minimum area bounding rectangles

Shazam:

minbb<- function(pts){

   ch = chull(pts)
   pts=pts[ch,]
   np = nrow(pts)
   pts=rbind(pts,pts[1,])
   minbba = Inf ; bbth = NA; rotmin = NA
   for(i in 1:np){
     th = pi-atan2(pts[i+1,2]-pts[i,2],pts[i+1,1]-pts[i,1])
     prot = rotxy(pts,th)
     bba = diff(range(prot[,1])) * diff(range(prot[,2]))
     if(bba<  minbba){
       xyb=cbind(
         c(min(prot[,1]),max(prot[,1]),max(prot[,1]),min(prot[,1])),
         c(min(prot[,2]),min(prot[,2]),max(prot[,2]),max(prot[,2]))
         )
       xyb=rbind(xyb,xyb[1,])
       xyb= rotxy(xyb,-th)

       rotmin=prot
       minbba = bba
       bbth = th
     }
   }
   return(list(minbba=minbba,theta=th,pts=rotmin,box=xyb))

}

rotxy = function(pts,angle){
   co = cos(angle)
   si = sin(angle)
   cbind(co * pts[,1] - si * pts[,2], si * pts[,1] + co * pts[,2])
}

And usage:

  >  pts=cbind(runif(60),runif(60))
  >  bb=minbb(pts)
  >  plot(bb$box,type="l")
  >  points(pts)
  >  pts2=rotxy(pts,pi/1.6)
  >  bb2=minbb(pts2)
  >  plot(bb2$box,type="l")
  >  points(pts2)

Thanks Barry for the great tips.  The MATLAB code will be a huge help -
should be relatively straightforward to implement in R.

  Wrote this myself with a helpful rotate function nabbed from
spatstat. Could be optimised a bit, I reckon.

Barry