Find the minimum arbitrarily oriented bounding box from the convex hull

obox.scala

case class Point(x: Double, y: Double)

def orientedBoundingBox(hull: Seq[Point]) = {
  val (area, rect) = (1 until hull.size).map { i =>
    val (u, v) = (hull(i-1), hull(i))
    val angle = math.atan((u.x - v.x) / (u.y - v.y))
    
    val rotated = hull.map(rotate(_, angle))
    val xs = rotated.map(_.x)
    val ys = rotated.map(_.y)
    val (x1, y1) = (xs.min, ys.min)
    val (x2, y2) = (xs.max, ys.max)

    val area = (x2 - x1) * (y2 - y1)
    val p1 = rotate(Point(x1, y1), -angle)
    val p2 = rotate(Point(x1, y2), -angle)
    val p3 = rotate(Point(x2, y2), -angle)
    val p4 = rotate(Point(x2, y1), -angle)
    (area, (p1, p2, p3, p4))
  }.minBy(_._1)
  rect
}

def rotate(p: Point, angle: Double) = {
  val cs = math.cos(angle)
  val sn = math.sin(angle)
  val x = p.x * cs - p.y * sn
  val y = p.x * sn + p.y * cs
  Point(x, y)
}