AAE — Arc Algo Engine

Redrawing air traffic around an airport

Recentering OpenSky Traffic: Arbitrary-Center, Multi-Projection Visualization on a Single GPU
Poster presentation at the 14th OpenSky Symposium, Madrid, 29–30 October 2026. The accompanying short paper has been submitted to the Journal of Open Aviation Science. This page is the web companion to the poster. 日本語版 →

Resumen. Todo mapa proyecta la Tierra en un plano a costa de sacrificar alguna propiedad geométrica; por ello, el mapa «correcto» depende de la pregunta que se quiera responder. En aviación, lo esencial es medir la distancia y el rumbo desde un punto de referencia. Arc Algo Engine (AAE) permite situar cualquier punto del globo en el centro de 20 proyecciones distintas mediante una rotación esférica previa y una tabla de búsqueda inversa (LUT), todo ello ejecutado en una sola GPU. Al observar las mismas rutas desde Madrid-Barajas en tres proyecciones diferentes, quedan patentes tanto las ventajas de cada representación como sus compromisos geométricos.

1The "right" map depends on the question

Aviation asks: "From this airport, in which direction, and how far?" The Mercator projection preserves local angles, but preserves neither distance nor bearing. The azimuthal equidistant projection preserves both — measured from the single point placed at its center. That is why putting the airport at the center matters. AAE can place any point on Earth at the center of any of its 20 projections, driven by the exact same underlying data.

Azimuthal equidistant projection centered on Madrid-Barajas: 2,000 km range rings and four routes drawn as great circles (solid) and rhumb lines (dashed) over a dark basemap.

Range rings every 2,000 km form true circles. Bearing and distance from the airport can be read directly. The outer rim is the antipode (20,000 km).

Mercator projection with the central meridian at Madrid's longitude: the same four routes, great circles bowing poleward and rhumb lines drawn straight.

The same four routes. Rhumb lines (dashed) appear straight, but high latitudes are stretched and distance ratios break down.

Routes: MAD–DXB, DXB–HND, MAD–HND, and MAD–JFK. Solid = great circle (shortest path), dashed = rhumb line (constant bearing). The conference poster overlays these routes with 44 Spanish-registered aircraft from a single OpenSky snapshot (23:27 UTC, 23 September 2026). Coastlines: GSHHG / Airports: Natural Earth

Three kinds of line

Airports are specified by three-letter IATA codes (MAD, DXB, HND, JFK), with coordinates resolved from the Natural Earth airports dataset. Lines are computed geometrically on the sphere and projected through the same forward pipeline as point data, ensuring consistent clipping across all projections.

LineMeaningStraight (or true circle) in
Great circleShortest path between two airports on the sphereGnomonic (all); Azimuthal equidistant (only routes through the center)
Rhumb linePath of constant compass bearingMercator (standard orientation)
Range ringLocus of equal distance from one airportAzimuthal equidistant (forms a true circle only for the airport at the center)
Degenerate cases — such as a range ring enclosing a pole or a great circle between antipodes — are handled without numerical failure, and segments crossing the map boundary are clipped cleanly without streaking across the frame.

2The center is not a general-purpose fix

In an azimuthal projection, any great circle through the center is straight by construction, so routes radiating out of Madrid appear straight. However, a route that does not pass through Madrid remains curved: on a Madrid-centered azimuthal equidistant map, the Dubai–Tokyo route (9,240 km) bows outward from its straight-line chord by up to 1,050 km (11% of its total length). Choosing a projection means choosing which geometric question to answer.

QuestionProjectionPreservesCost
Distance and bearing from hereAzimuthal equidistantBoth, measured from the centerShapes distort increasingly toward the rim
Is the shortest path straight?GnomonicAll great circles are straightLimited to within 60° of the center
Which region is larger?Equal EarthRelative areaLocal angles and shapes are not preserved
Constant-bearing courseMercatorLocal angles (rhumb lines are straight)Preserves neither distance nor area
Equal Earth projection with the same four routes and Madrid range rings; rings become ellipses and routes are curved.

Area is preserved. Routes curve and range rings deform into ellipses, but comparisons of regional and airspace size become accurate.

ADS-B AIS APRS SGP4 syslog N inputs One record typelon, lat, t, … Rotation Rsets the center Azimuthal eq. Mercator Equal Earth Gnomonic … 20 in all M projections N + M connections, not N × M. Adding an input leaves the projections untouched, and vice versa. Center shifts are handled entirely by R.

Observations from N sources are normalized into a single record type, rotated on the sphere by R, and sent to M projections.

3Moving the center

A 40-second clip of the azimuthal equidistant projection as its center moves continuously from Madrid to Tokyo. Range rings remain fixed circles on the globe but deform dynamically across the map plane. The second clip overlays the same motion with positions of aircraft, ships, and ground stations at a single timestamp. Silent; captions in English and Japanese (enable CC).

Range rings and four routes only. Coastlines: GSHHG
Aircraft (ADS-B), ships (AIS), and ground stations (APRS) captured on 16 October 2026. OpenSky Network / aisstream.io / APRS-IS / Coastlines: GSHHG

4How it is drawn

Re-projecting raw vector polygons from scratch for every new center proved too fragile for interactive use: seam crossings and pole enclosures shift continuously with the center, and six iterations of a forward polygon rasterizer failed to eliminate topological edge cases. Instead, AAE bakes base geometry once into a static equirectangular intermediate sheet whose seam is fixed at ±180°. For any chosen center and projection, an inverse look-up table (LUT) maps each output screen pixel back to its source coordinate (inverse project, rotate by Rᵀ, and sample the sheet). Moving the center simply updates the rotation matrix R and rebuilds the LUT. Dynamic point observations and route vectors travel the opposite way, forward-projected using the same R.

ItemValueConditions
Center change to frame ready16.4 ms (median)including 6.0 ms for LUT generation (at 1,920 × 1,080)
100,000 points drawn3.1 msat 1,920 × 1,080, median of 20 frames
Projections registered20no per-projection branches; dispatched via declared attributes
GPUSingle NVIDIA RTX 4000 SFF AdaCuPy + custom CUDA kernels for scanline fill, sampling, and compositing; no graphics API
This work compares map projections rather than competing software tools: standard ADS-B trackers use Web Mercator because local angle preservation and pre-rendered rectangular tiles match their operational needs. AAE is a single-author local application, not a hosted web service. The source code is currently private while the scope of a future release (such as an API) is under consideration.

5Paper, data, contact

ItemDetails
Venue14th OpenSky Symposium, Madrid (CRIDA), 29–30 October 2026
FormatPoster (Poster Session, 29 October, 16:20–17:20)
Short paperSubmitted to the Journal of Open Aviation Science (4 pages); a link will be added upon publication
AuthorIndependent Researcher, Tokyo
Contactmapshift.dev [at] gmail.com
Please put "AAE" in the subject line.
KeywordsADS-B visualization / OpenSky Network API / map projection / GPU-accelerated visualization / azimuthal equidistant

Open data statement

DataSourceTerms
Aircraft state vectors (ADS-B)The OpenSky NetworkNon-commercial research terms; underlying raw records are not redistributed
Airport coordinatesNatural Earth 10m airports v5.0.0Public domain
Coastlines / landNatural Earth 110m; GSHHG 2.3.7 (Wessel & Smith)Public domain / LGPL
Generative AI tools were used only for language proofreading and typesetting assistance.