FA-70711 / GIS polygon topology / Open access

WKT polygon and multipolygon ring structure: multipolygon nesting · case 01

Multipolygons are read as one polygon whose rings are polygons.

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

ROOT CAUSE

The extra nesting level of MULTIPOLYGON is not unwrapped.

VERIFIED REPAIR

At the multipolygon nesting step restore `polys = [tree] if words[0] == 'POLYGON' else tree`, leaving the rest of the model unchanged.

Unsuccessful approach: Single-part multipolygons are still wrapped one level too deep.

Case contract

Input: a WKT string. The keyword (case-insensitive) must be POLYGON or MULTIPOLYGON, else None; "<keyword> EMPTY" returns []. Otherwise parse the parenthesised body into polygons -> rings -> positions, keeping only x and y of every position (Z/M ordinates are dropped). Every ring must have at least 4 positions and be closed in x/y, else None. Return a list of polygons (a POLYGON gives a one-element list).

Why this case matters

WKT is the lingua franca between databases and GIS tools; losing a dimension or nesting level corrupts rings.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    s = x.strip()
    up = s.upper()
    words = up.replace('(', ' ( ').split()
    if not words or words[0] not in ('POLYGON', 'MULTIPOLYGON'):
        return None
    if len(words) == 2 and words[1] == 'EMPTY':
        return []
    if '(' not in s:
        return None
    body = s[s.index('('):]
    stack = [[]]
    cur = ''
    for ch in body:
        if ch == '(':
            stack.append([])
        elif ch in '),':
            if cur.strip():
                nums = [float(t) for t in cur.split()]
                stack[-1].append(nums[:2])
            cur = ''
            if ch == ')':
                done = stack.pop()
                stack[-1].append(done)
        else:
            cur += ch
    tree = stack[0][0]
    polys = [tree]
    for poly in polys:
        for ring in poly:
            if len(ring) < 4 or ring[0] != ring[-1]:
                return None
    return polys
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', 'POLYGON ((0 0, 4 0, 4 4, 0 4, 0 0))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 4.0], [0.0, 0.0]]]]), ('control #1', 'POLYGON ((0 0, 10 0, 10 10, 0 10, 0 0), (2 2, 2 4, 4 4, 2 2))', [[[[0.0, 0.0], [10.0, 0.0], [10.0, 10.0], [0.0, 10.0], [0.0, 0.0]], [[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [2.0, 2.0]]]]), ('regression #2', 'POLYGON Z ((0 0 5, 4 0 5, 4 4 6, 0 0 5))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #3', 'POLYGON ZM ((0 0 5 1, 4 0 5 2, 4 4 6 3, 0 0 5 1))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #4', 'POLYGON M ((0 0 7, 4 0 8, 4 4 9, 0 0 7))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('boundary #5', 'POLYGON EMPTY', []), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]), ('regression #8', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]])], [('regression #3', 'POLYGON ZM ((0 0 5 1, 4 0 5 2, 4 4 6 3, 0 0 5 1))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #4', 'POLYGON M ((0 0 7, 4 0 8, 4 4 9, 0 0 7))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('boundary #5', 'POLYGON EMPTY', []), ('boundary #6', 'polygon empty', []), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]), ('regression #8', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]]), ('regression #9', 'multipolygon (((-1.5 -2, 3e2 0, 0 1e1, -1.5 -2)))', [[[[-1.5, -2.0], [300.0, 0.0], [0.0, 