FA-69846 / Map projection transforms / Open access

Spherical web mercator forward projection: latitude clamp · case 01

Polar latitudes project far outside the square web mercator extent.

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

ROOT CAUSE

Latitude is clamped to the geographic range [-90, 90] instead of the square-world limit 85.05112878, so near-polar points produce enormous northings.

VERIFIED REPAIR

At the latitude clamp step restore `lat = max(-85.05112878, min(85.05112878, lat))`, leaving the rest of the model unchanged.

Unsuccessful approach: Only the northern clamp was restored; southern polar latitudes still escape the square extent.

Case contract

Input [lon, lat] in degrees. Longitude is first wrapped into the half-open range [-180, 180); latitude is clamped to +/-85.05112878. Return [x, y] metres on a sphere of radius 6378137 with y growing northward, each rounded to 3 decimals.

Why this case matters

Web map tiles, vector tile encoders and map viewers all start from this forward transform; small mistakes shift features by kilometres or mirror them across the equator.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    lon, lat = x
    lon = ((lon + 180.0) % 360.0) - 180.0
    lat = max(-90.0, min(90.0, lat))
    R = 6378137.0
    px = R * math.radians(lon)
    py = R * math.log(math.tan(math.pi / 4 + math.radians(lat) / 2))
    return [round(px, 3), round(py, 3)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression #0', [190.0, 10.0], [-18924313.435, 1118889.975]), ('regression #1', [-200.0, -20.0], [17811118.527, -2273030.927]), ('boundary #2', [180.0, 0.0], [-20037508.343, -0.0]), ('boundary #3', [-180.0, 45.0], [-20037508.343, 5621521.486]), ('regression #4', [545.0, 5.0], [-19480910.889, 557305.257]), ('boundary #5', [0.0, 89.0], [0.0, 20037508.343]), ('boundary #6', [10.0, -88.0], [1113194.908, -20037508.343]), ('boundary #7', [0.0, 85.05112878], [0.0, 20037508.343])], [('boundary #3', [-180.0, 45.0], [-20037508.343, 5621521.486]), ('regression #4', [545.0, 5.0], [-19480910.889, 557305.257]), ('boundary #5', [0.0, 89.0], [0.0, 20037508.343]), ('boundary #6', [10.0, -88.0], [1113194.908, -20037508.343]), ('boundary #7', [0.0, 85.05112878], [0.0, 20037508.343]), ('control #8', [0.0, 0.0], [0.0, -0.0]), ('regression #9', [-540.0, 30.0], [-20037508.343, 3503549.844]), ('boundary #13', [-120.0, -87.25], [-13358338.895, -20037508.343])], [('boundary #6', [10.0, -88.0], [1113194.908, -20037508.343]), ('boundary #7', [0.0, 85.05112878], [0.0, 20037508.343]), ('control #8', [0.0, 0.0], [0.0, -0.0]), ('regression #9', [-540.0, 30.0], [-20037508.343, 3503549.844]), ('regression #10', [-250.0, 12.5], [12245143.987, 1402665.19]), ('regression #11', [-359.5, -40.0], [55659.745, -4865942.28]), ('boundary #12', [45.0, -86.5], [5009377.086, -20037508.343]), ('boundary #13', [-120.0, -87.25], [-13358338.895, -20037508.343])], [('regression #9', [-540.0, 30.0], [-20037508.343, 3503549.844]), ('regression #10', [-250.0, 12.5], [12245143.987, 1402665.19]), ('regression #11', [-359.5, -40.0], [55659.745, -4865942.28]), ('boundary #12', [45.0, -86.5], [5009377.086, -20037508.343]), ('boundary #13', [-120.0, -87.25], [-13358338.895, -20037508.343]), ('regression #14', [-181.0, 0.5], [19926188.852, 55660.452]), ('control #15', [-17.048, 10.042], [-1897774.679, 1123637.827]), ('control #16', [151.867, -5.771], [16905757.108, -643513.79])], [('boundary #5', [0.0, 89.0], [0.0, 20037508.343]), ('boundary #12', [45.0, -86.5], [5009377.086, -20037508.343]), ('regression #14', [-181.0, 0.5], [19926188.852, 55660.452]), ('control #15', [-17.048, 10.042], [-1897774.679, 1123637.827]), ('control #16', [151.867, -5.771], [16905757.108, -643513.79]), ('control #17', [2.807, 14.681], [312473.811, 1652463.738]), ('control #18', [-112.892, 2.001], [-12567079.955, 222795.596]), ('control #19', [46.498, 49.22], [5176133.683, 6312273.571])]]
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
regression #0	`[-18924313.435, 1118889.975]`	`[-18924313.435, 1118889.975]`	Passed
regression #1	`[17811118.527, -2273030.927]`	`[17811118.527, -2273030.927]`	Passed
boundary #2	`[-20037508.343, -0.0]`	`[-20037508.343, -0.0]`	Passed
boundary #3	`[-20037508.343, 5621521.486]`	`[-20037508.343, 5621521.486]`	Passed
regression #4	`[-19480910.889, 557305.257]`	`[-19480910.889, 557305.257]`	Passed
boundary #5	`[0.0, 30240971.958]`	`[0.0, 20037508.343]`	Failed
boundary #6	`[1113194.908, -25819498.514]`	`[1113194.908, -20037508.343]`	Failed
boundary #7	`[0.0, 20037508.343]`	`[0.0, 20037508.343]`	Passed

