Create a patch which includes all the histogram profiles

Hi, I have several profiles/skylines of histograms:

hold on
for i = 1 : 10
    X = normrnd(3000,10,[1,1000 ]);
    histogram(X, 100 , 'DisplayStyle','stairs');
end
hold off

and I would like to create a patch which includes all the histogram profiles in this way (possibly, including the "highest" and the "lowest" lines/profiles, here in red):

Any idea?

[Sim]

Hi, any suggestion here? :)

Answer 1

[AndresVar]

If you can use uniform bin edges for all series then it can be simplified

Here it is plotting white over the another color. You can improve the fill method to draw a single polygon (instead of 2), so it's truly the patch area. (there many similar question about "shading between two curves")

see:

Histogram bin counts - MATLAB histcounts (mathworks.com)

Create filled 2-D patches - MATLAB fill (mathworks.com)

clear;

numSeries = 10; % number of histograms
X = normrnd(3000,10,[numSeries,1000]); % the data

% specify the bin edges (same for all series)
binLimits = [min(X(:)) max(X(:))];
binWdith = 0.8;
numBins = ceil(diff(binLimits)/binWdith);

% get counts and binEdges
counts = zeros([numSeries,numBins]);
for ii = 1 : size(X,1)
    [counts(ii,:),binEdges]=histcounts(X(ii,:), 'BinLimits',binLimits,'BinWidth',binWdith);
end

% get top and bottom
counts_top = max(counts);
counts_bottom = min(counts);

% plot with 'BinCounts'
figure;
hold on;
histogram(BinEdges=binEdges,BinCounts=counts_top,FaceColor='m',LineStyle='none',FaceAlpha=0.3);
histogram(BinEdges=binEdges,BinCounts=counts_bottom,FaceColor='w',FaceAlpha=1,LineStyle='none');

% original histograms
for ii = 1:numSeries
    histogram(X(ii,:),binEdges=binEdges,DisplayStyle="stairs");
end
hold off
title('using histogram')

% can also use fill
figure;
x=sort([binEdges(1:end-1) binEdges(2:end)]);
x=[x x(end) x(1)]; % close the polygon
y=[repelem(counts_top,2) 0 0]; % close with y=0
fill(x,y,'r');
hold on;
y=[repelem(counts_bottom,2) 0 0];
fill(x,y,'w');
title('using fill')

[Sim]

Thanks a lot @AndresVar, an amazing solution!!! :)

Answer 2

[Sim]

@AndresVar: I also got a solution.... it has a few bugs, but it works in the way I was thinking...

clear all; close all; clc;

% histograms, bin counts and bin edges
hold on
for i = 1 : 10
    X = normrnd(3000,10,[1,1000 ]);
    h = histogram(X, 10 ,'FaceColor',[0.7 0.7 0.7]);%, 'DisplayStyle','stairs');
    y(:,i) = h.BinCounts;
    x(:,i) = h.BinEdges;
end

% get coordinates of all the horizontal lines forming the histograms
k = 1;
for i = 1 : 10
    xr = []; yr = []; l = [];
    xr = repelem(x(:,i),2);
    yr = repelem(y(:,i),2);
    l = [xr(2:end-1) yr];
    for j = 1 : 2 : size(l,1)-1
        %         line(l([j j+1],1),l([j j+1],2),...
        %             'LineStyle','-','color',ColorOdrCustom(i,:), 'LineWidth',1);
        % get the coordinates of all the lines
        % | x_start | x_end | y_start | y_end |
        lc(k,:) = [l(j,1) l(j+1,1) l(j,2) l(j+1,2)];
        k = k + 1;
    end
end


% Calculate the "external" curve and store the x1 and y1 coordinates
M = []; I = [];
[M,I] = min(lc(:,1));
s = lc(I,1); % start x
e = lc(I,2); % end x
v = lc(I,3); % value
% first point on the left
x1 = []; y1 = [];
x1(1) = s;
y1(1) = v;

k = 2;
while ~isempty(e)
    f = []; M = []; I = []; m = [];
    f = find(lc(:,1)>s & lc(:,1)<=e);   

    
    if max(lc(f,3)) >= v
        m = []; M = []; I = [];
        m = find(lc(f,3)>= v);
        [M,I] = min(lc(f(m),1));
        
