private def init(window: Window): Grid = {
    val dx = (window.upRight._2 - window.lowLeft._2) / window.number
    val dy = (window.upRight._1 - window.lowLeft._1) / window.number
    def buildNodes(acc: Seq[Node], coor: (Int, Int)) = {
      val x = dx * coor._2 + window.lowLeft._2
      val y = dy * coor._1 + window.lowLeft._1
      coor match {
        case (r, c) if r == 0 => acc :+ Node(window.low(x, y), x, y)
        case (r, c) if c == 0 => acc :+ Node(window.left(x, y), x, y)
        case (r, c) if r == window.number - 1 => acc :+ Node(window.up(x, y), x, y)
        case (r, c) if c == window.number - 1 => acc :+ Node(window.right(x, y), x, y)
        case _ => acc :+ Node(0, x, y)
      }
    }
    val nodes = (0 until window.number) map { row => (0 until window.number) map { col => (row, col) } }
    val grid = nodes map { nodes => nodes.foldLeft(Seq[Node]())(buildNodes) }
    Grid(grid)
  }