Add segments of circles to ggplot based on product of x & y

Question

I want to add shaded areas to a chart to help people understand where bad, ok, and good points can fit.

• Good = x*y>=.66
• Ok = x*y>=.34
• Bad = x*y<.34

Generating the right sequence of data to correctly apply the curved boundaries to the chart is proving tough.

1. What is the most elegant way to generate the curves?
2. Bonus Q: How would you do this to produce non-overlapping areas so that different colours could be used?

Updates

I've managed to do in a rather hacky way the drawing of the circle segments. I updated the MRE to use the revised segMaker function.

MRE

library(ggplot2)
pts<-seq(0,1,.02)

x<-sample(pts,50,replace=TRUE)
y<-sample(pts,50,replace=TRUE)

# What function will generate correct sequence of values as these are linear?
segMaker<-function(x,by){
# Original
#  data.frame(x=c(seq(0,x,by),0)
#             ,y=c(seq(x,0,-by),0)
#  )

  zero <- data.frame(x = 0, y = 0)
  rs <- seq(0, pi, by)
  xc <- x * cos(rs)
  yc <- x * sin(rs)
  gr <- data.frame(x = xc, y = yc)
  gr <- rbind(gr[gr$x >= 0, ], zero)
  return(gr)
}

firstSeg  <-segMaker(.34,0.02)
secondSeg <-segMaker(.66,0.02)
thirdSeg  <-segMaker(1,0.02)

ggplot(data.frame(x,y),aes(x,y, colour=x*y))+
  geom_point() +
  geom_polygon(data=firstSeg, fill="blue", alpha=.25)+
  geom_polygon(data=secondSeg, fill="blue", alpha=.25)+
  geom_polygon(data=thirdSeg, fill="blue", alpha=.25)

Current & desired shadings

Answer 1

You can create a data frame with the boundaries between each region and then use geom_ribbon to plot it. Here's an example using the conditions you supplied (which result in boundaries that are the reciprocal function, rather than circles, but the idea is the same, whichever function you use for the boundaries):

library(ggplot2)

# Fake data
pts<-seq(0,1,.02)

set.seed(19485)
x<-sample(pts,50,replace=TRUE)
y<-sample(pts,50,replace=TRUE)

df = data.frame(x,y)

# Region boundaries
x = seq(0.001,1.1,0.01)

bounds = data.frame(x, ymin=c(-100/x, 0.34/x, 0.66/x),
                    ymax=c(0.34/x, 0.66/x, 100/x), 
                    g=rep(c("Bad","OK","Good"), each=length(x)))

bounds$g = factor(bounds$g, levels=c("Bad","OK","Good"))

ggplot() +
  coord_cartesian(ylim=0:1, xlim=0:1) +
  geom_ribbon(data=bounds, aes(x, ymin=ymin, ymax=ymax, fill=g), colour="grey50", lwd=0.2) +
  geom_point(data=df, aes(x,y), colour="grey20") +
  scale_fill_manual(values=hcl(c(15, 40, 240), 100, 80)) +
  #scale_fill_manual(values=hcl(c(15, 40, 240), 100, 80, alpha=0.25)) + # If you want the fill colors to be transparent
  labs(fill="") +
  guides(fill=guide_legend(reverse=TRUE))

For circular boundaries, assuming we want boundaries at r=1/3 and r=2/3:

# Calculate y for circle, given r and x
cy = function(r, x) {sqrt(r^2 - x^2)}

n = 200
x = unlist(lapply(c(1/3,2/3,1), function(to) seq(0, to, len=n)))
bounds = data.frame(x, ymin = c(rep(0, n), 
                                cy(1/3, seq(0, 1/3, len=n/2)), rep(0, n/2), 
                                cy(2/3, seq(0, 2/3, len=2*n/3)), rep(0, n/3)),
                    ymax = c(cy(1/3, seq(0,1/3,len=n)), 
                             cy(2/3, seq(0,2/3,len=n)), 
                             rep(1,n)),
                    g=rep(c("Bad","OK","Good"), each=n))
bounds$g = factor(bounds$g, levels=c("Bad","OK","Good"))

Answer 2

If you can use a github package, ggforce adds geom_arc_bar():

# devtools::install_github('thomasp85/ggforce')

library(ggplot2)
library(ggforce)
pts<-seq(0,1,.02)

x<-sample(pts,50,replace=TRUE)
y<-sample(pts,50,replace=TRUE)

arcs <- data.frame(
  x0 = 0,
  y0 = 0,
  start = 0,
  end = pi / 2,
  r0 = c(0, 1/3, 2/3),
  r = c(1/3, 2/3, 1), 
  fill = c("bad", "ok", "good")
)

ggplot() + 
  geom_arc_bar(data = arcs, 
               aes(x0 = x0, y0 = y0, start = start, end = end, r0 = r0, r = r, 
                   fill = fill), alpha = 0.6) + 
  geom_point(data = data.frame(x = x, y = y),
             aes(x = x, y = y))