        % if there are several left endpoints with the same x-value, take
        % the "highest" one
        if length(find(lc(f(m),1)==M)) > 1
            lc2 = []; f2 = []; M2 = []; I2 = []; I = [];
            lc2 = lc(f(m),:);
            f2 = find(lc2(:,1)==M);
            [M2,I2] = max(lc2(f2,3));
            [~,I] = ismember(lc2(f2(I2),:),lc(f(m),:),'rows');
        end
        x1(k)   = lc(f(m(I)),1); % store the x endpoint
        y1(k)   = y1(k-1);       % store the y endpoint
        x1(k+1) = x1(k);         % store the replica x endpoint
        y1(k+1) = lc(f(m(I)),3); % store the replica y endpoint
        s = lc(f(m(I)),1); % start x
        e = lc(f(m(I)),2); % end x
        v = lc(f(m(I)),3); % value
        k = k + 2;
    else
        f2 = [];
        f2 = find(lc(f,1)<e & lc(f,2)>e);
        M = []; I2 = []; I = [];
        [M,I2] = max(lc(f(f2),3));
        [~,I] = ismember(lc(f(f2(I2)),:),lc(f,:),'rows');
        x1(k)   = e;           % store the x endpoint
        y1(k)   = y1(k-1);     % store the y endpoint
        x1(k+1) = x1(k);       % store the replica x endpoint
        if ~isempty(lc(f(I),3))
            y1(k+1) = lc(f(I),3);  % store the replica y endpoint
        else
            y1(k+1) = 0;
        end
        s = lc(f(I),1); % start x
        e = lc(f(I),2); % end x
        v = lc(f(I),3); % value
        k = k + 2;
    end
end


% Calculate the "internal" curve and store the x2 and y2 coordinates
M = []; I = [];
[M,I] = min(lc(:,1));
s = lc(I,1) % start x
e = lc(I,2) % end x
v = lc(I,3); % value
x2 = []; y2 = [];
x2(1) = e;
y2(1) = v;

k = 2;
while ~isempty(e)
    f = []; M = []; I = [];  m = [];
    f = find(lc(:,1)<=e & lc(:,2)>e);  

    if all(lc(f,3) >=  v)
        M = []; I2 = []; I = [];
        [M,I2] = min(lc(f,3))
        [~,I] = ismember(lc(f(I2),:),lc(f,:),'rows')
        
        x2(k) = x2(k-1);          % store the x endpoint
        if ~isempty(lc(f(I),3))
            x2(k+1) = lc(f(I),2); % store the replica x endpoint
            y2(k)   = lc(f(I),3); % store the y endpoint
            y2(k+1) = lc(f(I),3); % store the replica y endpoint
        else
            x2(k+1) = x2(k-1);
            y2(k) = 0;
            y2(k+1) = 0;
        end
        s = lc(f(I),1); % start x
        e = lc(f(I),2); % end x
        v = lc(f(I),3); % value
        k = k + 2;
    else
        m = []; M = []; I = [];
        m = find(lc(f,3)<= v);
        [M,I] = min(lc(f(m),1));
        x2(k)   = lc(f(m(I)),1); % store the x endpoint
        y2(k)   = y2(k-1);       % store the y endpoint
        x2(k+1) = x2(k);         % store the replica x endpoint
        y2(k+1) = lc(f(m(I)),3); % store the replica y endpoint
        s = lc(f(m(I)),1); % start x
        e = lc(f(m(I)),2); % end x
        v = lc(f(m(I)),3); % value
        k = k + 2;
    end
end

% add initial points to both curves
x1 = [x1(1) x1];
y1 = [0 y1];
x2 = [x2(1) x2];
y2 = [0 y2];

% plot both "external" and "internal" curves, together with the patch
plot(x1,y1,'-','LineWidth',2,'color','blue')
plot(x2,y2,'-','LineWidth',2,'color','red')
p1 = patch([x1 fliplr(x2)], [y1 fliplr(y2)], 'green');
p1.FaceAlpha = 0.1 ; 

hold off

This is the result: