class Vector2D protected[mathutil] (val x: Double, val y: Double) {
  val length: Double = math.sqrt(x * x + y * y)

  def unary_-  : Vector2D = new Vector2D(-x, -y)
  def normalize: Vector2D = new Vector2D(x / length, y / length)

  /** Returns the normal vector */
  def normal: Vector2D = new Vector2D(-y, x)

  def +(that: Vector2D): Vector2D = new Vector2D(x + that.x, y + that.y)
  def -(that: Vector2D): Vector2D = new Vector2D(x - that.x, y - that.y)
  def *(scalar: Double): Vector2D = new Vector2D(x * scalar, y * scalar)
  def /(scalar: Double): Vector2D = new Vector2D(x / scalar, y / scalar)

  /** Returns the scalar product */
  def *(that: Vector2D): Double = x * that.x + y * that.y

  /** Returns the angle in degrees */
  def \/(that: Vector2D): Double =
    math.toDegrees(math.acos((this * that) / (length * that.length)))
}