FA-70115 / Map projection transforms / Member archive

Spherical Lambert conformal conic forward: origin radius · case 05

False origins are shifted north or south by hundreds of kilometres.

Member previewVariant 5 · 3 implementations · 8 checks per implementation

Case contract

Input [lon, lat, lon0, lat0, lat1, lat2] degrees, sphere R = 6371000, all latitudes strictly inside (-90, 90) and on the cone side of the equator. t(p) = tan(pi/4 + p/2). n = ln(cos p1/cos p2)/ln(t(p2)/t(p1)), or sin(p1) for a tangent cone (lat1 == lat2). F = cos(p1)*t(p1)**n/n; rho = R*F/t(phi)**n; rho0 = R*F/t(p0)**n; 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

Aeronautical charts and many national grids use conformal conics; a wrong cone constant distorts whole regions.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
control #5	`[4256679.54, -3348221.07]`	`[4256679.54, 2162268.41]`	Failed

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