10.0], [-1.5, -2.0]]]]), ('boundary #10', 'POLYGON ((0 0, 4 0, 4 4, 0 1))', None)], [('boundary #6', 'polygon empty', []), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]), ('regression #8', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]]), ('regression #9', 'multipolygon (((-1.5 -2, 3e2 0, 0 1e1, -1.5 -2)))', [[[[-1.5, -2.0], [300.0, 0.0], [0.0, 10.0], [-1.5, -2.0]]]]), ('boundary #10', 'POLYGON ((0 0, 4 0, 4 4, 0 1))', None), ('boundary #11', 'POLYGON ((0 0, 4 0, 0 0))', None), ('control #12', 'Polygon((1 1,5 1,5 5,1 1))', [[[[1.0, 1.0], [5.0, 1.0], [5.0, 5.0], [1.0, 1.0]]]]), ('boundary #13', 'LINESTRING (0 0, 1 1)', None)], [('regression #9', 'multipolygon (((-1.5 -2, 3e2 0, 0 1e1, -1.5 -2)))', [[[[-1.5, -2.0], [300.0, 0.0], [0.0, 10.0], [-1.5, -2.0]]]]), ('boundary #10', 'POLYGON ((0 0, 4 0, 4 4, 0 1))', None), ('boundary #11', 'POLYGON ((0 0, 4 0, 0 0))', None), ('control #12', 'Polygon((1 1,5 1,5 5,1 1))', [[[[1.0, 1.0], [5.0, 1.0], [5.0, 5.0], [1.0, 1.0]]]]), ('boundary #13', 'LINESTRING (0 0, 1 1)', None), ('boundary #14', 'MULTIPOLYGON EMPTY', []), ('control #15', '  POLYGON ((0 0, -3 0, -3 -3, 0 0))  ', [[[[0.0, 0.0], [-3.0, 0.0], [-3.0, -3.0], [0.0, 0.0]]]]), ('regression #16', 'MULTIPOLYGON Z (((0 0 1, 2 0 1, 2 2 1, 0 0 1)), ((9 9 0, 8 9 0, 8 8 0, 9 9 0)))', [[[[0.0, 0.0], [2.0, 0.0], [2.0, 2.0], [0.0, 0.0]]], [[[9.0, 9.0], [8.0, 9.0], [8.0, 8.0], [9.0, 9.0]]]])], [('control #0', 'POLYGON ((0 0, 4 0, 4 4, 0 4, 0 0))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 4.0], [0.0, 0.0]]]]), ('control #1', 'POLYGON ((0 0, 10 0, 10 10, 0 10, 0 0), (2 2, 2 4, 4 4, 2 2))', [[[[0.0, 0.0], [10.0, 0.0], [10.0, 10.0], [0.0, 10.0], [0.0, 0.0]], [[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [2.0, 2.0]]]]), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]), ('regression #8', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]]), ('boundary #14', 'MULTIPOLYGON EMPTY', []), ('control #15', '  POLYGON ((0 0, -3 0, -3 -3, 0 0))  ', [[[[0.0, 0.0], [-3.0, 0.0], [-3.0, -3.0], [0.0, 0.0]]]]), ('regression #16', 'MULTIPOLYGON Z (((0 0 1, 2 0 1, 2 2 1, 0 0 1)), ((9 9 0, 8 9 0, 8 8 0, 9 9 0)))', [[[[0.0, 0.0], [2.0, 0.0], [2.0, 2.0], [0.0, 0.0]]], [[[9.0, 9.0], [8.0, 9.0], [8.0, 8.0], [9.0, 9.0]]]]), ('boundary #17', 'POLYGON ((0 0 1, 4 0 1, 4 4 1, 0 0 2))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]])]]
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	`[[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 4.0], [0.0, 0.0]]]]`	`[[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 4.0], [0.0, 0.0]]]]`	Passed
control #1	`[[[[0.0, 0.0], [10.0, 0.0], [10.0, 10.0], [0.0, 10.0], [0.0, 0.0]], [[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [2.0, 2.0]]]]`	`[[[[0.0, 0.0], [10.0, 0.0], [10.0, 10.0], [0.0, 10.0], [0.0, 0.0]], [[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [2.0, 2.0]]]]`	Passed
regression #2	`[[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]`	`[[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]`	Passed
regression #3	`[[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]`	`[[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]`	Passed
regression #4	`[[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]`	`[[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]`	Passed
boundary #5	`[]`	`[]`	Passed
regression #7	`None`	`[[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]`	Failed
regression #8	`None`	`[[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]]`	Failed

