squarenet 0.2.4

Sparse local operations for point clouds in any dimension.

---

❒ 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)

---

🚀 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

🧠 Quick Start

-> exemples/00_getting_started.ipynb

from squarenet import SquareNet
import numpy as np

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

IJKL = (5, 11, 7, 13)
sqnet = SquareNet(IJ_=IJKL) # Define grid dimensions, here 4D
sqnet.fit(points)

# Map any property of the points to the grid e.g. the norm, could be anything else
Xpts = np.linalg.norm(points, axis = 1) #(N, *C)
Xmap = sqnet.map(Xpts) #(5, 11, 7, 13, *C)
Xrec = sqnet.invert_map(Xmap)   #(N, *C) 

Compute Local Views

# views enhance Xpts with a view in a rectangular neighborhood 
# (in the grid) with radius *wr and size *ws = 2wr+1
Xview = sqnet.views(Xpts, wr=5, invert_map = True) #(N, *C, *ws)

🗺️ Visualizing the Mapping

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

sqnet = SquareNet(IJ_=(400, 400))
sqnet.fit("france") #require !pip install shapely
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