FA-70128 / Map projection transforms / Member archive

Spherical Albers equal-area conic forward: cone constant averaging · case 03

Area totals drift and meridians converge twice as fast as intended.

Member previewVariant 3 · 3 implementations · 8 checks per implementation

Case contract

Input [lon, lat, lon0, lat0, lat1, lat2] degrees, sphere R = 6371000, lat1 != -lat2. n = (sin p1 + sin p2)/2; C = cos(p1)**2 + 2*n*sin(p1); rho = R*sqrt(C - 2*n*sin(phi))/n; rho0 likewise at lat0; theta = n*dlon with dlon wrapped to [-180, 180). x = rho*sin(theta), y = rho0 - rho*cos(theta), rounded to 2 decimals.

Why this case matters

Continental statistics maps use Albers because it preserves area; a wrong constant silently biases area totals.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
control #2	`[1732222.4, -5374949.58]`	`[2661851.12, -4920407.16]`	Failed

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