SHA-256 / fb3bfb31770d716a6049fd12e48313b01245574aa4dd2c93ac07510650edc24a

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    s = x.strip()
    up = s.upper()
    words = up.replace('(', ' ( ').split()
    if not words or words[0] not in ('POLYGON', 'MULTIPOLYGON'):
        return None
    if len(words) == 2 and words[1] == 'EMPTY':
        return []
    if '(' not in s:
        return None
    body = s[s.index('('):]
    stack = [[]]
    cur = ''
    for ch in body:
        if ch == '(':
            stack.append([])
        elif ch in '),':
            if cur.strip():
                nums = [float(t) for t in cur.split()]
                stack[-1].append(nums[:2])
            cur = ''
            if ch == ')':
                done = stack.pop()
                stack[-1].append(done)
        else:
            cur += ch
    tree = stack[0][0]
    polys = tree if words[0] == 'MULTIPOLYGON' and len(tree) > 1 else [tree]
    for poly in polys:
        for ring in poly:
            if len(ring) < 4 or ring[0] != ring[-1]:
                return None
    return polys
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', 'POLYGON ((0 0, 4 0, 4 4, 0 4, 0 0))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 4.0], [0.0, 0.0]]]]), ('control #1', 'POLYGON ((0 0, 10 0, 10 10, 0 10, 0 0), (2 2, 2 4, 4 4, 2 2))', [[[[0.0, 0.0], [10.0, 0.0], [10.0, 10.0], [0.0, 10.0], [0.0, 0.0]], [[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [2.0, 2.0]]]]), ('regression #2', 'POLYGON Z ((0 0 5, 4 0 5, 4 4 6, 0 0 5))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #3', 'POLYGON ZM ((0 0 5 1, 4 0 5 2, 4 4 6 3, 0 0 5 1))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #4', 'POLYGON M ((0 0 7, 4 0 8, 4 4 9, 0 0 7))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('boundary #5', 'POLYGON EMPTY', []), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]), ('regression #8', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]])], [('regression #3', 'POLYGON ZM ((0 0 5 1, 4 0 5 2, 4 4 6 3, 0 0 5 1))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #4', 'POLYGON M ((0 0 7, 4 0 8, 4 4 9, 0 0 7))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('boundary #5', 'POLYGON EMPTY', []), ('boundary #6', 'polygon empty', []), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]), ('regression #8', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]]), ('regression #9', 'multipolygon (((-1.5 -2, 3e2 0, 0 1e1, -1.5 -2)))', [[[[-1.5, -2.0], [300.0, 0.0], [0.0, 10.0], [-1.5, -2.0]]]]), ('boundary #10', 'POLYGON ((0 0, 4 0, 4 4, 0 1))', None)], [('boundary #6', 'polygon empty', []), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]), ('regression #8', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]]), ('regression #9', 'multipolygon (((-1.5 -2, 3e2 0, 0 1e1, -1.5 -2)))', [[[[-1.5, -2.0], [300.0, 0.0], [0.0, 10.0], [-1.5, -2.0]]]]), ('boundary #10', 'POLYGON ((0 0, 4 0, 4 4, 0 1))', None), ('boundary #11', 'POLYGON ((0 0, 4 0, 0 0))', None), ('control #12', 'Polygon((1 1,5 