friend ostream &operator<<(ostream &os, const PointDesc &p) {
    os << "PointDesc{"
       << "ijk:" << "{" << p.i << "," << p.j << "," << p.k << "}, "
       << "xyz:" << "{" << p.x << "," << p.y << "," << p.z << "}, "
       << "idx:" << p.idx << ", "
       << "dijk:" << "{" << p.di << "," << p.dj << "," << p.dk << "}"
       << "}";
    return os;
  }