Quadratic equation to find the interception point of 2 moving targets. http://gamedev.stackexchange.com/questions/25277/how-to-calculate-shot-angle-and-velocity-to-hit-a-moving-target

QuadraticInterception.scala

import math._

object QuadraticInterception extends App {
  val me = Pos(100, 100)
  val tgt = Pos(400, 400)
  val tgtDirection = Pos(0, -100)

  println(me.intercept(tgt, tgtDirection))

  case class Pos(x: Int, y: Int) {
    def dist2(p: Pos) = sqr(x - p.x) + sqr(y - p.y)
    def dist(p: Pos) = sqrt(dist2(p))
    def +(p: Pos) = Pos(x + p.x, y + p.y)
    def -(p: Pos) = Pos(x - p.x, y - p.y)
    def /(i: Int) = Pos(x / i, y / i)
    def *(i: Double) = Pos((x * i).toInt, (y * i).toInt)
    def scalar(p: Pos) = x * p.x + y * p.y

    def intercept(tgt: Pos, tgtDirection: Pos): Option[Pos] = {
      val mySpeed = 99
      val tgtSpeed = 100

      val toTarget = tgt - this
      val a = sqr(tgtSpeed) - sqr(mySpeed)
      val b = 2 * (tgtDirection scalar toTarget)
      val c = toTarget scalar toTarget

      val p = -b / (2.0 * a)
      val q = sqrt(sqr(b) - 4 * a * c) / (2 * a)
      val t1 = p - q
      val t2 = p + q
      if (t1 > 0 || t2 > 0) {
        val t = if (t1 > t2 && t2 > 0) t2 else t1
        val aimSpot = tgt + tgtDirection * t
        Some(aimSpot)
      } else None
    }
  }

  def sqr(i: Long) = i * i
}