Squarenet gridification as a bridge between unstructured point clouds and Taichi stencil kernel

[ArmanddeCacqueray]

Hi everyone,

Modern ML frameworks are extremely efficient on regular tensor grids, but many real-world datasets come as unstructured point clouds. The challenge is to bridge these two representations while preserving geometric structure.

I've been working on SquareNet, a bijective gridification algorithm for point clouds.
Core idea: map an unstructured point cloud to a regular tensor through a bijective assignment—one point → one cell, invertible and neighborhood-preserving: X(N, D) → X(n₁, n₂, …, n_d, D) with optional padding when N ≠ n₁ × n₂ × … × n_d, and back. The Cartesian Sort algorithm makes this scalable: millions of 2D/3D points in seconds, fully vectorized, on both CPU and GPU (with PyTorch). Each point in the cloud is assigned a unique multi-index, and together these multi-indices form a regular tensor that is spatially coherent and ready for further geometric processing.

SquareNet is, for example, the underlying representation behind following blue-noise sampling method RGBN, enabling fast many-body simulations that scale to 1M particles.

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Connection to Taichi

On the SquareNet tensor representation, neighbor access reduces to simple [i±k, j±k] indexing—no kd-tree, no graph traversal. The gridification procedure is very flexible: holes, peaks, folds, and clusters are all supported. The global geometry of the point cloud is preserved while producing a tensor that is ready for efficient stencil operations in Taichi. Since Taichi makes stencil-based algorithms so natural and efficient in Python, I thought it could be exciting to bring that same programming model to arbitrary point clouds.

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Question

I'm curious whether this kind of bijective gridification preprocessing has been explored in the Taichi ecosystem, or whether there would be interest in an example benchmarks or tutorial combining SquareNet gridification + Taichi stencil/MPM kernels. I'd be happy to contribute a notebook or example if the community finds it useful.