FA-70213 / Map projection transforms / Member archive

Azimuthal equidistant range and bearing: radial scale · case 03

Distant points are drawn much too close to the centre.

Member previewVariant 3 · 3 implementations · 8 checks per implementation

Case contract

Input [lon, lat, lon0, lat0]; sphere R = 6371000 centred on (lon0, lat0). cos c is clamped to [-1, 1], c = acos. Points with c > pi - 1e-6 (the antipode neighbourhood) return None. k = 1 at the centre (c < 1e-12) else c/sin c. x = R k cos(p) sin(dl); y = R k (cos(p0) sin(p) - sin(p0) cos(p) cos(dl)). Return [x rounded to 1 decimal, y rounded to 1 decimal, hypot(x, y)/1000 km rounded to 3, azimuth clockwise from north in [0, 360) rounded to 4].

Why this case matters

Radio coverage, flight-range rings and seismology plots use this projection to read range and bearing directly.

One recorded failure

Sample boundary fixture

This sample comes from the broken implementation of a controlled reproducer.

Boundary fixture	Actual	Expected	Outcome
control #2	`[3475729.7, -2458592.2, 4257.39, 125.2741]`	`[7727165.8, -5465888.2, 9464.937, 125.2741]`	Failed

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