# [R] Plotting Venn diagrams in R

David States dstates at bioinformatics.med.umich.edu
Tue Feb 4 00:38:02 CET 2003

```Last year there was a request seeking functions to plot Venn diagrams in
R.   Seeing no reply and for other reasons needing this, I wrote a quick
routine.  The general problem of creating a Venn diagram with overlap
areas proportional to the number of counts in each overlap is over
determined.  An approximate solution is to make the area of the circles
and pair wise overlap areas proportional to the number of counts in
each.  Using just the pair wise overlaps ignores (or hopes for the best
on :) ) the area of the three-way overlap.  R code that implements this
is shown below.

Usage: A, B and C are Boolean vectors of equal length, e.g.

A = runif(100) < 0.5
B = runif(100) < 0.4
C = runif(100) < 0.6

d = list()
d\$table = table(A,B,C)
d\$labels = c("A","B","C")

plot.venn.diagram(d)

This is pre-alpha code, caveat emptor.  In particular, the code to
position the labels needs work.  If someone wants to convert this to a
package or add it to an existing package, feel free to do so.

To optimize the solution over all of the overlaps or if you have more
than three sets, you can use a random sampling approach, but
implementing this in R is too slow to be useful.

David

David J. States, M.D., Ph.D.
Professor of Human Genetics
Director of Bioinformatics
University of Michigan School of Medicine
Medical Science Building I, Room 5443
Ann Arbor, MI 48109
USA

venn.overlap <-
function(r, a, b, target = 0)
{
#
# calculate the overlap area for circles of radius a and b
# with centers separated by r
# target is included for the root finding code
#
pi = acos(-1)
if(r >= a + b) {
return( - target)
}
if(r < a - b) {
return(pi * b * b - target)
}
if(r < b - a) {
return(pi * a * a - target)
}
s = (a + b + r)/2
triangle.area = sqrt(s * (s - a) * (s - b) * (s - r))
h = (2 * triangle.area)/r
aa = 2 * atan(sqrt(((s - r) * (s - a))/(s * (s - b))))
ab = 2 * atan(sqrt(((s - r) * (s - b))/(s * (s - a))))
sector.area = aa * (a * a) + ab * (b * b)
overlap = sector.area - 2 * triangle.area
return(overlap - target)
}

plot.venn.diagram <-
function(d)
{
#
# Draw Venn diagrams with proportional overlaps
# d\$table = 3 way table of overlaps
# d\$labels = array of character string to use as labels
#
pi = acos(-1)
csz = 0.1
# Normalize the data
n = length(dim(d\$table))
c1 = vector(length = n)
c1 = sum(d\$table[2,  ,  ])
c1 = sum(d\$table[, 2,  ])
c1 = sum(d\$table[,  , 2])
n1 = c1
#
c2 = matrix(nrow = n, ncol = n, 0)
c2[1, 2] = sum(d\$table[2, 2,  ])
c2[2, 1] = c2[1, 2]
c2[1, 3] = sum(d\$table[2,  , 2])
c2[3, 1] = c2[1, 3]
c2[2, 3] = sum(d\$table[, 2, 2])
c2[3, 2] = c2[2, 3]
n2 = c2
#
c3 = d\$table[2, 2, 2]
n3 = c3
c2 = c2/sum(c1)
c3 = c3/sum(c1)
c1 = c1/sum(c1)
n = length(c1)
# Radii are set so the area is proporitional to number of counts
pi = acos(-1)
r = sqrt(c1/pi)
r12 = uniroot(venn.overlap, interval = c(max(r - r, r - r,
0) + 0.01, r + r - 0.01), a = r, b = r[
2], target = c2[1, 2])\$root
r13 = uniroot(venn.overlap, interval = c(max(r - r, r - r,
0) + 0.01, r + r - 0.01), a = r, b = r[
3], target = c2[1, 3])\$root
r23 = uniroot(venn.overlap, interval = c(max(r - r, r - r,
0) + 0.01, r + r - 0.01), a = r, b = r[
3], target = c2[2, 3])\$root
s = (r12 + r13 + r23)/2
x = vector()
y = vector()
x = 0
y = 0
x = r12
y = 0
angle = 2 * atan(sqrt(((s - r12) * (s - r13))/(s * (s - r13))))
x = r13 * cos(angle)
y = r13 * sin(angle)
xc = cos(seq(from = 0, to = 2 * pi, by = 0.01))
yc = sin(seq(from = 0, to = 2 * pi, by = 0.01))
cmx = sum(x * c1)
cmy = sum(y * c1)
x = x - cmx
y = y - cmy
rp=sqrt(x*x + y*y)
frame()
par(usr = c(-1, 1, -1, 1), pty = "s")
box()
for(i in 1:3) {
lines(xc * r[i] + x[i], yc * r[i] + y[i])
}
xl = (rp + (0.7 * r)) * x/rp
yl = (rp + (0.7 * r)) * y/rp
text(xl, yl, d\$labels)
text(xl, yl - csz, d\$table[2, 1, 1])
xl = (rp + (0.7 * r)) * x/rp
yl = (rp + (0.7 * r)) * y/rp
text(xl, yl, d\$labels)
text(xl, yl - csz, d\$table[1, 2, 1])
xl = (rp + (0.7 * r)) * x/rp
yl = (rp + (0.7 * r)) * y/rp
text(xl, yl, d\$labels)
text(xl, yl - csz, d\$table[1, 1, 2])
#
text((x + x)/2, (y + y)/2, d\$table[2, 2, 1])
text((x + x)/2, (y + y)/2, d\$table[2, 1, 2])
text((x + x)/2, (y + y)/2, d\$table[1, 2, 2])
#
text(0, 0, n3)
list(r = r, x = x, y = y, dist = c(r12, r13, r23), count1 = c1, count2 =
c2, labels = d\$labels)
}

```