1,5 5,1 1))', [[[[1.0, 1.0], [5.0, 1.0], [5.0, 5.0], [1.0, 1.0]]]]), ('boundary #13', 'LINESTRING (0 0, 1 1)', None)], [('regression #9', 'multipolygon (((-1.5 -2, 3e2 0, 0 1e1, -1.5 -2)))', [[[[-1.5, -2.0], [300.0, 0.0], [0.0, 10.0], [-1.5, -2.0]]]]), ('boundary #10', 'POLYGON ((0 0, 4 0, 4 4, 0 1))', None), ('boundary #11', 'POLYGON ((0 0, 4 0, 0 0))', None), ('control #12', 'Polygon((1 1,5 1,5 5,1 1))', [[[[1.0, 1.0], [5.0, 1.0], [5.0, 5.0], [1.0, 1.0]]]]), ('boundary #13', 'LINESTRING (0 0, 1 1)', None), ('boundary #14', 'MULTIPOLYGON EMPTY', []), ('control #15', '  POLYGON ((0 0, -3 0, -3 -3, 0 0))  ', [[[[0.0, 0.0], [-3.0, 0.0], [-3.0, -3.0], [0.0, 0.0]]]]), ('regression #16', 'MULTIPOLYGON Z (((0 0 1, 2 0 1, 2 2 1, 0 0 1)), ((9 9 0, 8 9 0, 8 8 0, 9 9 0)))', [[[[0.0, 0.0], [2.0, 0.0], [2.0, 2.0], [0.0, 0.0]]], [[[9.0, 9.0], [8.0, 9.0], [8.0, 8.0], [9.0, 9.0]]]])], [('control #0', 'POLYGON ((0 0, 4 0, 4 4, 0 4, 0 0))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 4.0], [0.0, 0.0]]]]), ('control #1', 'POLYGON ((0 0, 10 0, 10 10, 0 10, 0 0), (2 2, 2 4, 4 4, 2 2))', [[[[0.0, 0.0], [10.0, 0.0], [10.0, 10.0], [0.0, 10.0], [0.0, 0.0]], [[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [2.0, 2.0]]]]), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]), ('regression #8', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]]), ('boundary #14', 'MULTIPOLYGON EMPTY', []), ('control #15', '  POLYGON ((0 0, -3 0, -3 -3, 0 0))  ', [[[[0.0, 0.0], [-3.0, 0.0], [-3.0, -3.0], [0.0, 0.0]]]]), ('regression #16', 'MULTIPOLYGON Z (((0 0 1, 2 0 1, 2 2 1, 0 0 1)), ((9 9 0, 8 9 0, 8 8 0, 9 9 0)))', [[[[0.0, 0.0], [2.0, 0.0], [2.0, 2.0], [0.0, 0.0]]], [[[9.0, 9.0], [8.0, 9.0], [8.0, 8.0], [9.0, 9.0]]]]), ('boundary #17', 'POLYGON ((0 0 1, 4 0 1, 4 4 1, 0 0 2))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]])]]
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	`[[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 4.0], [0.0, 0.0]]]]`	`[[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 4.0], [0.0, 0.0]]]]`	Passed
control #1	`[[[[0.0, 0.0], [10.0, 0.0], [10.0, 10.0], [0.0, 10.0], [0.0, 0.0]], [[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [2.0, 2.0]]]]`	`[[[[0.0, 0.0], [10.0, 0.0], [10.0, 10.0], [0.0, 10.0], [0.0, 0.0]], [[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [2.0, 2.0]]]]`	Passed
regression #2	`[[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]`	`[[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]`	Passed
regression #3	`[[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]`	`[[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]`	Passed
regression #4	`[[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]`	`[[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]`	Passed
boundary #5	`[]`	`[]`	Passed
regression #7	`[[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]`	`[[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]`	Passed
regression #8	`None`	`[[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]]`	Failed

