Turning Radio Coordinates Into Sky Art

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Your RC aircraft traces a perfect helix through the morning sky, each GPS position automatically broadcast via APRS to ground stations across the province. But there’s a problem: APRS speaks in latitude and longitude degrees, whilst your CAD sculpture design thinks in cartesian metres. You need coordinate transformation—the mathematical bridge that lets different systems share the same spatial reality.

The 1980s computer graphics revolution made this transformation ubiquitous. Every pixel on every screen required converting from the programmer’s logical coordinates into the display’s physical ones. The principle remains unchanged: multiply by a transformation matrix.

10 REM Convert lat/lon to local XY metres
20 LAT = 43.6532: LON = -79.3832
30 REFLAT = 43.6500: REFLON = -79.3800
40 DLAT = (LAT - REFLAT) * 111320
50 DLON = (LON - REFLON) * 111320 * COS(REFLAT * 3.14159/180)
60 PRINT "Position: "; DLAT; "m N, "; DLON; "m E"

BASIC’s straightforward approach multiplies degree differences by Earth’s circumference factors. Those magic numbers—111,320 metres per degree—come from our planet’s 40,075 km circumference divided by 360 degrees.

Haskell offers a more elegant abstraction:

type Coord = (Double, Double)
type Point = (Double, Double)

gpsTrack :: [Coord]
gpsTrack = [(43.6532, -79.3832), (43.6540, -79.3810)]

transform :: Coord -> Coord -> Point
transform (refLat, refLon) (lat, lon) = 
  let dlat = (lat - refLat) * 111320
      dlon = (lon - refLon) * 111320 * cos (refLat * pi / 180)
  in (dlat, dlon)

skyPath = map (transform origin) gpsTrack
  where origin = (43.65, -79.38)

The functional approach treats transformation as a mapping operation—your entire flight path becomes a simple map over GPS coordinates. This mathematical elegance mirrors the sculpture itself: what appears complex in the sky reduces to clean geometric relationships when viewed through the right coordinate system. Whether you’re programming graphics or plotting aerial art, the fundamental insight remains: changing perspective is just matrix multiplication away.