sclass OnePath {
  new ByteBuffer steps;
  
  static final Pt[] directions = {
    pt(0, 0),
    pt(-1, -1),
    pt(0, -1),
    pt(1, -1),
    pt(1, 0),
    pt(1, 1),
    pt(0, 1),
    pt(-1, 1),
    pt(-1, 0)
  };
  
  *() {}
  *(S path) {
    int n = l(path);
    steps.allocate(n);
    for i to n:
      steps.add(parseDigit(path, i));
  }
  
  *(Iterable<Pt> points) {
    var it = iterator(points);
    if (empty(it)) ret;
    Pt p = it.next();
    while (it.hasNext()) {
      Pt p2 = it.next();
      steps.add(ptToDigit(ptMinus(p2, p)));
      p = p2;
    }
  }
  
  int size aka length() { ret steps.size(); }
  
  toString {
    ret singleDigitBytesToString(steps);
  }
  
  // includes first point, so returns length()+1 points in total
  ItIt<Pt> pointIterator(Pt startPt default origin()) {
    ret new ItIt<Pt> {
      int i = 0, n = length();
      Pt p = startPt;
      
      public bool hasNext() { ret i <= n; }
      
      public Pt next() {
        var p = this.p;
        if (i < n) this.p = translatePt(this.p, getStepAsPt(i));
        ++i;
        ret p;
      }
    };
  }
  
  Pt getStepAsPt(int i) {
    ret directions[steps.get(i)];
  }
  
  static int ptToDigit(Pt p) {
    ret p.y < 0 ? p.x < 0 ? 1 : p.x == 0 ? 2 : 3
      : p.y == 0 ? p.x < 0 ? 8 : p.x == 0 ? 0 : 4
      : p.x < 0 ? 7 : p.x == 0 ? 6 : 5;
  }
  
  Pt drift() {
    ret last(pointIterator());
  }
}