Error of merging and splitting blocks

[Siwensun]

Thanks for your great job. The performance is solid and consistent in my own experiments. But I still have some confusion about the calculation of "error of merging and splitting blocks" in your code and paper.

1. In the paper, the error of merging blocks is Ns times the current error if parent's error is unavailable. However, all the siblings will contribute Ns times error if merging, which means the error of merging blocks will be Ns^2 compared with the current error in total. So, how could the error be consistent across scales?
2. In the paper, the error of splitting blocks is the sum of children's errors if children's error is available. But in your code, it seems to be Ns times of the sum of children's errors as shown below.

err_children = np.sum([child.err for child in self.children])
err_split = area * err_children    # here, area is parent's area

3. Why the block volume is still block_size**2 in OctTree in the code?

Hope you can correct my understanding of this work. Thank you very much!