SHA-256 / 674e54c0553b6515880e8c6716e5810de89ad26383eb173d4097fcebf0644464

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    lon, lat = x
    lon = ((lon + 180.0) % 360.0) - 180.0
    lat = min(85.05112878, lat)
    R = 6378137.0
    px = R * math.radians(lon)
    py = R * math.log(math.tan(math.pi / 4 + math.radians(lat) / 2))
    return [round(px, 3), round(py, 3)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression #0', [190.0, 10.0], [-18924313.435, 1118889.975]), ('regression #1', [-200.0, -20.0], [17811118.527, -2273030.927]), ('boundary #2', [180.0, 0.0], [-20037508.343, -0.0]), ('boundary #3', [-180.0, 45.0], [-20037508.343, 5621521.486]), ('regression #4', [545.0, 5.0], [-19480910.889, 557305.257]), ('boundary #5', [0.0, 89.0], [0.0, 20037508.343]), ('boundary #6', [10.0, -88.0], [1113194.908, -20037508.343]), ('boundary #7', [0.0, 85.05112878], [0.0, 20037508.343])], [('boundary #3', [-180.0, 45.0], [-20037508.343, 5621521.486]), ('regression #4', [545.0, 5.0], [-19480910.889, 557305.257]), ('boundary #5', [0.0, 89.0], [0.0, 20037508.343]), ('boundary #6', [10.0, -88.0], [1113194.908, -20037508.343]), ('boundary #7', [0.0, 85.05112878], [0.0, 20037508.343]), ('control #8', [0.0, 0.0], [0.0, -0.0]), ('regression #9', [-540.0, 30.0], [-20037508.343, 3503549.844]), ('boundary #13', [-120.0, -87.25], [-13358338.895, -20037508.343])], [('boundary #6', [10.0, -88.0], [1113194.908, -20037508.343]), ('boundary #7', [0.0, 85.05112878], [0.0, 20037508.343]), ('control #8', [0.0, 0.0], [0.0, -0.0]), ('regression #9', [-540.0, 30.0], [-20037508.343, 3503549.844]), ('regression #10', [-250.0, 12.5], [12245143.987, 1402665.19]), ('regression #11', [-359.5, -40.0], [55659.745, -4865942.28]), ('boundary #12', [45.0, -86.5], [5009377.086, -20037508.343]), ('boundary #13', [-120.0, -87.25], [-13358338.895, -20037508.343])], [('regression #9', [-540.0, 30.0], [-20037508.343, 3503549.844]), ('regression #10', [-250.0, 12.5], [12245143.987, 1402665.19]), ('regression #11', [-359.5, -40.0], [55659.745, -4865942.28]), ('boundary #12', [45.0, -86.5], [5009377.086, -20037508.343]), ('boundary #13', [-120.0, -87.25], [-13358338.895, -20037508.343]), ('regression #14', [-181.0, 0.5], [19926188.852, 55660.452]), ('control #15', [-17.048, 10.042], [-1897774.679, 1123637.827]), ('control #16', [151.867, -5.771], [16905757.108, -643513.79])], [('boundary #5', [0.0, 89.0], [0.0, 20037508.343]), ('boundary #12', [45.0, -86.5], [5009377.086, -20037508.343]), ('regression #14', [-181.0, 0.5], [19926188.852, 55660.452]), ('control #15', [-17.048, 10.042], [-1897774.679, 1123637.827]), ('control #16', [151.867, -5.771], [16905757.108, -643513.79]), ('control #17', [2.807, 14.681], [312473.811, 1652463.738]), ('control #18', [-112.892, 2.001], [-12567079.955, 222795.596]), ('control #19', [46.498, 49.22], [5176133.683, 6312273.571])]]
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
regression #0	`[-18924313.435, 1118889.975]`	`[-18924313.435, 1118889.975]`	Passed
regression #1	`[17811118.527, -2273030.927]`	`[17811118.527, -2273030.927]`	Passed
boundary #2	`[-20037508.343, -0.0]`	`[-20037508.343, -0.0]`	Passed
boundary #3	`[-20037508.343, 5621521.486]`	`[-20037508.343, 5621521.486]`	Passed
regression #4	`[-19480910.889, 557305.257]`	`[-19480910.889, 557305.257]`	Passed
boundary #5	`[0.0, 20037508.343]`	`[0.0, 20037508.343]`	Passed
boundary #6	`[1113194.908, -25819498.514]`	`[1113194.908, -20037508.343]`	Failed
boundary #7	`[0.0, 20037508.343]`	`[0.0, 20037508.343]`	Passed

