A5 Geospatial Extension for DuckDB

A high-performance DuckDB extension that provides functions for the A5 global geospatial index - a millimeter-accurate, equal-area indexing system for geospatial data.

✨ What is A5?

A5 is an innovative geospatial index that partitions the world into pentagonal cells based on a geodesic grid. Key features include:

• 🌍 Global Coverage: Seamless indexing from global to millimeter scales
• 📐 Equal Area: All cells at the same resolution level have identical area (OGC compliant)
• 🔍 31 Resolution Levels: From world-spanning cells to sub-30mm² precision
• ⚡ Fast Spatial Operations: Optimized for aggregation, filtering, and spatial joins

🎯 Use Cases

Spatial Data Aggregation

Group point data spatially to understand distributions:

-- Analyze restaurant density by A5 cells
SELECT a5_lonlat_to_cell(longitude, latitude, 15) as cell_id, COUNT(*) as restaurant_count
FROM restaurants
GROUP BY cell_id
ORDER BY restaurant_count DESC;

🚀 Quick Start

Installation

The a5 extension is available as a DuckDB Community Extension:

INSTALL a5 FROM community;
LOAD a5;

Basic Usage

-- Get the A5 cell for a specific location (latitude, longitude, resolution)
SELECT a5_lonlat_to_cell(-74.0060, 40.7128, 15) as nyc_cell;  -- Times Square
┌─────────────────────┐
│      nyc_cell       │
│       uint64        │
├─────────────────────┤
│ 2742821848331845632 │
└─────────────────────┘

-- Find the area of that cell in square meters
SELECT a5_cell_area(15) as cell_area_m2;
┌───────────────────┐
│   cell_area_m2    │
│      double       │
├───────────────────┤
│ 31669.04205949599 │
└───────────────────┘

-- Get the center coordinates of a cell
SELECT a5_cell_to_lonlat(a5_lonlat_to_cell(-74.0060, 40.7128, 15)) as center_coords;
┌─────────────────────────────────────────┐
│              center_coords              │
│                double[2]                │
├─────────────────────────────────────────┤
│ [-74.00764805615836, 40.71280225138428] │
└─────────────────────────────────────────┘

-- Find parent cell at lower resolution
SELECT a5_cell_to_parent(a5_lonlat_to_cell(-74.0060, 40.7128, 15), 10) as parent_cell;
┌─────────────────────┐
│     parent_cell     │
│       uint64        │
├─────────────────────┤
│ 2742821365684895744 │
└─────────────────────┘

-- Get all children cells at higher resolution
SELECT a5_cell_to_children(a5_lonlat_to_cell(-74.0060, 40.7128, 10), 11) as child_cells;
┌──────────────────────────────────────────────────────────────────────────────────────┐
│                                     child_cells                                      │
│                                       uint64[]                                       │
├──────────────────────────────────────────────────────────────────────────────────────┤
│ [2742820953368035328, 2742821228245942272, 2742821503123849216, 2742821778001756160] │
└──────────────────────────────────────────────────────────────────────────────────────┘

Code Example: Generate GeoJSON for Cell

To generate a GeoJSON polygon for the A5 cell above use this SQL along with DuckDB's spatial extension:

SELECT
    ST_AsGeoJSON(
        ST_MakePolygon(
            ST_MakeLine(
                list_transform(
                    a5_cell_to_boundary(
                        a5_lonlat_to_cell(-3.7037, 40.41677, 10)
                    ),
                    x -> ST_Point(x[1], x[2])
                )
            )
        )
    ) as g

This produces:

{
    "type":"Polygon",
    "coordinates":[
        [
            [-3.639321611065313,40.44502900567739],
            [-3.6973300524360155,40.44427170464865],
            [-3.7459288918337563,40.424159040292615],
            [-3.70791029038422,40.394201800420205],
            [-3.654438659632305,40.4080830654645],
            [-3.639321611065313,40.44502900567739]
        ]
    ]
}

