package mathutil {
  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)))
  }

  object Position {
    def apply(that: Vector2D): Vector2D       = that
    def apply(x: Double, y: Double): Vector2D = new Vector2D(x, y)
  }

  object Direction {
    def apply(that: Vector2D): Vector2D       = apply(that.x, that.y)
    def apply(x: Double, y: Double): Vector2D = new Vector2D(x, y).normalize
  }
}