         
end

I have used this function by Malcolm McLean to then generate a plot of this density.

function [ f ] = DataDensityPlot( x, y, levels )
    map = dataDensity(x, y, 256, 256);
    map = map - min(min(map));
    map = floor(map ./ max(max(map)) * (levels-1));
    f = figure();
    
    image(map);
    colormap(jet(levels));
    set(gca, 'XTick', [1 256]);
    set(gca, 'XTickLabel', [min(x) max(x)]);
    set(gca, 'YTick', [1 256]);
    set(gca, 'YTickLabel', [min(y) max(y)]);
    uiwait;
end

However, this creates a contourmap as shown.

Instead, I would like to generate a plot where the colour directly corresponds to the density of points rather than having contours, similar to this:

I would very much appreciate suggestions on how to manipulate the function to create the desired colourmap. Thanks in advance

[Cris LaPierre]

Duplicate of this post?

[Cai Chin]

Hi, sorry about that, I deleted the previous question. This one includes more detail and a different approach

Answer 1

[Cris LaPierre]

It looks like your comparison image has had the color axis manually adjusted (rt click on colorbar and select "Interactive Colormap Shift"), but is either a hist3 or imagesc plot.

I'd be inclined to use hist3.

load v.mat
load w.mat

figure
hist3([v,w],'Nbins',[275 275],"EdgeColor","none",'CDataMode','auto')
view(2)
axis tight
colormap jet
caxis([0 250])
colorbar

●

[Cris LaPierre]

It's showing up weird here. Here's what it looks like after playing with the colobar.

For what it's worth, I think the image you shared actually has the w values reversed. Note what I have as positive it has as negative, and vice versa. That may suggest that was created using imagesc, which has (0,0) in the top left instead of bottom left. Then the tick labels were updated, but the underlying values do not follow.

[Cai Chin]

Thank you very much for this - it is exactly what I wanted. May I please ask how you adjusted the colorbar? I have looked into the help documentation but cannot seem to find how you adjusted the gradient effect. Thanks again

[Cris LaPierre]

Rt click on colorbar and select "Interactive Colormap Shift", then position the cursor on the color bar and click and drag it to modify the color ranges. For example, I clicked on the green area and dragged it down to about 50.

[Cai Chin]

Ah yes, thanks again.