R-raster extraction along SpatialLine: relate extracted values to actual distance - r

Question

When extracting values of a raster along a SpatialLine in R, how to relate these values to the actual distance along this line?
Suppose I want to extract the value of the R logo along the following line:
library(raster)
r <- raster(system.file("external/rlogo.grd", package="raster"))
x=c(5, 95)
y=c(20, 50)
line = SpatialLines(list(Lines(Line(cbind(x,y)), ID="a")))
plot(r)
plot(line, add=TRUE)
I can extract the values and plot them - but how to replace the x values (1:length(vals) below) by the actual distance (starting e.g. at 0 from the left side of the line)?
vals <- extract(r, line)[[1]]
plot(1:length(vals), vals, type='o')
I could combine the extraction of the cells with xyFromCell to get the coordinates of the extracted cells as suggested here, but it is not clear to me how to go further.

Answer 1

I'm not sure what you're exactly asking, but if you looking for distances between the leftmost coordinate of the line segment and the centres of the cells which the line passes through, then you can find the distances like this:
x <- extract(r, l, cellnumbers=TRUE)[[1]]
xy <- xyFromCell(r, x[,1]) # get cell coordinates where the line passes
start <- xy[which.min(xy[,1]),] # leftmost coordinate of the line
d <- apply(xy, 1, function(x, start) sqrt(sum((x-start)^2)), start=start) # find distances between the line segment start and the cells
plot(1:length(d), d, type='o')

Answer 2

Here is a solution (partly on the basis of #jvj's input) through an attempt to compute the orthogonal projections of the cell centres provided by raster::extract on the line and then compute the distances along the line.
(This is an R-beginners script, likely easily improvable, but seems to work (and is of course only for rasters with projection respecting distances))
vals <- extract(r, line, cellnumbers=TRUE)[[1]]
cellsxy <- xyFromCell(r, vals[,1]) # coordinates of intersected cells (likely not ON the line)
linexy = spsample(line, 1000, "regular") # get the line as points
linexy <- matrix(cbind(linexy$x, linexy$y), ncol=2) # easier than Spatial object for later
orthoproj <- c() # to store the orthogonal projections of cells centres on the line
for (i in 1:nrow(cellsxy)) {
xypt = cellsxy[i,]
min.index <- which.min(spDistsN1(linexy, xypt))
orthopt <- linexy[min.index, ] # orthogonal projections = smaller distance
orthoproj <- c(orthoproj, c(orthopt[1], orthopt[2]))
}
orthoproj <- matrix(orthoproj, ncol=2, byrow=T)
orthoproj <- data.frame(x=orthoproj[,1], y=orthoproj[,2])
orthoproj <- orthoproj[order(orthoproj[,1]),] # reorder with increasing distance
orthoproj <- data.frame(x=orthoproj$x, y=orthoproj$y)
start <- linexy[which.min(linexy[,1]),] # leftmost coordinate of the line
dists <- apply(orthoproj, 1,
function(xy, start) sqrt(sum((xy-start)^2)),
start=start) # distances between 'start' and the orthogonal projections
plot(dists, rev(vals[,2]), type='o') # !! beware: order of 'vals' and 'dists'
# depending on the order in which cellnumbers are returned
# in raster::extract and the shape of your line !!