sclass QuadTreeBitMatrix > WidthAndHeightImpl {
  sclass Node {}
  sclass Prim > Node {}
  sclass On  > Prim {} static new On  on;
  sclass Off > Prim {} static new Off off;
  sclass Composite > Node {
    Node a, b, c, d;
  }
  
  Node root = off;
  
  *() {}
  *(int *width, int *height) {}
  
  int half(int x) { ret roundUpToPowerOfTwo((x+1)/2); }
  int halfX(Rect r) { ret r.x+half(r.w); }
  int halfY(Rect r) { ret r.y+half(r.h); }
  
  Rect rectA(Rect r) { ret rect(r.x, r.y, half(r.w), half(r.h)); }
  Rect rectB(Rect r) { ret rectFromPoints(r.x+half(r.w), r.y, r.x2(), r.y2()); }
  Rect rectC(Rect r) { ret rectFromPoints(r.x, r.y+half(r.h), r.x+half(r.w), r.y2()); }
  Rect rectD(Rect r) { ret rectFromPoints(r.x+half(r.w), r.y+half(r.h), r.x2(), r.y2()); }
  
  bool get(int x, int y) {
    Node node = root;
    Rect r = rect(0, 0, width, height);
    while (node instanceof Composite) {
      cast node to Composite;
      int hx = halfX(r), hy = halfY(r);
      node = y < hy
        ? x < hx ? node.a : node.b
        : x < hx ? node.c : node.d;
    }
    ret node == on;
  }
  
  // dev.
  void set(int x, int y, bool b) {
    Node parent = null, node = root;
    Rect r = rect(0, 0, width, height);
    
    if (node instanceof Composite) {
      cast node to Composite;
      int hx = halfX(r), hy = halfY(r);
      node = y < hy
        ? x < hx ? node.a : node.b
        : x < hx ? node.c : node.d;
    }
    if (node == on) == b) et;
  }
}