FA-70046 / Map projection transforms / Open access

Equirectangular projection with standard parallel: forward longitude wrap · case 01

Points across the antimeridian from the central meridian project a whole world-width away.

Verified by executionVariant 1 · 8 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

The longitude difference is not wrapped into [-180, 180).

THE FAILURE

The longitude difference is not wrapped into [-180, 180).

Unsuccessful approach: Only positive overflows are wrapped; differences below -180 remain unwrapped.

Case contract

Input [mode, a, b, lon0, lat0, lat1] on a sphere R = 6371007. mode "fwd": a=lon, b=lat; dlon = lon-lon0 wrapped into [-180, 180); x = R*rad(dlon)*cos(rad(lat1)), y = R*rad(lat-lat0). mode "inv": a=x, b=y; lon = lon0 + deg(x/(R*cos(rad(lat1)))) wrapped into [-180, 180), lat = lat0 + deg(y/R). Forward results round to 2 decimals, inverse results to 6.

Why this case matters

Plate carree style grids with a true-scale parallel are common for regional rasters and simple web previews.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    mode, a, b, lon0, lat0, lat1 = x
    R = 6371007.0
    k = math.cos(math.radians(lat1))
    if mode == 'fwd':
        dlon = a - lon0
        return [round(R * math.radians(dlon) * k, 2), round(R * math.radians(b - lat0), 2)]
    lon = lon0 + math.degrees(a / (R * k))
    lon = ((lon + 180.0) % 360.0) - 180.0
    lat = lat0 + math.degrees(b / R)
    return [round(lon, 6), round(lat, 6)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', ['fwd', 29.215, -48.839, -100.0, 20.0, 0.0], [14368068.23, -7654555.97]), ('control #1', ['fwd', 58.849, -45.676, 10.0, 20.0, -37.5], [4309310.45, -7302846.03]), ('control #2', ['fwd', 69.272, -46.02, 150.0, 0.0, 45.0], [-6347382.14, -5117196.15]), ('control #3', ['fwd', -110.417, -65.782, -100.0, 0.0, -37.5], [-918956.11, -7314632.7]), ('control #4', ['fwd', 103.06, -41.789, 150.0, 20.0, 30.0], [-4520215.78, -6870630.87]), ('control #5', ['fwd', -157.356, -5.165, 10.0, 0.0, 45.0], [-13158662.23, -574322.43]), ('control #9', ['fwd', -176.6, 10.306, 10.0, 0.0, -37.5], [15296821.45, 1145976.17]), ('regression #21', ['fwd', -170.0, -5.0, 170.0, 0.0, 0.0], [2223900.98, -555975.24])], [('control #3', ['fwd', -110.417, -65.782, -100.0, 0.0, -37.5], [-918956.11, -7314632.7]), ('control #4', ['fwd', 103.06, -41.789, 150.0, 20.0, 30.0], [-4520215.78, -6870630.87]), ('control #5', ['fwd', -157.356, -5.165, 10.0, 0.0, 45.0], [-13158662.23, -574322.43]), ('control #6', ['fwd', 59.325, 61.191, 150.0, 20.0, 30.0], [-8731797.31, 4580235.26]), ('control #7', ['fwd', -27.732, -15.271, 150.0, 0.0, -37.5], [-15678977.34, -1698059.59]), ('control #8', ['fwd', -101.988, -64.848, 0.0, 20.0, 45.0], [-8018987.33, -9434677.5]), ('regression #20', ['fwd', 170.0, 10.0, -170.0, 0.0, 30.0], [-1925954.74, 1111950.49]), ('regression #21', ['fwd', -170.0, -5.0, 170.0, 0.0, 0.0], [2223900.98, -555975.24])], [('control #6', ['fwd', 59.325, 61.191, 150.0, 20.0, 30.0], [-8731797.31, 4580235.26]), ('control #7', ['fwd', -27.732, -15.271, 150.0, 0.0, -37.5], [-15678977.34, -1698059.59]), ('control #8', ['fwd', -101.988, -64.848, 0.0, 20.0, 45.0], [-8018987.33, -9434677.5]), ('control #9', ['fwd', -176.6, 10.306, 10.0, 0.0, -37.5], [15296821.45, 1145976.17]), ('control #10', ['inv', -9574741.6, -6948175.3, 10.0, 20.0, 45.0], [-111.774572, -42.486373]), ('control #11', ['inv', 14726764.0, 5249990.3, 150.0, 0.0, 30.0], [-57.070508, 47.214245]), ('control #12', ['inv', 10315651.1, 166980.2, 10.0, -10.0, 45.0], [141.197691, -8.498313]), ('regression #21', ['fwd', -170.0, -5.0, 170.0, 0.0, 0.0], [2223900.98, -555975.24])], [('control #9', ['fwd', -176.6, 10.306, 10.0, 0.0, -37.5], [15296821.45, 1145976.17]), ('control #10', ['inv', -9574741.6, -6948175.3, 10.0, 20.0, 45.0], [-111.774572, -42.486373]), ('control #11', ['inv', 14726764.0, 5249990.3, 150.0, 0.0, 30.0], [-57.070508, 47.214245]), ('control #12', ['inv', 10315651.1, 166980.2, 10.0, -10.0, 45.0], [141.197691, -8.498313]), ('control #13', ['inv', 5503696.2, -7904836.4, 0.0, 0.0, 0.0], [49.495875, -71.089824]), ('control #14', ['inv', 2270255.8, 547031.0, 150.0, 0.0, 45.0], [178.873826, 4.919563]), ('control #15', ['inv', 6171735.4, 4391661.0, 150.0, -10.0, 0.0], [-154.496311, 29.495113]), ('regression #21', ['fwd', -170.0, -5.0, 170.0, 0.0, 0.0], [2223900.98, -555975.24])], [('control #9', ['fwd', -176.6, 10.306, 10.0, 0.0, -37.5], [15296821.45, 1145976.17]), ('control #13', ['inv', 5503696.2, -7904836.4, 0.0, 0.0, 0.0], [49.495875, -71.089824]), ('control #14', ['inv', 2270255.8, 547031.0, 150.0, 0.0, 45.0], [178.873826, 4.919563]), ('control #15', ['inv', 6171735.4, 4391661.0, 150.0, -10.0, 0.0], [-154.496311, 29.495113]), ('control #16', ['inv', 5573045.0, 6790547.5, 10.0, -10.0, 45.0], [80.879737, 51.068794]), ('control #17', ['inv', -1605712.3, 6233155.6, 10.0, 0.0, 0.0], [-4.440502, 56.056053]), ('control #18', ['inv', 11534249.9, -2599094.3, 0.0, 0.0, 45.0], [146.696214, -23.374191]), ('regression #20', ['fwd', 170.0, 10.0, -170.0, 0.0, 30.0], [-1925954.74, 1111950.49])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
control #0	`[14368068.23, -7654555.97]`	`[14368068.23, -7654555.97]`	Passed
control #1	`[4309310.45, -7302846.03]`	`[4309310.45, -7302846.03]`	Passed
control #2	`[-6347382.14, -5117196.15]`	`[-6347382.14, -5117196.15]`	Passed
control #3	`[-918956.11, -7314632.7]`	`[-918956.11, -7314632.7]`	Passed
control #4	`[-4520215.78, -6870630.87]`	`[-4520215.78, -6870630.87]`	Passed
control #5	`[-13158662.23, -574322.43]`	`[-13158662.23, -574322.43]`	Passed
control #9	`[-16461285.37, 1145976.17]`	`[15296821.45, 1145976.17]`	Failed
regression #21	`[-37806316.6, -555975.24]`	`[2223900.98, -555975.24]`	Failed

