Space-filling-nets

The discrete space-filling (or serialization) problem consists in organizing spatial data so that geometric processing can be performed efficiently.

Space-filling curves solve this by mapping multidimensional data to a one-dimensional ordering. However, this unfolding can break local spatial relationships: nearby points may become distant in the resulting order.

This project is about Space Filling Nets: instead of reducing the data to one dimension, they construct a regular multidimensional grid passing through all points. Each point receives a multidimensional index $[i,j,k,\ldots]$, preserving the spatial structure of the original point cloud.

It is split into two repositories:

• Squarenet: Python implementation for converting $[N,D]$ point clouds into structured grids.
• Cartesian Grid Sort: mathematical details of the optimization algorithm.