FA-70276 / Map projection transforms / Open access

Affine geotransform inverse to pixel indices: row origin offset · case 01

Rows count upward from the origin for north-up rasters, sampling mirrored rows.

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

ROOT CAUSE

The row offset is measured as origin minus point, as if the raster had a positive pixel height.

VERIFIED REPAIR

At the row origin offset step restore `dy = gy - gt[3]`, leaving the rest of the model unchanged.

Unsuccessful approach: Using the absolute offset makes rasters with a positive pixel height index the wrong rows above the origin.

Case contract

Input [gx, gy, gt, width, height] with a six-term affine gt: X = gt0 + col*gt1 + row*gt2, Y = gt3 + col*gt4 + row*gt5, where (gt0, gt3) is the outer corner of pixel (0, 0). Invert with the 2x2 determinant, take floor of the fractional column and row, and return [col, row] if inside [0, width) x [0, height), otherwise None (also None for a singular transform).

Why this case matters

Point sampling of rasters and click-to-pixel lookups rely on this inverse; half-pixel or sign mistakes read the neighbouring cell.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    gx, gy, gt, width, height = x
    det = gt[1] * gt[5] - gt[2] * gt[4]
    if det == 0:
        return None
    dx = gx - gt[0]
    dy = gt[3] - gy
    col = (gt[5] * dx - gt[2] * dy) / det
    row = (-gt[4] * dx + gt[1] * dy) / det
    c, r = math.floor(col), math.floor(row)
    if c < 0 or r < 0 or c >= width or r >= height:
        return None
    return [c, r]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [501757.3953, 4199818.2948, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], [58, 6]), ('control #1', [-171.8788, 83.4562, [-180.0, 0.25, 0.0, 90.0, 0.0, -0.25], 100, 80], [32, 26]), ('control #2', [1046.5787, 4959.4742, [1000.0, 2.0, 0.5, 5000.0, 0.4, -2.0], 100, 80], [17, 23]), ('control #3', [515.0875, 607.7306, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], [32, 35]), ('control #4', [76.2652, 18.2363, [0.0, 1.0, 0.0, 0.0, 0.0, 1.0], 100, 80], [76, 18]), ('control #14', [43.3467, 82.4576, [0.0, 1.0, 0.0, 0.0, 0.0, 1.0], 100, 80], None), ('control #18', [1072.1342, 274.3213, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], None), ('control #20', [500293.3311, 4197517.5517, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], None)], [('control #1', [-171.8788, 83.4562, [-180.0, 0.25, 0.0, 90.0, 0.0, -0.25], 100, 80], [32, 26]), ('control #2', [1046.5787, 4959.4742, [1000.0, 2.0, 0.5, 5000.0, 0.4, -2.0], 100, 80], [17, 23]), ('control #5', [500628.6941, 4200027.3496, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], None), ('control #6', [-155.5787, 74.1746, [-180.0, 0.25, 0.0, 90.0, 0.0, -0.25], 100, 80], [97, 63]), ('control #7', [1081.9041, 4971.5191, [1000.0, 2.0, 0.5, 5000.0, 0.4, -2.0], 100, 80], [35, 21]), ('control #14', [43.3467, 82.4576, [0.0, 