squarenet 0.1.1

Sparse local operations for point clouds in any dimension.

---

🟦 SquareNet

SquareNet maps unstructured point clouds into structured D-dimensional grids. By building a bijective mapping, it replaces expensive spatial queries ($k$-NN, radius search) with simple array slicing.

---

🚀 Why SquareNet?

• Speed: $O(N)$ local operations via vectorized sliding windows.
• Memory: Contiguous memory access instead of irregular spatial lookups.
• Simplicity: Pure NumPy-based logic, no heavy spatial dependencies.

📦 Installation

pip install squarenet
# To include the demo (shapely)
pip install "squarenet[demo]"

🧠 Quick Start

from squarenet import SquareNet
import numpy as np

# Initialize and Fit
N = 5*11*7*13
d = 4
IJKL = (5, 11, 7, 13)

sqnet = SquareNet(IJ=IJKL) # Define grid dimensions, here 4D
points = np.random.rand(N, d)
sqnet.fit(points)

# Map cloud index to grid index: (N, *) -> (5, 11, 7, 13, *)
grid_X = sqnet.map(cloud_X)
cloud_X = sqnet.invert_map(grid_X)   (5, 11, 7, 13, *) ->  (N, *) 

# Compute Local Gram Matrix (Sparse)
# Only computes interactions within a local window
G = sqnet.gram(points, ws=5)

🗺️ Visualizing the Mapping

You can use the built-in checkerboard to verify neighborhood preservation:

sqnet = SquareNet(IJ=(200, 200))
sqnet.fit("france")
sqnet.checkerboard()

📈 Key Applications

• Point Cloud Processing: Fast local feature aggregation.
• Kernel Methods: Efficient sparse approximation of large kernels.
• Deep Learning: Pre-structuring irregular data for CNN/Transformer inputs.

---

License: MIT | Author: ArmanddeCacqueray