mortie

Mortie is a library for applying morton indexing to healpix grids. Morton numbering (also called z-ordering) facilitates several geospatial operators such as buffering and neighborhood look-ups, and can generally be thought of as a type of geohashing.

This particular implementation focuses on hierarchical healpix maps, and is mostly inspired from this paper.

Performance

Mortie uses Rust-accelerated morton indexing functions for high performance. The Rust implementation provides dramatic speedups:

Dataset Size	Rust	Python (reference)	Speedup
1,000 values	1.93 ms	4.14 ms	2.1x
100,000 values	1.85 ms	410.59 ms	222x
1.2M coordinates	102.51 ms	5.1 sec	50x

Pre-built wheels are available for Linux, macOS, and Windows. The Rust extension is required and is included in all pip-installed wheels.

Installation

pip install mortie

For development builds with Rust, see BUILDING.md.

Spatial Buffer

Mortie provides a morton_buffer function for expanding a set of morton cells by a configurable border ring. This is useful for... well, buffering.

import numpy as np
import mortie

# Convert coordinates to morton cells at order 6
cells = np.unique(mortie.geo2mort(lats, lons, order=6))

# Expand by 1-cell ring (8-connected neighbors)
border = mortie.morton_buffer(cells, k=1)
expanded = np.union1d(cells, border)

All input indices must be at the same order. The function returns only the new border cells, not the input cells themselves.

Polygon Coverage

morton_coverage computes the set of morton indices that cover a polygon defined by lat/lon vertices. It uses a top-down hierarchical descent over the HEALPix tree: starting from the 12 base cells it keeps cells inside the polygon, prunes cells outside, and refines cells the boundary passes through down to the requested order. Cost scales with the polygon's boundary, not its area — interior regions collapse to a few coarse cells, so a large but simple polygon is cheap. Vertex count still matters (a one-time O(V) edge/seed setup, plus per-boundary-cell work that grows with local edge density), but far more gently than the old O(cells × vertices) approach — a 1M-vertex polygon covers in ~1 s, roughly 40× faster than before.

import mortie

# Define polygon vertices (lat, lon in degrees)
lats = [40.0, 40.0, 50.0, 50.0]
lons = [-125.0, -115.0, -115.0, -125.0]

# Flat cover — every cell at order 6
cells = mortie.morton_coverage(lats, lons, order=6)

# Compact Multi-Order Coverage — coarse interior, fine boundary (usually far smaller)
moc = mortie.morton_coverage_moc(lats, lons, order=10)

# Adaptive boundary: stop at an angular tolerance, or cap the cell count
moc_tol = mortie.morton_coverage_moc(lats, lons, order=10, tolerance=0.5)   # degrees
moc_bud = mortie.morton_coverage_moc(lats, lons, order=10, max_cells=500)

The function handles concave polygons, antimeridian-crossing polygons, and polar regions. Multipart polygons and holes are supported by passing a list of rings (even-odd fill): disjoint parts are unioned and a nested ring carves a hole, so a donut is [outer, hole]. Helpers compress_moc (merge 4-sibling groups) and moc_to_order (densify a MOC to a flat order) round out the API. See docs/coverage_methods.md for the full method/precision/runtime trade-offs and a benchmark matrix.

Dependencies

numpy. All HEALPix operations use the Rust-native healpix crate bundled in the compiled extension — no external HEALPix library is needed.

Funding

Initial funding of this work was supported by the ICESat-2 project science office, at the Laboratory for Cryospheric Sciences (NASA Goddard, Section 615).

References

[1] Youngren, Robert W., and Mikel D. Petty. "A multi-resolution HEALPix data structure for spherically mapped point data." Heliyon 3.6 (2017): e00332. doi: 10.1016/j.heliyon.2017.e00332