1.0, 0.0, 0.0, 0.0, 1.0], 100, 80], None), ('control #18', [1072.1342, 274.3213, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], None), ('control #20', [500293.3311, 4197517.5517, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], None)], [('control #2', [1046.5787, 4959.4742, [1000.0, 2.0, 0.5, 5000.0, 0.4, -2.0], 100, 80], [17, 23]), ('control #3', [515.0875, 607.7306, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], [32, 35]), ('control #8', [1154.1901, 783.547, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], [94, 30]), ('control #9', [38.71, 51.2013, [0.0, 1.0, 0.0, 0.0, 0.0, 1.0], 100, 80], [38, 51]), ('control #10', [500787.7801, 4199579.3798, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], [26, 14]), ('control #14', [43.3467, 82.4576, [0.0, 1.0, 0.0, 0.0, 0.0, 1.0], 100, 80], None), ('control #18', [1072.1342, 274.3213, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], None), ('control #20', [500293.3311, 4197517.5517, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], None)], [('control #3', [515.0875, 607.7306, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], [32, 35]), ('control #6', [-155.5787, 74.1746, [-180.0, 0.25, 0.0, 90.0, 0.0, -0.25], 100, 80], [97, 63]), ('control #11', [-179.8182, 72.2686, [-180.0, 0.25, 0.0, 90.0, 0.0, -0.25], 100, 80], [0, 70]), ('control #12', [1181.1787, 4910.1448, [1000.0, 2.0, 0.5, 5000.0, 0.4, -2.0], 100, 80], [75, 60]), ('control #13', [651.582, 912.3698, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], [37, 6]), ('control #14', [43.3467, 82.4576, [0.0, 1.0, 0.0, 0.0, 0.0, 1.0], 100, 80], None), ('control #18', [1072.1342, 274.3213, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], None), ('control #20', [500293.3311, 4197517.5517, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], None)], [('control #4', [76.2652, 18.2363, [0.0, 1.0, 0.0, 0.0, 0.0, 1.0], 100, 80], [76, 18]), ('control #6', [-155.5787, 74.1746, [-180.0, 0.25, 0.0, 90.0, 0.0, -0.25], 100, 80], [97, 63]), ('control #14', [43.3467, 82.4576, [0.0, 1.0, 0.0, 0.0, 0.0, 1.0], 100, 80], None), ('control #15', [500583.8568, 4199766.5953, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], [19, 7]), ('control #16', [-155.0962, 71.5551, [-180.0, 0.25, 0.0, 90.0, 0.0, -0.25], 100, 80], [99, 73]), ('control #17', [1052.7736, 4892.5715, [1000.0, 2.0, 0.5, 5000.0, 0.4, -2.0], 100, 80], [12, 56]), ('control #18', [1072.1342, 274.3213, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], None), ('control #20', [500293.3311, 4197517.5517, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], None)]]
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	`None`	`[58, 6]`	Failed
control #1	`None`	`[32, 26]`	Failed
control #2	`None`	`[17, 23]`	Failed
control #3	`None`	`[32, 35]`	Failed
control #4	`None`	`[76, 18]`	Failed
control #14	`None`	`None`	Passed
control #18	`None`	`None`	Passed
control #20	`None`	`None`	Passed