Visualizing that A5 cell shows:

{
    "type":"Polygon",
    "coordinates":[
        [
            [-3.639321611065313,40.44502900567739],
            [-3.6973300524360155,40.44427170464865],
            [-3.7459288918337563,40.424159040292615],
            [-3.70791029038422,40.394201800420205],
            [-3.654438659632305,40.4080830654645],
            [-3.639321611065313,40.44502900567739]
        ]
    ]
}

Loading

📚 API Reference

Core Functions

a5_lonlat_to_cell(latitude, longitude, resolution) -> UBIGINT

Returns the A5 cell ID for given coordinates and resolution level.

Parameters:

• latitude (DOUBLE): Latitude in decimal degrees (-90 to 90)
• longitude (DOUBLE): Longitude in decimal degrees (-180 to 180)
• resolution (INTEGER): Resolution level (0-30, where 0 is coarsest)

Example:

SELECT a5_lonlat_to_cell(-0.1278, 51.5074, 12) as london_cell;
┌─────────────────────┐
│     london_cell     │
│       uint64        │
├─────────────────────┤
│ 7161033366718906368 │
└─────────────────────┘

a5_cell_area(resolution) -> DOUBLE

Returns the area of an A5 cell in the specified resolution in square meters.

Example:

SELECT a5_cell_area(5) as area_m2;
┌────────────────────┐
│      area_m2       │
│       double       │
├────────────────────┤
│ 33207397446.578068 │
└────────────────────┘

a5_get_resolution(cell_id) -> INTEGER

Returns the resolution level of an A5 cell.

Example:

SELECT a5_get_resolution(207618739568) as resolution;
┌────────────┐
│ resolution │
│   int32    │
├────────────┤
│     27     │
└────────────┘

Spatial Relationships

a5_cell_to_parent(cell_id, target_resolution) -> UBIGINT

Returns the parent cell at a coarser resolution level.

Example:

SELECT a5_cell_to_parent(207618739568, 10) as parent_cell;
┌──────────────────┐
│   parent_cell    │
│      uint64      │
├──────────────────┤
│   549755813888   │
└──────────────────┘

a5_cell_to_children(cell_id, target_resolution) -> UBIGINT[]

Returns all children cells at a finer resolution level.

Example:

SELECT unnest(a5_cell_to_children(207618739568, 28)) as child_cells;
┌──────────────┐
│ child_cells  │
│    uint64    │
├──────────────┤
│ 207618739528 │
│ 207618739544 │
│ 207618739560 │
│ 207618739576 │
└──────────────┘

Geometric Properties

a5_cell_to_lonlat(cell_id) -> DOUBLE[2]

Returns the center coordinates [longitude, latitude] of a cell.

Example:

SELECT a5_cell_to_lonlat(207618739568) as center;
┌─────────────────────────────────────────┐
│                 center                  │
│                double[2]                │
├─────────────────────────────────────────┤
│ [-129.0078555564143, 52.76769886727584] │
└─────────────────────────────────────────┘

a5_cell_to_boundary(cell_id, [closed_ring, [segments]]) -> DOUBLE[2][]

Returns the boundary vertices of a cell as an array of [latitude, longitude] pairs.

Parameters:

• cell_id (UBIGINT): The A5 cell
• closed_ring (BOOLEAN): Whether to close the ring by repeating the first point at the end. Defaults to true.
• segments (INTEGER): Number of segments to use for each edge. If this argument is not supplied or a value is supplied that is <= 0, a resolution-appropriate value will be used.

