Outline of overlapping shape tester...

Overlap.scala

case class Point(x:Double,y:Double)
case class Rectangle(p1:Point,p2:Point) {
  def overlaps(that:Rectangle):Boolean =
    // Rectangle overlap test
}

trait Overlapable {
  def boundingRectangle:Rectangle
  def convexHulls:Seq[Seq[Point]]
  def overlaps(that:Seq[Seq[Point]]):Boolean
}

object Rectangle {
  implicit def rectangleOverlapable(r:Rectangle):Overlapable = new Overlapable {
    def boundingRectangle:Rectangle = r
    def convexHulls:Seq[Seq[Point]] = Seq(Seq(Point(r.p1.x,r.p1.y),
                                              Point(r.p1.x,r.p2.y),
                                              Point(r.p2.x,r.p2.y),
                                              Point(r.p2.x,r.p1.y)))
    def overlaps(that:Seq[Seq[Point]]):Boolean =
      that.foldLeft(False) {
        (s,hull) => hull.foldLeft((s,hull(0))) {
          case ((r,prevPt),pt) => {
            // psuedo code
            if (lineIntersects(prevPt,pt,r)) (r || True,pt)
            else (r || False,pt)
          }
        }
      }
  }
}

object Test {
  def overlaps(o1:Overlapable,o2:Overlapable):Boolean = 
    if (o1.boundingRectangle.overlaps(o2.boundingRectangle)) o1.overlaps(o2)
    else false
}

object Main {
  def main(args:Array[String]):Unit {
    val r1 = Rectangle(Point(<x1>,<y1>),Point(<x2>,<y2>))
    val r2 = Rectangle(Point(<x3>,<y3>),Point(<x4>,<y4>))
    println(Test.overlaps(r1,r2))
  }
}