How to find the coordinates of the intersection points between two SpatialLines objects (or SpatialLines and SpatialPolygon edges)

I am try to find the co-ordinates of points where SpatialLines cross the edge of a SpatialPolygon. I have searched and searched, but can only find results such as over which tell me which lines cross but not where, or gIntersection which cut the lines down to sections within the polygon.

Here is a subset of my data:

# Required packages
library(rgeos)
library(sp)
library(maptools)
library(raster)
library(grDevices)

# Create convex hull
# Points to create hull
Hull_pts <- structure(list(x = c(38.87584, 38.89215, 38.87062, 38.86157, 38.72808, 38.22315, 38.12702, 38.05936, 37.95169, 37.96915, 38.14758, 38.22325, 38.34001, 38.6394, 38.6447),
y = c(4.17092, 4.05521, 3.93639, 3.9168, 3.85601, 3.89487, 4.17066, 4.38951, 4.98351, 4.99706, 5.12187, 5.17153, 5.16003, 4.77422, 4.76607)),
.Names = c("x", "y"),
row.names = c(1574L, 1540L, 1490L, 1482L, 1457L, 1473L, 294L, 1718L, 1131L, 974L, 2838L, 2101L, 111L, 1914L, 1909L),
class = "data.frame")

# Create SpatialLines of Hull
Hull_lines <- list()
for (i in 1:length(Hull_pts\$x)-1) {
Hull_lines[i] <- Lines(list(
Line(rbind(Hull_pts[i,1:2], Hull_pts[i+1,1:2])))
, ID=i)
Hull_lines <- Lines(list(
Line(rbind(Hull_pts[15,1:2], Hull_pts[1,1:2])))
, ID="15")
}
# Make it a SpatialLines object
Hull_spLines <- SpatialLines(Hull_lines, proj4string = CRS("+proj=longlat +datum=WGS84 +ellps=WGS84 +towgs84=0,0,0"))

# Create SpatialPolygon of Hull (as alternative)
Hull_poly <- SpatialPolygons(list(
Polygons(list(
Polygon(Hull_pts))
, "ID"))
, proj4string=CRS("+proj=longlat +datum=WGS84"))

# Outer points
Site <- c(seq(1,10,1))
x <- c(38.21467,37.22799, 38.22852, 39.42621, 37.85457, 38.10600, 37.84077, 38.02475, 38.07228, 37.40716)
y <- c(6.327209, 5.691638, 6.237393, 5.382760, 6.042394, 6.078254, 6.007846, 5.973651, 6.044092, 5.746368)
Sites <- data.frame(Site, x, y)
xy <- Sites[2:3]
Sites2 <- SpatialPointsDataFrame(coords=xy, data=Sites)
projection(Sites2) <- CRS('+proj=longlat +datum=WGS84')
crs(Sites2) <- "+proj=longlat +datum=WGS84"

# Create lines
for (i in 1:length(Sites\$x)) {
Line(rbind(c(38.35419, 4.483533), Sites[i,2:3])))
, ID=Sites[i,1])
# Make SpatialLines object
Radial_spLines <- SpatialLines(Radial_lines, proj4string = CRS("+proj=longlat +datum=WGS84 +ellps=WGS84 +towgs84=0,0,0"))

# Plot
plot(Hull_spLines, xlim=c(37,40.5), ylim=c(2.5,6.6), axes=T)
points(Sites2\$x, Sites2\$y, pch=20, col="blue")
plot(Centre, add=T, col="red", pch="+", cex=1.5)

What I need to find are the co-ordinates of the points where the radial lines cross the polygon, as achieved here: http://uk.mathworks.com/help/map/ref/polyxpoly.html. I know this is possible in ArcGIS, and it doesn't seem like it should be that difficult.

Does anyone have any ideas?

Other users might be interested to know that I have managed to solve this. Rather than extracting the points directly, I used gIntersection in the rgeos package to truncate the lines to within the polygon, and then extracted the outer point.

# Cut radial lines at polygon edge
Centre_edge_lines <- gIntersection(Radial_spLines, Hull_poly, byid=T)

# Extract edge points from lines
for (i in 1:length(Sites\$x)){     # i-th list element, 2 and 4 are edge co-ords (1 and 3 are centre point)
Sites\$Edge_x[i] <- coordinates(Centre_edge_lines)[[i]][]
Sites\$Edge_y[i] <- coordinates(Centre_edge_lines)[[i]][]
}

Thanks for this answer. Just to clarify for other users, if you use coordinates(gIntersection(inputline, inputpoly)) it returns lists of coordinates. Each list is a line segment split by the polygon layer. If you then extract the first and last item from each of these list items, you will get the intersecting points. I wrote up a little generic function to to this. It could probably be simplfied, but it works.

intersectedline=gIntersection(SpatialLine, SpatialPoly, byid=T)

intersectpts=function(intersectedline, SpatialPoly){
x=2*rep(NA, length(intersectedline))
y=2*rep(NA, length(intersectedline))
xylast=cbind(x,y)
xy1=cbind(x,y)

for(i in 1:length(intersectedline)){
xy1[i,] <- coordinates(intersectedline)[[i]][][1,]
lastpoint=length(coordinates(intersectedline)[[i]][][,1])
xylast[i,] <- coordinates(intersectedline)[[i]][][lastpoint,]
i=i+1
}

xy=rbind(xy1,xylast)

plot(SpatialPoly)
lines(intersectedline, col="red")
points(xy, col="blue")

return(xy)
}