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HilbertSFC

Ultra-fast 2D & 3D Hilbert space-filling curve encode/decode kernels for Python.

2D Hilbert curves for nbits 1..5 3D Hilbert curves animation grid for nbits 1..4

2D Hilbert curves (nbits 1..5) and 3D Hilbert curves (nbits 1..4).

New in v0.3.0: PyTorch API + GPU-accelerated kernels with Triton!
New in v0.4.0: Morton/z-order curves

This library is performance-first and implemented entirely in Python. It provides fast Hilbert encode/decode kernels for both CPU and GPU, with convenient high-level APIs for NumPy and PyTorch, low-level kernel accessors, and clean integration with torch.compile for fusion with surrounding operations. For completeness, it also includes Morton/z-order curve kernels.

The hot kernels are JIT-compiled with Numba (CPU) and Triton (GPU) and tuned for:

  • Branchless, fully unrolled inner loops
  • Small, L1-cache-friendly lookup tables (LUTs)
  • Reduced dependency chains for better ILP and MLP (e.g. state-independent lookups)
  • Multi-threading for batch processing
  • SIMD via LLVM vector intrinsics (CPU)
  • Reduced register pressure (GPU)

When and why to use HilbertSFC?

If you have 2D or 3D coordinates and need a 1D ordering that preserves spatial locality, the Hilbert space-filling curve is a strong choice: points that are close in Euclidean space tend to remain close after mapping to a Hilbert index. HilbertSFC is designed for high-throughput workloads, such as spatial indexing (GIS/databases), scientific computing, and machine/deep learning, where Hilbert curve mapping performance matters.