calculateInterceptShotPosition.lua

function calculateInterceptShotPosition(pShooter, pTarget0, vTarget, sProjectile)
  local R = pTarget0 - pShooter
  local a = vTarget.x^2 + vTarget.y^2 - sProjectile^2
  local b = 2 * (R.x * vTarget.x + R.y * vTarget.y)
  local c = R.x^2 + R.y^2

  if R:len2() < 1 then
    return nil
  end

  if math.abs(a) < 1 then
    if math.abs(b) < 1 then
      return nil
    end

    return -c/b;
  end

  local discriminant = b*b - 4 * a * c;

  if discriminant < 0 then
    return nil
  end

  if discriminant > 0 then
    local quad = math.sqrt(discriminant);
    local t1 = (-b + quad)/(2*a);
    local t2 = (-b - quad)/(2*a);

    if (t1 < 0) and (t2 < 0) then
      return nil
    elseif t2 < 0 and t1 >= 0 then
      return t1
    elseif t1 < 0 and t2 >= 0 then
      return t2
    elseif t1 < t2 then
      return t1
    else
      return t2
    end
  end

  return -b / (2*a);
end