SHA-256 / d96e80d58bd1c4d44e6511cfd958b52cbf47d128614a2e8c16829d75b11811e7

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    gx, gy, gt, width, height = x
    det = gt[1] * gt[5] - gt[2] * gt[4]
    if det == 0:
        return None
    dx = gx - gt[0]
    dy = abs(gy - gt[3])
    col = (gt[5] * dx - gt[2] * dy) / det
    row = (-gt[4] * dx + gt[1] * dy) / det
    c, r = math.floor(col), math.floor(row)
    if c < 0 or r < 0 or c >= width or r >= height:
        return None
    return [c, r]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [501757.3953, 4199818.2948, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], [58, 6]), ('control #1', [-171.8788, 83.4562, [-180.0, 0.25, 0.0, 90.0, 0.0, -0.25], 100, 80], [32, 26]), ('control #2', [1046.5787, 4959.4742, [1000.0, 2.0, 0.5, 5000.0, 0.4, -2.0], 100, 80], [17, 23]), ('control #3', [515.0875, 607.7306, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], [32, 35]), ('control #4', [76.2652, 18.2363, [0.0, 1.0, 0.0, 0.0, 0.0, 1.0], 100, 80], [76, 18]), ('control #14', [43.3467, 82.4576, [0.0, 1.0, 0.0, 0.0, 0.0, 1.0], 100, 80], None), ('control #18', [1072.1342, 274.3213, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], None), ('control #20', [500293.3311, 4197517.5517, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], None)], [('control #1', [-171.8788, 83.4562, [-180.0, 0.25, 0.0, 90.0, 0.0, -0.25], 100, 80], [32, 26]), ('control #2', [1046.5787, 4959.4742, [1000.0, 2.0, 0.5, 5000.0, 0.4, -2.0], 100, 80], [17, 23]), ('control #5', [500628.6941, 4200027.3496, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], None), ('control #6', [-155.5787, 74.1746, [-180.0, 0.25, 0.0, 90.0, 0.0, -0.25], 100, 80], [97, 63]), ('control #7', [1081.9041, 4971.5191, [1000.0, 2.0, 0.5, 5000.0, 0.4, -2.0], 100, 80], [35, 21]), ('control #14', [43.3467, 82.4576, [0.0, 1.0, 0.0, 0.0, 0.0, 1.0], 100, 80], None), ('control #18', [1072.1342, 274.3213, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], None), ('control #20', [500293.3311, 4197517.5517, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], None)], [('control #2', [1046.5787, 4959.4742, [1000.0, 2.0, 0.5, 5000.0, 0.4, -2.0], 100, 80], [17, 23]), ('control #3', [515.0875, 607.7306, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], [32, 35]), ('control #8', [1154.1901, 783.547, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], [94, 30]), ('control #9', [38.71, 51.2013, [0.0, 1.0, 0.0, 0.0, 0.0, 1.0], 100, 80], [38, 51]), ('control #10', [500787.7801, 4199579.3798, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], [26, 14]), ('control #14', [43.3467, 82.4576, [0.0, 1.0, 0.0, 0.0, 0.0, 1.0], 100, 80], None), ('control #18', [1072.1342, 274.3213, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], None), ('control #20', [500293.3311, 4197517.5517, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], None)], [('control #3', [515.0875, 607.7306, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], [32, 35]), ('control #6', [-155.5787, 74.1746, [-180.0, 0.25, 0.0, 90.0, 0.0, -0.25], 100, 80], [97, 63]), ('control #11', [-179.8182, 72.2686, [-180.0, 0.25, 0.0, 90.0, 0.0, -0.25], 100, 80], [0, 70]), ('control #12', [1181.1787, 4910.1448, [1000.0, 2.0, 0.5, 5000.0, 0.4, -2.0], 100, 80], [75, 60]), ('control #13', [651.582, 912.3698, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], [37, 6]), ('control #14', [43.3467, 82.4576, [0.0, 1.0, 0.0, 0.0, 0.0, 1.0], 100, 80], None), ('control #18', [1072.1342, 274.3213, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], None), ('control #20', [500293.3311, 4197517.5517, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], None)], [('control #4', [76.2652, 18.2363, [0.0, 1.0, 0.0, 0.0, 0.0, 1.0], 100, 80], [76, 18]), ('control #6', [-155.5787, 74.1746, [-180.0, 0.25, 0.0, 90.0, 0.0, -0.25], 100, 80], [97, 63]), ('control #14', [43.3467, 82.4576, [0.0, 1.0, 0.0, 0.0, 0.0, 1.0], 100, 80], None), ('control #15', [500583.8568, 4199766.5953, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], [19, 7]), ('control #16', [-155.0962, 71.5551, [-180.0, 0.25, 0.0, 90.0, 0.0, -0.25], 100, 80], [99, 73]), ('control #17', [1052.7736, 4892.5715, [1000.0, 2.0, 0.5, 5000.0, 0.4, -2.0], 100, 80], [12, 56]), ('control #18', [1072.1342, 274.3213, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], None), ('control #20', [500293.3311, 4197517.5517, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], None)]]
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	`None`	`[58, 6]`	Failed
control #1	`None`	`[32, 26]`	Failed
control #2	`None`	`[17, 23]`	Failed
control #3	`None`	`[32, 35]`	Failed
control #4	`[76, 18]`	`[76, 18]`	Passed
control #14	`None`	`None`	Passed
control #18	`None`	`None`	Passed
control #20	`None`	`None`	Passed

