How to draw rotated axes in R?

plot, r

Solution

The following uses `base` functions and a couple of functions that we define ourselves.

While you requested a method that doesn't require calculating coordinates of segments' end points, I think this is impossible. However, we can define a simple helper function that uses some basic trigonometry to calculate the coordinates given the angle (clockwise from the positive y-axis) and the segment length. We do this below, as well as defining a function that plots a rotated axis.

get.coords <- function(a, d, x0, y0) {
  a <- ifelse(a <= 90, 90 - a, 450 - a)
  data.frame(x = x0 + d * cos(a / 180 * pi), 
             y = y0+ d * sin(a / 180 * pi))
}

rotatedAxis <- function(x0, y0, a, d, symmetrical=FALSE, tickdist, ticklen, ...) {
  if(isTRUE(symmetrical)) {
    axends <- get.coords(c(a, a + 180), d, x0, y0)    
    tick.d <- c(seq(0, d, tickdist), seq(-tickdist, -d, -tickdist))      
  } else {
    axends <- rbind(get.coords(a, d, x0, y0), c(x0, y0))
    tick.d <- seq(0, d, tickdist)
  }
  invisible(lapply(apply(get.coords(a, d=tick.d, x0, y0), 1, function(x) {
    get.coords(a + 90, c(-ticklen, ticklen), x[1], x[2])
  }), function(x) lines(x$x, x$y, ...)))
  lines(axends$x, axends$y, ...)
}

`get.coords` takes arguments `a` (a vector of angles), `d` (a vector of segment lengths), and `x0` and `y0`, the coordinates of the known point. Vectors `a` and `d` are recycled as necessary. The function returns a `data.frame` with elements `x` and `y` giving the coordinates corresponding to each angle/length pair.

`rotatedAxis` plots an axis between `x0, y0` and the point `d` units away along the line at angle `a`. If `symmetrical` is `TRUE`, the axis extends `d` units in opposite directions. Tick marks, of height `ticklen` are plotted `tickdist` units apart.

Plotting of the circle uses `get.coords` to calculate coordinates along the circumference, and plots the line connecting these with `polygon` (inspired by @timriffe).

Below we use these functions to replicate the plot provided by the OP.

# Set up plotting device
plot.new()
plot.window(xlim=c(-70, 70), ylim=c(-70, 70), asp=1)

# Plot circle with radius = 60 units and centre at the origin.
polygon(get.coords(seq(0, 360, length.out=1000), 60, 0, 0), lwd=2)

# Plot a polygon with vertices along six axes, at distances of 17, 34, 44, 40,
# 35, and 10 units from the centre.
poly.pts <- get.coords(seq(0, 300, 60), c(17, 34, 44, 40, 35, 10), 0, 0)
polygon(poly.pts$x, poly.pts$y, col='gray', lwd=2)

# Plot the rotated axes
rotatedAxis(0, 0, a=60, d=60, symmetrical=TRUE, tickdist=10, ticklen=1)
rotatedAxis(0, 0, a=120, d=60, symmetrical=TRUE, tickdist=10, ticklen=1)
rotatedAxis(0, 0, a=180, d=60, symmetrical=TRUE, tickdist=10, ticklen=1)

# Add text labels to circumference
text.coords <- get.coords(seq(0, 300, 60), 65, 0, 0)
text(text.coords$x, text.coords$y, c('I', 'A', 'S', 'E', 'C', 'R'))    

# Plot a second point and connect to centre by a line
point2 <- get.coords(145, 50, 0, 0)
points(point2, pch=20, cex=2)
segments(0, 0, point2$x, point2$y, lwd=3)

# Plot central point
points(0, 0, pch=21, bg=1, col=0, lwd=2, cex=2)

(Edit: I heavily edited this post - without changing it's general message drastically - in order to make it easier to read and more generally applicable. Additions/changes include that I now define a function to plot rotated axes, plot the circle by calculating coordinates of vertices along the circumference and plotting with `polygon`, as inspired by @timriffe.)

Problem

Original source