Drawing Venn Diagrams using Matlab

How can we use Matlab to draw Venn diagrams?

Download the Matlab code for this exercise from venn.zip.

Simple Venn diagrams

imshow(a)

Matlab code for creating logical images a and b

xp = linspace(-1,1,256);
x = ones(size(xp))'*xp;
y = xp'*ones(size(xp));
a = sqrt((x+0.3).^2+y.^2)<0.6;
b = sqrt((x-0.3).^2+y.^2)<0.6;
r1 = max(find(xp<-0.7));
r2 = min(find(xp>0.7));
a = a(r1:r2,:);
b = b(r1:r2,:);

If you do not have the Matlab Image Processing toolbox, you could use the following commands to show logical images:

imagesc(a);
axis equal;

Simple Venn diagrams can be displayed using the logical images just obtained:

imshow(xor(a,b))

Conversion to RGB color

The following Matlab code will generate an RGB image of a Venn diagram with a white (FALSE) background yellow (TRUE) foreground.

z = xor(a,b);
p = ones(size(z));
rgb = cat(3,p,p,and(p,~z));
imshow(rgb)

The problem with this image is that the diagram background blends with the page background.

Creating borders

The following Matlab code creates some border images

% generate outlined box
sz = size(a);
u = ones(sz);
u(1:2,:)=0;
u(:,1:2)=0;
u(sz(1)-(0:1),:)=0;
u(:,sz(2)-(0:1))=0;

% generate edge images
se = strel('disk',2);
ae = a - imerode(a,se);
be = b - imerode(b,se);

ue = double(and(u,~(ae|be)));

This code uses some simple morphological image processing operations, and does require the Image Processing toolbox.

imshow(u);	imshow(be);	imshow(ue);

Final Venn diagram

The following code produces the final Venn diagram

% generate example venn diagram
z = xor(a,b);
rgb = cat(3,ue,ue,and(ue,~z));
imshow(rgb);

Maintained by John Loomis, last updated 29 May 2004