plot circle segment defined by three points with ggplot2

Question

How can I plot the circle segment defined by three points with `ggplot2`?

I can only find the geom_curve function and that does define a segment by two points and the curvature argument.

Reproducible example:

df <- data.frame(
  x = c(1,2,3),
  y = c(2,2.5,1)
)
library(ggplot2)
p <- ggplot(data = df, aes(x = x, y = y)) + geom_point(col = "red") + xlim(0,4) + ylim(0,4)
p + geom_curve(aes(x = x[1], y = y[1], xend = x[3], yend = y[3]))

With changing the curvature argument I can come close to what I want:

p + geom_curve(aes(x = x[1], y = y[1], xend = x[3], yend = y[3]), curvature = -.8)

How can I calculate the curvature value given the three points (in order the segment really passes the middle point)?

Or even better: Are there alternative geom_ functions out there (in ggplot2 or an extension) that calculate segments by three points?

And the bonus question: Is there an alternative geom_ that really plots circle segments (since the geom_curve is not a circle segment but some fancy curve which can be seen best when setting curvature > 1)?

Edit after comment: ggforce::geom_bezier doesn't seem to do the trick. I tried:

library(ggforce)
df <- data.frame(
  x = c(1,2,3),
  y = c(2,2.5,1),
  type = "quadratic",
  point = c("end", "control", "end")
)
library(ggplot2)
p <- ggplot(data = df, aes(x = x, y = y)) + geom_point(col = "red") + xlim(0,4) + ylim(0,4)
p + geom_bezier(aes(x = x, y = y, group = type, linetype = type), data = df)

@zx8754: Thx for your hint, but I can't see how geom_bezier should do the trick, see my edit.. — symbolrush
– symbolrush, Commented Mar 26, 2019 at 13:08

IceCreamToucan · Accepted Answer · 2019-03-26 14:18:02Z

10

Here's an option following the method shown by @Zaz here

Create function for calculating center and radius of circle

library(dplyr)

get_circle <- function(df){
  # df: three-row data frame containing columns x and y
  mat <- 
    df %>% 
      transmute(ss = x^2 + y^2, x, y, ones = 1) %>% 
      as.matrix

  center <- 
    c(x = det(mat[,c('ss', 'y', 'ones')]), y = -det(mat[,c('ss', 'x', 'ones')])
    )/(2*det(mat[,c('x', 'y', 'ones')]))

  r <- sqrt(sum((unlist(df[1, c('x', 'y')]) - center)^2))

  list(center = center, r = r)
}

Plot circle for given 3 points

library(ggplot2)
df <- data.frame(
  x = c(1,2,3),
  y = c(2,2.5,1)
)

circle <- get_circle(df)

ggplot(data = df, aes(x = x, y = y)) + 
  geom_point(col = "red") +
  with(circle,
       annotate("path",
        x = center['x'] + r*cos(seq(0,2*pi, length.out = 100)),
        y = center['y'] + r*sin(seq(0,2*pi, length.out = 100))))

edited Mar 26, 2019 at 14:18

answered Mar 26, 2019 at 13:43

IceCreamToucan

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2 Comments

symbolrush Over a year ago

Thx for your answer. Can we also just plot the circle segment (as in my question and Stéphane Laurents answer) using your approach?

IceCreamToucan Over a year ago

huh, somehow I completely missed that part of the question. I can't think of a better method than the one Stéphane gives. If you want to use get_circle instead of circumcircle to create the circle object, you should still be able to use the second half of that answer (after the first code block), since the circle object created should be exactly the same.

Stéphane Laurent · Accepted Answer · 2019-03-26 14:02:21Z

Here is a solution. Firstly, a function to compute the circumcircle of three points:

circumcircle <- function(p1,p2,p3){
  x1 <- p1[1]; y1 <- p1[2]
  x2 <- p2[1]; y2 <- p2[2]
  x3 <- p3[1]; y3 <- p3[2]
  a <- det(cbind(rbind(p1,p2,p3),1))
  q1 <- c(crossprod(p1))
  q2 <- c(crossprod(p2))
  q3 <- c(crossprod(p3))
  q <- c(q1,q2,q3)
  x <- c(x1,x2,x3)
  y <- c(y1,y2,y3)
  Dx <- det(cbind(q,y,1))
  Dy <- -det(cbind(q,x,1))
  c <- det(cbind(q,x,y))
  center <- 0.5*c(Dx,Dy)/a
  r <- sqrt(c(crossprod(center-p1)))
  list(center = center, radius = r)
}

df <- data.frame(
  x = c(1,2,3),
  y = c(2,2.5,1)
)

p1 <- c(df[1,"x"], df[1,"y"])
p2 <- c(df[2,"x"], df[2,"y"])
p3 <- c(df[3,"x"], df[3,"y"])

circle <- circumcircle(p1, p2, p3)

Now,

angle <- function(p, c){
  M <- p-c
  Arg(M[1] + 1i*M[2])
}

a1 <- angle(p1, circle$center)
a2 <- angle(p2, circle$center)
a3 <- angle(p3, circle$center)
angle0 <- min(c(a1,a2,a3))
angle1 <- max(c(a1,a2,a3))

path <- function(n=10){
  theta <- seq(angle0, angle1, length.out = n)
  as.data.frame(
    sweep(circle$radius*cbind(x=cos(theta), y=sin(theta)), 2, circle$center, "+")
  )
}

And the plot:

ggplot() + 
  geom_point(aes(x=x, y=y), data=df) + 
  geom_path(aes(x=x, y=y), data = path(100))

With an aspect ratio of 1:

ggplot() + 
  geom_point(aes(x=x, y=y), data=df) + 
  geom_path(aes(x=x, y=y), data = path(100)) + 
  coord_fixed()

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How can I plot the circle segment defined by three points with `ggplot2`?