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shade overlapping portions of circles (or other shapes)

2 messages · Paul Johnson, Greg Snow

Paul Johnson
# 
I'm making some illustrations and it would be convenient to
automatically shade the overlapping portions of circles.  These
illustrations are for Social Choice theory, a field in political
science and economics.  I've wrestled together some examples so you
can see what I mean, but have not mastered the "color overlapping
sections" problem (as you will see):

http://pj.freefaculty.org/scraps/t-m15g.pdf

The shaded area does not overlap perfectly, mainly because I isolated
the points manually with locator(). Tedious!

I've not found R functions just for this.  Are there any packages?

You can get an idea of the problem if you run, for example

library(plotrix)
example(draw.circle)

See the red and the blue circles overlap?  What's the best way to
"shade in" that overlapping area.

I don't have Mathematica anymore, but they seem to be able to do this
more-or-less easily

http://mathematica.stackexchange.com/questions/2554/how-to-plot-venn-diagrams-with-mathematica

I want to make R do same ( or develop package to do it).

I was under some pressure to get a graph finished that I linked to
above. But I would not want to do it that way again. The shapes won't
always  be perfect circles, they may be ellipses or other convex
shapes.  But if I could understand the problem for circles, maybe I
could solve for others.

Do you have suggestions?

I am considering this. Collect the co-ordiates from the circle points

 C1 <- draw.circle(3.5,7,0.8,border="blue",lty=2,lwd=2)
 C2 <- draw.circle(2.5,8,0.6,border="red",lty=3,lwd=3)

Can I isolate the relevant arcs from C1 and C2? If I could, I'd join them

Cjoin <- list(x = c(C1$x, C2$x), y = c(C1$y, C2$y))

And use that for plotting.

pj


-- Paul E. Johnson
Professor, Political Science    Assoc. Director
1541 Lilac Lane, Room 504     Center for Research Methods
University of Kansas               University of Kansas
http://pj.freefaculty.org            http://quant.ku.edu
Greg Snow
# 
A quick and simple way would be to fill both circles with a
semi-transparent color (does not work on all devices), then the
overlapping area will will show up as a different color/shade due to
the alpha blending.  You might want to redraw the circles without fill
after the filled ones so that the 1st circle outline drawn is not
overlaid by the interior of the other circle.  This will mean that the
circles will be filled with a color other than the background (but
that may be a bonus).

plot(1:10, 1:10, type='n', asp=1)
theta <- seq(0,2*pi, length=400)
x1 <- 3*cos(theta)+4
y1 <- 3*sin(theta)+4
x2 <- 2*cos(theta)+6
y2 <- 2*sin(theta)+6
polygon(x1,y1, col="#0000ff55")
polygon(x2,y2, col="#00ff0055")


There are some of the spatial packages that will find the intersection
or overlay of 2 polygons that you could use to find the polygon that
represents the intersection and fill it.

library(sp)
library(rgeos)
x1 <- c(x1,x1[1])
y1 <- c(y1,y1[1])
x2 <- c(x2,x2[1])
y2 <- c(y2,y2[1])
p1 <- SpatialPolygons(list(Polygons(list(Polygon(cbind(rev(x1),rev(y1)))),ID=1)))
p2 <- SpatialPolygons(list(Polygons(list(Polygon(cbind(rev(x2),rev(y2)))),ID=2)))
tmp <- gIntersection( p1, p2 )
plot(p1, xlim=c(1,10), ylim=c(1,10))
plot(p2, add=TRUE)
plot(tmp, add=TRUE, col='green')

I hope that there is a simpler way than above, but it works.

The last option is to use math to figure out the intersection and
polygon to fill it.
On Wed, Aug 15, 2012 at 10:43 AM, Paul Johnson <pauljohn32 at gmail.com> wrote: