FA-70029 / Map projection transforms / Member archive

Spherical transverse mercator in a UTM grid: easting half factor · case 04

Distances from the central meridian are doubled.

Member previewVariant 4 · 3 implementations · 8 checks per implementation

Case contract

Input [lon, lat, zone, hemisphere] with |lat| <= 80 and lon within 4 degrees of the zone central meridian 6*zone-183. On a sphere R = 6371000 with k0 = 0.9996: B = cos(phi)*sin(dl); x = 0.5*k0*R*ln((1+B)/(1-B)); y = k0*R*atan2(tan(phi), cos(dl)). Easting = 500000 + x. Northing = y plus 10000000 when the requested grid hemisphere is "S" (the caller may deliberately project points just north of the equator in a southern grid). Return [easting, northing] rounded to 2 decimals.

Why this case matters

Survey exports and GPS receivers express positions as UTM eastings and northings; a wrong false origin or meridian moves points by hundreds of kilometres.

One recorded failure

Sample boundary fixture

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

Boundary fixture	Actual	Expected	Outcome
control #3	`[327314.08, 9851155.87]`	`[413657.04, 9851155.87]`	Failed

MEMBER ARCHIVE

The complete case is available to members.

This record includes three runnable implementations, regression fixtures, execution results, and source hashes.

Member access is invitation-based. Sign in with your invited account to inspect the sources.