SHA-256 / cd26e7772c91bc224632eb437b73b00f0b8e7eb7fbb7a1a1d7e45cf6545c796b

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    mode, a, b, lon0, lat0, lat1 = x
    R = 6371007.0
    k = math.cos(math.radians(lat1))
    if mode == 'fwd':
        dlon = a - lon0 - 360.0 if a - lon0 > 180.0 else a - lon0
        return [round(R * math.radians(dlon) * k, 2), round(R * math.radians(b - lat0), 2)]
    lon = lon0 + math.degrees(a / (R * k))
    lon = ((lon + 180.0) % 360.0) - 180.0
    lat = lat0 + math.degrees(b / R)
    return [round(lon, 6), round(lat, 6)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', ['fwd', 29.215, -48.839, -100.0, 20.0, 0.0], [14368068.23, -7654555.97]), ('control #1', ['fwd', 58.849, -45.676, 10.0, 20.0, -37.5], [4309310.45, -7302846.03]), ('control #2', ['fwd', 69.272, -46.02, 150.0, 0.0, 45.0], [-6347382.14, -5117196.15]), ('control #3', ['fwd', -110.417, -65.782, -100.0, 0.0, -37.5], [-918956.11, -7314632.7]), ('control #4', ['fwd', 103.06, -41.789, 150.0, 20.0, 30.0], [-4520215.78, -6870630.87]), ('control #5', ['fwd', -157.356, -5.165, 10.0, 0.0, 45.0], [-13158662.23, -574322.43]), ('control #9', ['fwd', -176.6, 10.306, 10.0, 0.0, -37.5], [15296821.45, 1145976.17]), ('regression #21', ['fwd', -170.0, -5.0, 170.0, 0.0, 0.0], [2223900.98, -555975.24])], [('control #3', ['fwd', -110.417, -65.782, -100.0, 0.0, -37.5], [-918956.11, -7314632.7]), ('control #4', ['fwd', 103.06, -41.789, 150.0, 20.0, 30.0], [-4520215.78, -6870630.87]), ('control #5', ['fwd', -157.356, -5.165, 10.0, 0.0, 45.0], [-13158662.23, -574322.43]), ('control #6', ['fwd', 59.325, 61.191, 150.0, 20.0, 30.0], [-8731797.31, 4580235.26]), ('control #7', ['fwd', -27.732, -15.271, 150.0, 0.0, -37.5], [-15678977.34, -1698059.59]), ('control #8', ['fwd', -101.988, -64.848, 0.0, 20.0, 45.0], [-8018987.33, -9434677.5]), ('regression #20', ['fwd', 170.0, 10.0, -170.0, 0.0, 30.0], [-1925954.74, 1111950.49]), ('regression #21', ['fwd', -170.0, -5.0, 170.0, 0.0, 0.0], [2223900.98, -555975.24])], [('control #6', ['fwd', 59.325, 61.191, 150.0, 20.0, 30.0], [-8731797.31, 4580235.26]), ('control #7', ['fwd', -27.732, -15.271, 150.0, 0.0, -37.5], [-15678977.34, -1698059.59]), ('control #8', ['fwd', -101.988, -64.848, 0.0, 20.0, 45.0], [-8018987.33, -9434677.5]), ('control #9', ['fwd', -176.6, 10.306, 10.0, 0.0, -37.5], [15296821.45, 1145976.17]), ('control #10', ['inv', -9574741.6, -6948175.3, 10.0, 20.0, 45.0], [-111.774572, -42.486373]), ('control #11', ['inv', 14726764.0, 5249990.3, 150.0, 0.0, 30.0], [-57.070508, 47.214245]), ('control #12', ['inv', 10315651.1, 166980.2, 10.0, -10.0, 45.0], [141.197691, -8.498313]), ('regression #21', ['fwd', -170.0, -5.0, 170.0, 0.0, 0.0], [2223900.98, -555975.24])], [('control #9', ['fwd', -176.6, 10.306, 10.0, 0.0, -37.5], [15296821.45, 1145976.17]), ('control #10', ['inv', -9574741.6, -6948175.3, 10.0, 20.0, 45.0], [-111.774572, -42.486373]), ('control #11', ['inv', 14726764.0, 5249990.3, 150.0, 0.0, 30.0], [-57.070508, 47.214245]), ('control #12', ['inv', 10315651.1, 166980.2, 10.0, -10.0, 45.0], [141.197691, -8.498313]), ('control #13', ['inv', 5503696.2, -7904836.4, 0.0, 0.0, 0.0], [49.495875, -71.089824]), ('control #14', ['inv', 2270255.8, 547031.0, 150.0, 0.0, 45.0], [178.873826, 4.919563]), ('control #15', ['inv', 6171735.4, 4391661.0, 150.0, -10.0, 0.0], [-154.496311, 29.495113]), ('regression #21', ['fwd', -170.0, -5.0, 170.0, 0.0, 0.0], [2223900.98, -555975.24])], [('control #9', ['fwd', -176.6, 10.306, 10.0, 0.0, -37.5], [15296821.45, 1145976.17]), ('control #13', ['inv', 5503696.2, -7904836.4, 0.0, 0.0, 0.0], [49.495875, -71.089824]), ('control #14', ['inv', 2270255.8, 547031.0, 150.0, 0.0, 45.0], [178.873826, 4.919563]), ('control #15', ['inv', 6171735.4, 4391661.0, 150.0, -10.0, 0.0], [-154.496311, 29.495113]), ('control #16', ['inv', 5573045.0, 6790547.5, 10.0, -10.0, 45.0], [80.879737, 51.068794]), ('control #17', ['inv', -1605712.3, 6233155.6, 10.0, 0.0, 0.0], [-4.440502, 56.056053]), ('control #18', ['inv', 11534249.9, -2599094.3, 0.0, 0.0, 45.0], [146.696214, -23.374191]), ('regression #20', ['fwd', 170.0, 10.0, -170.0, 0.0, 30.0], [-1925954.74, 1111950.49])]]
for label, args, expected in fixtures[N-1]:
    check(label, solve(args), expected)
print(json.dumps({"observations": observations, "passed": all(x["passed"] for x in observations)}, ensure_ascii=False))
raise SystemExit(0 if all(x["passed"] for x in observations) else 1)

Boundary fixture	Actual	Expected	Outcome
control #0	`[14368068.23, -7654555.97]`	`[14368068.23, -7654555.97]`	Passed
control #1	`[4309310.45, -7302846.03]`	`[4309310.45, -7302846.03]`	Passed
control #2	`[-6347382.14, -5117196.15]`	`[-6347382.14, -5117196.15]`	Passed
control #3	`[-918956.11, -7314632.7]`	`[-918956.11, -7314632.7]`	Passed
control #4	`[-4520215.78, -6870630.87]`	`[-4520215.78, -6870630.87]`	Passed
control #5	`[-13158662.23, -574322.43]`	`[-13158662.23, -574322.43]`	Passed
control #9	`[-16461285.37, 1145976.17]`	`[15296821.45, 1145976.17]`	Failed
regression #21	`[-37806316.6, -555975.24]`	`[2223900.98, -555975.24]`	Failed

SHA-256 / a415dfe27e895a517477ca86a4708ffe0d158fb241c140e3ee305c1b6347c0e3

HELD IN THE MEMBER ARCHIVE

The verified repair and its recorded checks are member-only.

This mechanism has 8 recorded checks per implementation. The open-access tier publishes the failure and the unsuccessful fix; the repaired source that passes every check, and the observations that prove it, are available to members.

Every case sharing this mechanism uses the same contract and the same repair, so this one record is held back for all of them.

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Verification & scope

Stipulated deterministic toy contract on a bounded input domain; results are rounded as stated and no conformance with any published standard or library is claimed. This reproducer isolates one failure mechanism. Results cover the supplied fixtures. Variants within a family share a test contract and should remain grouped when constructing evaluation splits. Related mechanisms with a shared evaluation_group must also remain together; these controlled models are not independent production incidents.

Observations recorded using Python 3.12.14 at 2026-09-29T14:48:17.040252+00:00.

Case digest / 35b5dd72e2f54c8a90f5a9fdb4b1a49a7d2e761bae0b6b95117e70ecc17ef14e