mortie

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Morty using 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.

Documentation

The full documentation — the generated API reference alongside the specification, interchange and coverage guides — is published at espg.github.io/mortie. Every page below is rendered there; the in-tree markdown links are the same content at the revision you are reading.

The normative encoding and conventions — the packed-word bit layout, the decimal string grammar, the order 0–29 resolution table, the morton-hive store layout, and the coverage-MOC serializations, all frozen for the 1.x series — are documented in docs/specification.md. Moving a packed word to and from the wider HEALPix ecosystem (cdshealpix / healpy (order, nested-pixel) pairs) is covered in docs/healpix_interchange.md.

Example notebooks

Runnable walkthroughs live in examples/; each opens on Binder from the badge in its first cell. Two of them need no downloads at all — morton_set_algebra.ipynb for the MOC boolean verbs, and toc_temporal_coverage.ipynb for the toc word (temporal order coverage: encoding, the conservative merge, the comparator-free sort, window predicates, and the UTC/GPS boundary).

Performance

Mortie's morton core is a Rust extension and the sole runtime path — there is no Python implementation to fall back on — so performance is reported as absolute throughput rather than a speedup ratio. Encoding (geo2mort) and decoding (mort2geo) run at tens of millions of morton indices per second on one core, staying within roughly 2× across orders 4–29.

See docs/benchmarks.md for the full cross-order table (raw encode / decode throughput and coverage timing at orders 4 / 12 / 18 / 29), regenerated in place by a committed script. Cell counts there are deterministic; timings are machine/run dependent.

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)

Latitude convention. Since 0.10 geo2mort and the coverage kernels take WGS84 geodetic latitude and map it to the authalic sphere, so cells are equal-area on the ellipsoid. Cell ids therefore differ from pre-0.10 mortie and from raw-spherical HEALPix libraries; pass latitude="geodetic-spherical" for the old behaviour. See docs/specification.md §9.

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

Project links

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Key dates

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  • Released:
Newer release available (0.9.11)

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Avatar for espg from gravatar.com espg

Credits

Author: Shane Grigsby (espg)

GitHub Statistics

Data verified by PyPI on Aug 17, 2026
The GitHub source repository was provided by the project maintainers and verified by PyPI at the time of upload. Stars, forks, and open issues/PRs are derived from that repository and have not been independently verified.

License

MIT License

Requires

Python >=3.10

Provides Extra

arro3 bench examples pandas pyarrow test

Tags

healpix geohashing morton index

Classifiers

Report project as malware

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