Can you fit a rectangle in a polygon?

gistfile1.r

require(rgeos)
require(sp)

makeRect <- function(origin, l1, l2, angle){
  sa = sin(angle)
  ca = cos(angle)
  x=origin[1] + c(0,l1*ca,l1*ca-l2*sa,-l2*sa,0)
  y=origin[2] + c(0,l1*sa,l1*sa+l2*ca,l2*ca,0)
  return(SpatialPolygons(list(Polygons(list(Polygon(cbind(x,y))),"Rectangle"))))
  return(cbind(origin[1]+x,origin[2]+y))
}


tryRandom <- function(w,h,p,n,all=TRUE){
  found=FALSE
  pb = bbox(p)
  if(all){
    foundRects = list()
  }
  for(i in 1:n){
    xr = runif(1,pb[1,1],pb[1,2])
    yr = runif(1,pb[2,1],pb[2,2])
    angle = runif(1,0,2*pi)
    rrect = makeRect(c(xr,yr),w,h,angle)
    if(gContains(p,rrect)){
      found=TRUE
      if(!all){
        break
      }else{
        foundRects[[length(foundRects)+1]]=rrect
      }
    }
  }
  if(found){
    if(all){
      return(foundRects)
    }else{
      return(rrect)
    }
  }else{
    warning("No rectangle fit")
    return(NA)
  }
  
}

# then, using the natural earth lakes data:
# > plot(lakes[125,],asp=1)

# lets see if we can put a 0.1 x 0.003 (degrees!) runway in:
# > rfit = tryRandom(0.1,0.003,lakes[125,],100)
# ignore these warnings, its because we havent set the CRS:
# There were 50 or more warnings (use warnings() to see the first 50)
# if there isn't a warning about not finding any fitting rectangles:
# > invisible(lapply(rfit,plot,add=TRUE,lwd=2,col="#80808080"))