Examples:

SELECT unnest(a5_cell_to_boundary(207618739568)) as boundary_points;
┌───────────────────────────────────────────┐
│              boundary_points              │
│                 double[2]                 │
├───────────────────────────────────────────┤
│ [-129.00785542696357, 52.767699205314614] │
│ [-129.00785579342767, 52.767698942751544] │
│ [-129.0078559316034, 52.76769861890205]   │
│ [-129.00785542684645, 52.76769862844177]  │
│ [-129.0078552032305, 52.767698940969176]  │
│ [-129.00785542696357, 52.767699205314614] │
└───────────────────────────────────────────┘

SELECT unnest(a5_cell_to_boundary(207618739568, false, 5)) as boundary_points;
┌───────────────────────────────────────────┐
│              boundary_points              │
│                 double[2]                 │
├───────────────────────────────────────────┤
│ [-129.00785550025637, 52.767699152801974] │
│ [-129.0078555735492, 52.76769910028939]   │
│ [-129.00785564684202, 52.76769904777675]  │
│ [-129.00785572013484, 52.767698995264155] │
│ [-129.00785579342767, 52.767698942751544] │
│ [-129.0078558210628, 52.76769887798164]   │
│ [-129.00785584869794, 52.767698813211744] │
│ [-129.00785587633308, 52.767698748441845] │
│ [-129.00785590396822, 52.76769868367194]  │
│ [-129.0078559316034, 52.76769861890205]   │
│ [-129.007855830652, 52.76769862081001]    │
│ [-129.00785572970062, 52.76769862271794]  │
│ [-129.0078556287492, 52.76769862462589]   │
│ [-129.00785552779783, 52.76769862653383]  │
│ [-129.00785542684645, 52.76769862844177]  │
│ [-129.00785538212327, 52.767698690947256] │
│ [-129.00785533740006, 52.76769875345273]  │
│ [-129.00785529267688, 52.7676988159582]   │
│ [-129.00785524795367, 52.7676988784637]   │
│ [-129.0078552032305, 52.767698940969176]  │
│ [-129.00785524797712, 52.767698993838245] │
│ [-129.00785529272372, 52.76769904670734]  │
│ [-129.00785533747032, 52.76769909957643]  │
│ [-129.00785538221695, 52.767699152445516] │
│ [-129.00785542696357, 52.767699205314614] │
├───────────────────────────────────────────┤
│                  25 rows                  │
└───────────────────────────────────────────┘

Utility Functions

a5_get_num_cells(resolution) -> UBIGINT

Returns the total number of A5 cells at a given resolution level.

Example:

SELECT a5_get_num_cells(15) as total_cells;
┌─────────────────┐
│   total_cells   │
│     uint64      │
├─────────────────┤
│   16106127360   │
└─────────────────┘

a5_get_res0_cells() -> UBIGINT[]

Returns all 12 base cells at resolution level 0.

Example:

SELECT unnest(a5_get_res0_cells()) as base_cells;
┌─────────────────────┐
│     base_cells      │
│       uint64        │
├─────────────────────┤
│  144115188075855872 │
│  432345564227567616 │
│  720575940379279360 │
│ 1008806316530991104 │
│ 1297036692682702848 │
│ 1585267068834414592 │
│ 1873497444986126336 │
│ 2161727821137838080 │
│ 2449958197289549824 │
│ 2738188573441261568 │
│ 3026418949592973312 │
│ 3314649325744685056 │
├─────────────────────┤
│       12 rows       │
└─────────────────────┘

🎯 Resolution Guide

Resolution	Cell Area (approx)	Use Case
0-5	42M km² - 33k km²	Continental/Country analysis
6-10	8k km² - 130 km²	Regional/State analysis
11-15	32 km² - 32 hectares	City/District analysis
16-20	8 hectares - 124 m²	Neighborhood/Building analysis
21-25	31 m² - 0.5 m²	Room/Vehicle analysis
26-30	8 cm² - 0.03 mm²	Precision measurements

📄 License

This project is licensed under the MIT License - see the LICENSE file for details.

🙏 Credits

• A5 Algorithm: This extension utilizes the a5 Rust crate created by felixpalmer
• A5 Specification: Based on the A5 geospatial index specification
• DuckDB Community: Built on the excellent DuckDB database system

🔗 Related Links

• A5 Official Website
• A5 Examples and Visualizations