Line with intersection method

Line.scala

case class Vec(i: Double, j: Double) {
  def unary_- = Vec(-i, -j)

  def +(v: Vec): Vec = Vec(i + v.i, j + v.j)
  def -(v: Vec): Vec = Vec(i - v.i, j - v.j)
  def *(s: Double): Vec = Vec(i * s, j * s)

  def cross(v: Vec): Int = i * v.j - j * v.i
}

case class Line(a: Vec, b: Vec) {
  /**
   * Find the intersection of 2 line segments, if any. Naturally, the result
   * may be non-integer, and the return type accomodates this thusly.
   *
   * Algo background:
   * https://stackoverflow.com/questions/563198/how-do-you-detect-where-two-line-segments-intersect
   */
  def intersect(line: Line): Option[Vec] = {
    // Segment starts
    val p = a
    val q = line.a
    // Offset vectors
    val r = b - a
    val s = line.b - line.a
    // Cache
    val r_x_s = r cross s
    val qp_x_r = (q - p) cross r
    val qp_x_s = (q - p) cross s
    // Cases
    if (r_x_s == 0 && qp_x_r == 0) {
      // Lines are collinear, and so intersect if they have any overlap
      // TODO (adu): Return some reasonable point on this line.
      None
    } else if (r_x_s == 0 && qp_x_r != 0) {
      None
    } else if (r_x_s != 0) {
      val t = qp_x_s / r_x_s
      val u = qp_x_r / r_x_s
      if (0 <= t && t <= 1 && 0 <= u && u <= 1) {
        Some(Vec(p.i + t * r.i, p.j + t * r.j))
      } else None
    } else None
  }
}