Get margin line locations in log space

Question

In a previous question I asked how to get margin line locations in user coordinates. I received an excellent answer in the form of the line2user function. However, I cannot figure out how to modify the function to work when either the x or y axis is on a log scale.

I have made a couple modifications to accommodate a log-scaled axis:

line2user <- function(line, side, log = "") {
  lh <- par('cin')[2] * par('cex') * par('lheight')
  x_off <- diff(grconvertX(0:1, 'inches', 'user'))
  y_off <- diff(grconvertY(0:1, 'inches', 'user'))
  usr <- par('usr') ## Added by me
  if (grepl("x", log)) usr[1:2] <- 10^usr[1:2] ## Added by me
  if (grepl("y", log)) usr[3:4] <- 10^usr[3:4] ## Added by me
  switch(side,
         `1` = usr[3] - line * y_off * lh,
         `2` = usr[1] - line * x_off * lh,
         `3` = usr[4] + line * y_off * lh,
         `4` = usr[2] + line * x_off * lh,
         stop("Side must be 1, 2, 3, or 4", call.=FALSE))
}

However, I cannot figure out how to properly adjust the xoff and yoff variables to draw the proper lines. Illustration:

setup_plot <- function(log = "") {
  par(mar = c(2, 10, 2, 2), oma = rep(2, 4))
  plot.new()
  plot.window(xlim = c(1, 10), ylim = c(1, 10), log = log)
  box(which = "plot", lwd = 2, col = "gray40")
  box(which = "figure", lwd = 2, col = "darkred")
  box(which = "outer", lwd = 2, col = "darkgreen")
  text(x = 0.5, y = 0.5, 
       labels = "Plot Region", 
       col = "gray40", font = 2)
  mtext(side = 3, text = "Figure region", line = 0.5, col = "darkred", font = 2)
  mtext(side = 3, text = "Device region", line = 2.5, col = "darkgreen", font = 2)
  for (i in 0:9) {
    mtext(side = 2, col = "darkred", text = paste0("Line", i), line = i)
  }
}

setup_plot(log = "x")
abline(v=line2user(line=0:9, side=2, log = "x"), xpd=TRUE, lty=2)

The compressed lines make sense after considering the following example:

plot(10)
diff(grconvertX(0:1, 'inches', 'user'))
## [1] 0.08121573 (on my device)

plot(10, log = "x")
diff(grconvertX(0:1, 'inches', 'user'))
## [1] 0.0297354 (on my device)

How can I get the correct x_off and y_off values when working with a log-scaled axis?

Answer 1

Here's a version that works with log-scale and linear scale axes. The trick is to express line locations in npc coordinates rather than user coordinates, since the latter are of course not linear when axes are on log scales.

line2user <- function(line, side) {
  lh <- par('cin')[2] * par('cex') * par('lheight')
  x_off <- diff(grconvertX(c(0, lh), 'inches', 'npc'))
  y_off <- diff(grconvertY(c(0, lh), 'inches', 'npc'))
  switch(side,
         `1` = grconvertY(-line * y_off, 'npc', 'user'),
         `2` = grconvertX(-line * x_off, 'npc', 'user'),
         `3` = grconvertY(1 + line * y_off, 'npc', 'user'),
         `4` = grconvertX(1 + line * x_off, 'npc', 'user'),
         stop("Side must be 1, 2, 3, or 4", call.=FALSE))
}

And here are a couple of examples, applied to your setup_plot with mar=c(5, 5, 5, 5):

setup_plot()
axis(1, line=5)
axis(2, line=5)
abline(h=line2user(0:4, 1), lty=3, xpd=TRUE)
abline(v=line2user(0:4, 2), lty=3, xpd=TRUE)
abline(h=line2user(0:4, 3), lty=3, xpd=TRUE)
abline(v=line2user(0:4, 4), lty=3, xpd=TRUE)

setup_plot(log='x')
axis(1, line=5)
axis(2, line=5)
abline(h=line2user(0:4, 1), lty=3, xpd=TRUE)
abline(v=line2user(0:4, 2), lty=3, xpd=TRUE)
abline(h=line2user(0:4, 3), lty=3, xpd=TRUE)
abline(v=line2user(0:4, 4), lty=3, xpd=TRUE)

setup_plot(log='y')
axis(1, line=5)
axis(2, line=5)
abline(h=line2user(0:4, 1), lty=3, xpd=TRUE)
abline(v=line2user(0:4, 2), lty=3, xpd=TRUE)
abline(h=line2user(0:4, 3), lty=3, xpd=TRUE)
abline(v=line2user(0:4, 4), lty=3, xpd=TRUE)

setup_plot(log='xy')
axis(1, line=5)
axis(2, line=5)
abline(h=line2user(0:4, 1), lty=3, xpd=TRUE)
abline(v=line2user(0:4, 2), lty=3, xpd=TRUE)
abline(h=line2user(0:4, 3), lty=3, xpd=TRUE)
abline(v=line2user(0:4, 4), lty=3, xpd=TRUE)