Triggering Implicit search by emulating double dispatch using simple dispatch

Point.scala

object Point {

  trait PointAdder[P2] {
    def add(p2: P2): Point3D
  }

  case class Point2D(x: Int, y: Int)
  case class Point3D(x: Int, y: Int, z: Int)

  implicit class Point2Adder(p1:Point2D) extends PointAdder[Point2D] {
    def add(p2: Point2D): Point3D = Point3D(p1.x + p2.x, p1.y + p2.y, 0)
  }

  implicit class Point3DAdder(p1:Point3D) extends PointAdder[Point3D] {
    def add(p2: Point3D): Point3D = Point3D(p1.x + p2.x, p1.y + p2.y, p1.z + p2.z)
  }

  implicit class Point2DPoint3DAdder(p1:Point2D) extends PointAdder[Point3D] {
    def add(p2: Point3D): Point3D = Point3D(p1.x + p2.x, p1.y + p2.y, p2.z)
  }

  implicit class Point3DPoint2DAdder(p1:Point3D) extends PointAdder[Point2D] {
    def add(p2: Point2D): Point3D = Point3D(p1.x + p2.x, p1.y + p2.y, p1.z)
  }

  def main(args: Array[String]) {
    val point1 = Point2D(1, 2)
    val point2 = Point3D(1, 2, 3)

    println(point1.add(point2))
  }

}