ruibin-liu / despace Goto Github PK

As shown in the README example and the Google Colab example, we can construct Z-order or Morton space filling curve patterns. In my original plan for presenting examples, I thought I should construct Hilbert-type space filling curves first. In fact, a Hilbert.py file is already in the examples folder.

The question is, how should I modify the algorithm so that we can construct Hilbert-type space filling curves?

Thoughts:

1. Change the sort order when switching to a new direction.
2. For implementation details, I can either create a new function similar to sort_divide but for Hilbert-type pattern sorting/indexing or keep the same function but change the behavior when a key word like pattern_type is specified to either Morton or Hilbert.

Currently, the sorted data loses the original indexing formation and at first thought it looks hard to keep the indexing information on the fly. Keeping the original indexing information can be essential in any practical usage because each data point typically represents a different object in a N-d space. Examples are atoms in molecules, planets or stars in galaxies, or locations in a map. On the contrary, it might not be important in image vectorization and volumetric data vectorization. An option/way to keep the original indexing information is needed.

Thoughts:

1. Skip the index column in the numpy array when doing sort. Technically, this enables skipping any columns.
2. In implementation, should also provide an option to add an index column if not already there but required to keep the information to the original data.

Currently, I can only use scatter plot and color the data points with indices. It'll be more helpful if arrows are added between two adjacent points like those space filling curves.

Currently, points or coordinates are sorted by the first dimension first and then the next dimensions. This makes the indexing/pseudo-grouping start from a corner and end at the furthest opposite corner. There is nothing wrong to organize the data in this way but it's interesting whether we can start from an arbitrary point and pseudo group points around it according to their distances to it.

Thoughts:

1. Transform each data points around the chosen point by absolute difference in each direction;
2. Sort the transformed data;
3. Transform the data back to their original values but keep the indexing.