//
// function to compute bounding box of two rectangles
//
// rectangles are represented using the "graphics convention":
//   (y, x, width, height)
// where (y, x) is the top left corner in the graphics coordinate system,
//   in which the y axis is horizontal and runs left to right 
//   and the x axis is vertical and runs top to bottom
// 
def bbox(rect1:(Int,Int,Int,Int), rect2:(Int,Int,Int,Int)) : (Int,Int,Int,Int) =
{
  // pull out components of the two input rectangles
  val (y1, x1, w1, h1) = rect1
  val (y2, x2, w2, h2) = rect2

  // find top left corner of bounding box
  val y = y1 min y2
  val x = x1 min x2

  // find bottom right corner of bounding box
  val yBR = (y1 + w1) max (y2 + w2)
  val xBR = (x1 + h1) max (x2 + h2)

  // find width, height
  val w = yBR - y
  val h = xBR - x

  // return bounding box as rectangle
  (y, x, w, h)
}

//
// utility function to display elements of rectangle in more-readable form
//
def showRectangle(r:(Int,Int,Int,Int)) {
  val (y,x,w,h) = r
  println("top left corner y (horizontal) " + y)
  println("top left corner x (vertical) " + x)
  println("width " + w)
  println("height " + h)
  println("bottom right corner y (horizontal) " + (y+w))
  println("bottom right corner x (vertical) " + (x+h))
}