Plot circles with alpha values in MATLAB

Question

I'm creating a scatter plot of some data, as you do, and I have a number of repeated data points which I'd like to plot as circles with some alpha value so that piling on of extra points at the same location is obvious.

As far as I can tell you cannot set the alpha properties of the little circles that you generate with plot(x, y, 'o'), so I've resorted to drawing thousands of little circles using patch() myself:

x = repmat([1:10], [1 10]);
y = round(10*rand(100, 1))/10;
xlim([0 11])
ylim([0 1])
p = ag_plot_little_circles(x', y, 10, [1 0 .4], 0.2);

function p = ag_plot_little_circles(x, y, circle, col, alpha)
%AG_PLOT_LITTLE_CIRCLES Plot circular circles of relative size circle
% Returns handles to all patches plotted

    % aspect is width / height
    fPos = get(gcf, 'Position');
    % need width, height in data values
    xl = xlim();
    yl = ylim();
    w = circle*(xl(2)-xl(1))/fPos(3);
    h = circle*(yl(2)-yl(1))/fPos(4);

    theta = 0:pi/5:2*pi;
    mx = w*sin(theta);
    my = h*cos(theta);
    num = 0;
    for k = 1:max(size(x))
        for f = 1:size(y,2)
            num = num+1;
            p(num) = patch(x(k)+mx, y(k,f)+my, col, 'FaceColor', col, 'FaceAlpha', alpha, 'EdgeColor', 'none');
        end
    end
end

As you can see, this is not optimal as I need to know and set the size of the plot (xlim and ylim) before I plot it so that the circles end up being circular. If I reshape the plot then they end up as ovals. I also end up with millions of objects, which is a pain when making legends.

Is there an easier way?

Answer 1

I have found no way to have a line marker with alpha in MATLAB.

If you look at line properties (the (mid) low level function behind plot), you will see that you can define markers, and their sole properties are their color (MarkerEdgeColor or MarkerFaceColor), which does not take any alpha (there is no MarkerFaceAlpha property).

So how you do it with patches seems the way to go.

The only thing I can propose to avoid having zillions of objects would be to group them in a hggroup, which will make them appear as a single object in the legend.

Answer 2

I tried to do a general function using patch. It's slow and a bit buggy, but it works OK for simple cases. MATLAB needs a real-line alpha though.

x and y are points to plot, w the width of the line, col the color and a the alpha value.

Example:

x = linspace(-2,2,100);
plotWithAlpha(x,sin(4*x),0.04,'r',0.2)


function [] = plotWithAlpha(x,y,w,col,a)
%function [] = plotWithAlpha(x,y,w,col,a)
    if(size(x,1) ~= 1)
       x = x.';
    end

    if(size(x,1) ~= 1)
       y = y.';
    end

    sz = length(x);

    % Calculate derrivatives of the curve
    X = csaps(1:sz(1),x,1);
    Y = csaps(1:sz(1),y,1);

    mx = fnval(fnder(X,1),1:sz(1)).';
    my = fnval(fnder(Y,1),1:sz(1)).';

    T = [mx my]; %tangent

    % Normalize tangents
    T = bsxfun(@rdivide,T,sqrt(sum(T.^2,2)));

    N = zeros(size(T));

    N(:,2) = 1;
    N(:,1) = -T(:,2)./T(:,1);

    N = bsxfun(@rdivide,N,sqrt(sum(N.^2,2)));

    N = N.';

    hold on

    for i = 2:length(x)
        X = [x(i-1)+w*N(1,i-1) x(i)+w*N(1,i) x(i-1)-w*N(1,i-1) x(i)-w*N(1,i)];
        Y = [y(i-1)+w*N(2,i-1) y(i)+w*N(2,i) y(i-1)-w*N(2,i-1) y(i)-w*N(2,i)];

        % Order the points
        D = pdist([X' Y']);
        D = squareform(D); D(D==0) = Inf;

        inds = 1;
        D(:,1) = Inf;

        [val ind] = min(D(1,:));
        inds(2) = ind;
        D(:,ind) = Inf;

        [val ind] = min(D(ind,:));
        inds(3) = ind;
        D(:,ind) = Inf;

        inds(4) = setxor(inds,1:4);

        X = X(inds);
        Y = Y(inds);

        patch(X,Y,col,'edgeColor','none','FaceAlpha',a)
    end

    hold off