Remove holes in polygon

I am trying to solve the following problem in R :

I have a polygon object defined by a list l with two components x and y. The order defines the edges of the polygon.

For instance :

l=list(
    x=c(-1.93400738955091,0.511747161547164,1.85047596846401,-1.4963460488281,-1.31613255558929,-0.0803828876660542,1.721752044722,-0.724002506376074,-2.08847609804132,2.13366860069641),
    y=c(-1.02967154136169,1.53216851658359,-1.39564869249673,-1.21266011692921,1.6419616619241,-1.87141898897228,0.946605074767527,1.49557080147009,0.324443917837958,-0.517303529772633)
)
plot(l,type="b",pch=16)
points(l$x[c(10,1)],l$y[c(10,1)],type="b",pch=16)

Now what I am interested in is to keep only the outer boundary (but not the convex hull) of this polygon. The following picture highlights the point I'd like to keep

points(
    x=c(-1.13927707377209,-1.31613255249992,-1.3598262571216,0.511747159281619,0.264900107013767,0.671727215417383,-0.724002505140328,-1.93400738893304,-1.4811931364624,-1.45298543105533,-2.08847609804132,-1.40787406113029,-1.3598262571216,0.278826441754518,1.85047596733123,1.48615105742673,1.48615105742673,2.13366860069641,1.38016944537233,1.38016944537233,1.17232981688283,1.17232981688283,1.72175204307433,0.671727215417383,-1.496346, -0.08038289, -0.2824999),
    y=c(1.13914087952916,1.64196166071069,0.949843643913108,1.53216851597378,1.27360509238768,1.18229006681548,1.49557080106148,-1.02967154055378,-0.972634663817139,-0.525818314106921,0.324443915423533,0.188755761926866,0.949843643913108,-1.30971824545964,-1.3956486896768,-0.59886540309968,-0.59886540309968,-0.517303527559411,-0.367082245352325,-0.367082245352325,0.0874657083966551,0.0874657083966551,0.94660507315481,1.18229006681548,-1.21266,-1.871419,-1.281255),
    pch=16,
    col="red",
    cex=0.75
)

I am really clueless about whether there are tools to easily do that. The closest I have found is the polysimplify function in the polyclip package, which identifies all the points I need, but also outputs some points I do not need (inner points where segments intersect).

I actually found a solution (below). The following function does what I want but I am unsure why it works (and whether it may fail).

Actually the function below correctly identifies the point I want but outputs them in the wrong order, so it is still useless to me...

polygon.clean<-function(poly){
  require(polyclip)
  poly.cleaned=polysimplify(poly)
  x=unlist(sapply(poly.cleaned,function(x)x$x))
  y=unlist(sapply(poly.cleaned,function(x)x$y))
  x.src=x[!x%in%x[duplicated(x)]]
  y.src=y[!y%in%y[duplicated(y)]]
  poly.cleaned=poly.cleaned[sapply(poly.cleaned,function(poly.sub,x,y){
    any(poly.sub$x%in%x&poly.sub$y%in%y)
  },x=x.src,y=y.src)]

  x=unlist(sapply(poly.cleaned,function(x){
    res=x$x
    if(length(res)==4){
      res=vector()
    }
    res
  }))
  y=unlist(sapply(poly.cleaned,function(x){
    res=x$y
    if(length(res)==4){
      res=vector()
    }
    res
  }))
  x=c(x,x.src)
  y=c(y,y.src)
  tester=duplicated(x)&duplicated(y)
  x=x[!tester]
  y=y[!tester]
  list(x=x,y=y)
}

plot(l,type="b",pch=16)
points(l$x[c(10,1)],l$y[c(10,1)],type="b",pch=16)
points(polygon.clean(l),pch=16,cex=0.75,col="red")

Using rgeos routines, you first "node" your linestring to create all the intersections, then "polygonize" it, then "union" it to dissolve its insides.

First make a SpatialLines version of your data with duplicated first/last point:

library(sp)
library(rgeos)
coords = cbind(l$x, l$y); coords=rbind(coords,coords[1,])
s = SpatialLines(list(Lines(list(Line(coords)),ID=1)))

Then:

s_outer = gUnaryUnion(gPolygonize(gNode(s)))

Plot it thus:

plot(s,lwd=5)
plot(s_outer, lwd=2,border="red",add=TRUE)

If you want the coordinates of the surrounding polygon they are in the returned object and can be extracted with:

s_outer@polygons[[1]]@Polygons[[1]]@coords

#                x           y
# [1,]  0.27882644 -1.30971825
# [2,] -0.08038289 -1.87141899
# [3,] -0.28886517 -1.27867953

Assuming there's only one polygon, which might not be the case - suppose your line traces a figure-of-eight - then you'll get two polygons touching at a point. We don't know how free your jaggly line is to do things like that...