SHA-256 / becbdf1fdf0da04b09949db6bcbfa3ceaf706412133b8487457134713819a9ae

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    lon, lat = x
    lon = ((lon + 180.0) % 360.0) - 180.0
    lat = max(-85.05112878, min(85.05112878, lat))
    R = 6378137.0
    px = R * math.radians(lon)
    py = R * math.log(math.tan(math.pi / 4 + math.radians(lat) / 2))
    return [round(px, 3), round(py, 3)]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('regression #0', [190.0, 10.0], [-18924313.435, 1118889.975]), ('regression #1', [-200.0, -20.0], [17811118.527, -2273030.927]), ('boundary #2', [180.0, 0.0], [-20037508.343, -0.0]), ('boundary #3', [-180.0, 45.0], [-20037508.343, 5621521.486]), ('regression #4', [545.0, 5.0], [-19480910.889, 557305.257]), ('boundary #5', [0.0, 89.0], [0.0, 20037508.343]), ('boundary #6', [10.0, -88.0], [1113194.908, -20037508.343]), ('boundary #7', [0.0, 85.05112878], [0.0, 20037508.343])], [('boundary #3', [-180.0, 45.0], [-20037508.343, 5621521.486]), ('regression #4', [545.0, 5.0], [-19480910.889, 557305.257]), ('boundary #5', [0.0, 89.0], [0.0, 20037508.343]), ('boundary #6', [10.0, -88.0], [1113194.908, -20037508.343]), ('boundary #7', [0.0, 85.05112878], [0.0, 20037508.343]), ('control #8', [0.0, 0.0], [0.0, -0.0]), ('regression #9', [-540.0, 30.0], [-20037508.343, 3503549.844]), ('boundary #13', [-120.0, -87.25], [-13358338.895, -20037508.343])], [('boundary #6', [10.0, -88.0], [1113194.908, -20037508.343]), ('boundary #7', [0.0, 85.05112878], [0.0, 20037508.343]), ('control #8', [0.0, 0.0], [0.0, -0.0]), ('regression #9', [-540.0, 30.0], [-20037508.343, 3503549.844]), ('regression #10', [-250.0, 12.5], [12245143.987, 1402665.19]), ('regression #11', [-359.5, -40.0], [55659.745, -4865942.28]), ('boundary #12', [45.0, -86.5], [5009377.086, -20037508.343]), ('boundary #13', [-120.0, -87.25], [-13358338.895, -20037508.343])], [('regression #9', [-540.0, 30.0], [-20037508.343, 3503549.844]), ('regression #10', [-250.0, 12.5], [12245143.987, 1402665.19]), ('regression #11', [-359.5, -40.0], [55659.745, -4865942.28]), ('boundary #12', [45.0, -86.5], [5009377.086, -20037508.343]), ('boundary #13', [-120.0, -87.25], [-13358338.895, -20037508.343]), ('regression #14', [-181.0, 0.5], [19926188.852, 55660.452]), ('control #15', [-17.048, 10.042], [-1897774.679, 1123637.827]), ('control #16', [151.867, -5.771], [16905757.108, -643513.79])], [('boundary #5', [0.0, 89.0], [0.0, 20037508.343]), ('boundary #12', [45.0, -86.5], [5009377.086, -20037508.343]), ('regression #14', [-181.0, 0.5], [19926188.852, 55660.452]), ('control #15', [-17.048, 10.042], [-1897774.679, 1123637.827]), ('control #16', [151.867, -5.771], [16905757.108, -643513.79]), ('control #17', [2.807, 14.681], [312473.811, 1652463.738]), ('control #18', [-112.892, 2.001], [-12567079.955, 222795.596]), ('control #19', [46.498, 49.22], [5176133.683, 6312273.571])]]
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
regression #0	`[-18924313.435, 1118889.975]`	`[-18924313.435, 1118889.975]`	Passed
regression #1	`[17811118.527, -2273030.927]`	`[17811118.527, -2273030.927]`	Passed
boundary #2	`[-20037508.343, -0.0]`	`[-20037508.343, -0.0]`	Passed
boundary #3	`[-20037508.343, 5621521.486]`	`[-20037508.343, 5621521.486]`	Passed
regression #4	`[-19480910.889, 557305.257]`	`[-19480910.889, 557305.257]`	Passed
boundary #5	`[0.0, 20037508.343]`	`[0.0, 20037508.343]`	Passed
boundary #6	`[1113194.908, -20037508.343]`	`[1113194.908, -20037508.343]`	Passed
boundary #7	`[0.0, 20037508.343]`	`[0.0, 20037508.343]`	Passed

SHA-256 / 6a73173f59bbd5550a90af75b2429fe683c7e9b2d6097100e10f1cb2f62a52bb

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 2026-09-29T14:48:15.194485+00:00.

Case digest / 7cdbaf8f689259b52ae4fcb956185aaca15fe6a6f019a0c6224700afb5bb41ba