Here is some R code. The paper says that they randomly shifted the path. I take that to mean they randomly shifted each node of the path. They say that the path was shifted between 0 and 30 but I think that it only makes sense to shift between -30 and 30.


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taking advantage of center of gravity rotation in the maptools package

    library(sp)
    library(maptools)
    
    #create the nodes of a spatiallines object
    set.seed(2)
    path.mat<-matrix(c(seq(1,60,3),(seq(1,60,3))+ceiling(abs(rnorm(60)*5))),ncol=2)
    path<-Lines(list(Line(path.mat)),ID="p")
    
    
    #randomly shift nodes between 0 and 30km 
    shiftx<-sample(seq(-30,30,0.01),nrow(path.mat))
    shifty<-sample(seq(-30,30,0.01),nrow(path.mat))
    npath.mat<-cbind(path.mat[,1]+shiftx,path.mat[,2]+shifty)
    npath<-Lines(list(Line(npath.mat)),ID="np")
    npathSL<-SpatialLines(list(npath))
    
    #randomly rotate between 0 and 360 degrees
    npath.rot<-elide(npathSL,rotate=sample(seq(0,360,0.01),1),center=apply(bbox(npathSL),1,mean))
    npath.rot.mat<-coordinates(npath.rot)[[1]][[1]]
    npath.rot<-Lines(list(Line(npath.rot.mat)),ID="npr")
    
    
    npath.alllines<-SpatialLines(list(path,npath,npath.rot))
    plot(npath.alllines,col=c("black","red","green"))