SHA-256 / 894e542526d4a0ecdc06dd63ab6b85b17ae94311e1174abb2afb72fdb4388c68

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    gx, gy, gt, width, height = x
    det = gt[1] * gt[5] - gt[2] * gt[4]
    if det == 0:
        return None
    dx = gx - gt[0]
    dy = gy - gt[3]
    col = (gt[5] * dx - gt[2] * dy) / det
    row = (-gt[4] * dx + gt[1] * dy) / det
    c, r = math.floor(col), math.floor(row)
    if c < 0 or r < 0 or c >= width or r >= height:
        return None
    return [c, r]
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', [501757.3953, 4199818.2948, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], [58, 6]), ('control #1', [-171.8788, 83.4562, [-180.0, 0.25, 0.0, 90.0, 0.0, -0.25], 100, 80], [32, 26]), ('control #2', [1046.5787, 4959.4742, [1000.0, 2.0, 0.5, 5000.0, 0.4, -2.0], 100, 80], [17, 23]), ('control #3', [515.0875, 607.7306, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], [32, 35]), ('control #4', [76.2652, 18.2363, [0.0, 1.0, 0.0, 0.0, 0.0, 1.0], 100, 80], [76, 18]), ('control #14', [43.3467, 82.4576, [0.0, 1.0, 0.0, 0.0, 0.0, 1.0], 100, 80], None), ('control #18', [1072.1342, 274.3213, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], None), ('control #20', [500293.3311, 4197517.5517, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], None)], [('control #1', [-171.8788, 83.4562, [-180.0, 0.25, 0.0, 90.0, 0.0, -0.25], 100, 80], [32, 26]), ('control #2', [1046.5787, 4959.4742, [1000.0, 2.0, 0.5, 5000.0, 0.4, -2.0], 100, 80], [17, 23]), ('control #5', [500628.6941, 4200027.3496, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], None), ('control #6', [-155.5787, 74.1746, [-180.0, 0.25, 0.0, 90.0, 0.0, -0.25], 100, 80], [97, 63]), ('control #7', [1081.9041, 4971.5191, [1000.0, 2.0, 0.5, 5000.0, 0.4, -2.0], 100, 80], [35, 21]), ('control #14', [43.3467, 82.4576, [0.0, 1.0, 0.0, 0.0, 0.0, 1.0], 100, 80], None), ('control #18', [1072.1342, 274.3213, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], None), ('control #20', [500293.3311, 4197517.5517, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], None)], [('control #2', [1046.5787, 4959.4742, [1000.0, 2.0, 0.5, 5000.0, 0.4, -2.0], 100, 80], [17, 23]), ('control #3', [515.0875, 607.7306, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], [32, 35]), ('control #8', [1154.1901, 783.547, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], [94, 30]), ('control #9', [38.71, 51.2013, [0.0, 1.0, 0.0, 0.0, 0.0, 1.0], 100, 80], [38, 51]), ('control #10', [500787.7801, 4199579.3798, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], [26, 14]), ('control #14', [43.3467, 82.4576, [0.0, 1.0, 0.0, 0.0, 0.0, 1.0], 100, 80], None), ('control #18', [1072.1342, 274.3213, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], None), ('control #20', [500293.3311, 4197517.5517, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], None)], [('control #3', [515.0875, 607.7306, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], [32, 35]), ('control #6', [-155.5787, 74.1746, [-180.0, 0.25, 0.0, 90.0, 0.0, -0.25], 100, 80], [97, 63]), ('control #11', [-179.8182, 72.2686, [-180.0, 0.25, 0.0, 90.0, 0.0, -0.25], 100, 80], [0, 70]), ('control #12', [1181.1787, 4910.1448, [1000.0, 2.0, 0.5, 5000.0, 0.4, -2.0], 100, 80], [75, 60]), ('control #13', [651.582, 912.3698, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], [37, 6]), ('control #14', [43.3467, 82.4576, [0.0, 1.0, 0.0, 0.0, 0.0, 1.0], 100, 80], None), ('control #18', [1072.1342, 274.3213, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], None), ('control #20', [500293.3311, 4197517.5517, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], None)], [('control #4', [76.2652, 18.2363, [0.0, 1.0, 0.0, 0.0, 0.0, 1.0], 100, 80], [76, 18]), ('control #6', [-155.5787, 74.1746, [-180.0, 0.25, 0.0, 90.0, 0.0, -0.25], 100, 80], [97, 63]), ('control #14', [43.3467, 82.4576, [0.0, 1.0, 0.0, 0.0, 0.0, 1.0], 100, 80], None), ('control #15', [500583.8568, 4199766.5953, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], [19, 7]), ('control #16', [-155.0962, 71.5551, [-180.0, 0.25, 0.0, 90.0, 0.0, -0.25], 100, 80], [99, 73]), ('control #17', [1052.7736, 4892.5715, [1000.0, 2.0, 0.5, 5000.0, 0.4, -2.0], 100, 80], [12, 56]), ('control #18', [1072.1342, 274.3213, [300.0, 10.0, -3.0, 900.0, 2.0, -10.0], 100, 80], None), ('control #20', [500293.3311, 4197517.5517, [500000.0, 30.0, 0.0, 4200000.0, 0.0, -30.0], 100, 80], None)]]
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	`[58, 6]`	`[58, 6]`	Passed
control #1	`[32, 26]`	`[32, 26]`	Passed
control #2	`[17, 23]`	`[17, 23]`	Passed
control #3	`[32, 35]`	`[32, 35]`	Passed
control #4	`[76, 18]`	`[76, 18]`	Passed
control #14	`None`	`None`	Passed
control #18	`None`	`None`	Passed
control #20	`None`	`None`	Passed

SHA-256 / 391eb0cc7e6b8a4517e6eb41c1010573eb7f1685858e0b7a2b7c6bb63c87ca83

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 2026-09-29T14:48:19.159837+00:00.

Case digest / b4a58dbd433bbf65315f1854a1c027241806e60a4a80fd4f07066cd957fd07e6