squarenet 1.1.1

Gridification for point clouds in any dimension (fast greedy optimal transport through Cartesian Sort).

---

❒ SquareNet

SquareNet maps unstructured point clouds to structured grids through a bijective transformation. It replaces expensive spatial queries (k-NN, radius search) with super fast sliding window operations. Think of it as a powerful alternative to kd-trees, voxelization, rasterization and neighborhood graphs. ✔ Works in any dimension ✔ Handles non-convex geometries ✔ Scales to millions of points (fast processing) ✔ Support for Pytorch and Jax

Animation ✨

🚀 Why SquareNet?

• Speed: $O(N)$ local operations via vectorized sliding windows.
• Memory: Contiguous memory access instead of irregular spatial lookups.
• Simplicity: No heavy spatial dependencies, pure native sorting logic

📦 Installation

pip install squarenet

🧠 Quick Start

-> 00_getting_started.ipynb

from squarenet import SquareNet
import numpy as np

# Initialize and Fit
N = 5*11*7*13
d = 4
X = np.random.rand(N, d)

IJKL = (5, 11, 7, 13)
sn = SquareNet(gridshape=IJKL)# Define grid dimensions, here 4D
sn.fit(X)

# Map any data indexed on the points e.g (N, *C) to the grid 
Xgrid = sn.map(X) #(5, 11, 7, 13, 4)
#and back
sn.invert_map(Xgrid)   # = X

Query neighbors

# d-dimensional query method
# approximate but super fast
sn.search_sorted(point) 

🗺️ Visualizing the Mapping

sn = SquareNet(gridshape=(400, 400))
sn.fit("france") 
sn.plot()

📈 Key Applications

• Point-Cloud Processing: Fast spatial querys (neighbors, intersections...).
• Kernel Methods: Efficient approximation of large kernels (sparse Gram matrix).
• Deep Learning: Tensorization of flat datasets (CNN-Ready)

-----

License: MIT | Author: ArmanddeCacqueray