SHA-256 / 4386b98820caee5a00e5950e401ec4d3bd196b2f6e1afda2dc969d5561067dd2

3 / The verified repair

Exit 0

"""Failure Map reference implementation. Python standard library only."""
import json
import math
N = 1
observations = []
def solve(x):
    s = x.strip()
    up = s.upper()
    words = up.replace('(', ' ( ').split()
    if not words or words[0] not in ('POLYGON', 'MULTIPOLYGON'):
        return None
    if len(words) == 2 and words[1] == 'EMPTY':
        return []
    if '(' not in s:
        return None
    body = s[s.index('('):]
    stack = [[]]
    cur = ''
    for ch in body:
        if ch == '(':
            stack.append([])
        elif ch in '),':
            if cur.strip():
                nums = [float(t) for t in cur.split()]
                stack[-1].append(nums[:2])
            cur = ''
            if ch == ')':
                done = stack.pop()
                stack[-1].append(done)
        else:
            cur += ch
    tree = stack[0][0]
    polys = [tree] if words[0] == 'POLYGON' else tree
    for poly in polys:
        for ring in poly:
            if len(ring) < 4 or ring[0] != ring[-1]:
                return None
    return polys
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
fixtures = [[('control #0', 'POLYGON ((0 0, 4 0, 4 4, 0 4, 0 0))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 4.0], [0.0, 0.0]]]]), ('control #1', 'POLYGON ((0 0, 10 0, 10 10, 0 10, 0 0), (2 2, 2 4, 4 4, 2 2))', [[[[0.0, 0.0], [10.0, 0.0], [10.0, 10.0], [0.0, 10.0], [0.0, 0.0]], [[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [2.0, 2.0]]]]), ('regression #2', 'POLYGON Z ((0 0 5, 4 0 5, 4 4 6, 0 0 5))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #3', 'POLYGON ZM ((0 0 5 1, 4 0 5 2, 4 4 6 3, 0 0 5 1))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #4', 'POLYGON M ((0 0 7, 4 0 8, 4 4 9, 0 0 7))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('boundary #5', 'POLYGON EMPTY', []), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]), ('regression #8', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]])], [('regression #3', 'POLYGON ZM ((0 0 5 1, 4 0 5 2, 4 4 6 3, 0 0 5 1))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('regression #4', 'POLYGON M ((0 0 7, 4 0 8, 4 4 9, 0 0 7))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]), ('boundary #5', 'POLYGON EMPTY', []), ('boundary #6', 'polygon empty', []), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]), ('regression #8', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]]), ('regression #9', 'multipolygon (((-1.5 -2, 3e2 0, 0 1e1, -1.5 -2)))', [[[[-1.5, -2.0], [300.0, 0.0], [0.0, 10.0], [-1.5, -2.0]]]]), ('boundary #10', 'POLYGON ((0 0, 4 0, 4 4, 0 1))', None)], [('boundary #6', 'polygon empty', []), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]), ('regression #8', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]]), ('regression #9', 'multipolygon (((-1.5 -2, 3e2 0, 0 1e1, -1.5 -2)))', [[[[-1.5, -2.0], [300.0, 0.0], [0.0, 10.0], [-1.5, -2.0]]]]), ('boundary #10', 'POLYGON ((0 0, 4 0, 4 4, 0 1))', None), ('boundary #11', 'POLYGON ((0 0, 4 0, 0 0))', None), ('control #12', 'Polygon((1 1,5 1,5 5,1 1))', [[[[1.0, 1.0], [5.0, 1.0], [5.0, 5.0], [1.0, 1.0]]]]), ('boundary #13', 'LINESTRING (0 0, 1 1)', None)], [('regression #9', 'multipolygon (((-1.5 -2, 3e2 0, 0 1e1, -1.5 -2)))', [[[[-1.5, -2.0], [300.0, 0.0], [0.0, 10.0], [-1.5, -2.0]]]]), ('boundary #10', 'POLYGON ((0 0, 4 0, 4 4, 0 1))', None), ('boundary #11', 'POLYGON ((0 0, 4 0, 0 0))', None), ('control #12', 'Polygon((1 1,5 1,5 5,1 1))', [[[[1.0, 1.0], [5.0, 1.0], [5.0, 5.0], [1.0, 1.0]]]]), ('boundary #13', 'LINESTRING (0 0, 1 1)', None), ('boundary #14', 'MULTIPOLYGON EMPTY', []), ('control #15', '  POLYGON ((0 0, -3 0, -3 -3, 0 0))  ', [[[[0.0, 0.0], [-3.0, 0.0], [-3.0, -3.0], [0.0, 0.0]]]]), ('regression #16', 'MULTIPOLYGON Z (((0 0 1, 2 0 1, 2 2 1, 0 0 1)), ((9 9 0, 8 9 0, 8 8 0, 9 9 0)))', [[[[0.0, 0.0], [2.0, 0.0], [2.0, 2.0], [0.0, 0.0]]], [[[9.0, 9.0], [8.0, 9.0], [8.0, 8.0], [9.0, 9.0]]]])], [('control #0', 'POLYGON ((0 0, 4 0, 4 4, 0 4, 0 0))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 4.0], [0.0, 0.0]]]]), ('control #1', 'POLYGON ((0 0, 10 0, 10 10, 0 10, 0 0), (2 2, 2 4, 4 4, 2 2))', [[[[0.0, 0.0], [10.0, 0.0], [10.0, 10.0], [0.0, 10.0], [0.0, 0.0]], [[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [2.0, 2.0]]]]), ('regression #7', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)), ((5 5, 6 5, 6 6, 5 5), (5.2 5.1, 5.8 5.8, 5.8 5.1, 5.2 5.1)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]), ('regression #8', 'MULTIPOLYGON (((0 0, 1 0, 1 1, 0 0)))', [[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]]), ('boundary #14', 'MULTIPOLYGON EMPTY', []), ('control #15', '  POLYGON ((0 0, -3 0, -3 -3, 0 0))  ', [[[[0.0, 0.0], [-3.0, 0.0], [-3.0, -3.0], [0.0, 0.0]]]]), ('regression #16', 'MULTIPOLYGON Z (((0 0 1, 2 0 1, 2 2 1, 0 0 1)), ((9 9 0, 8 9 0, 8 8 0, 9 9 0)))', [[[[0.0, 0.0], [2.0, 0.0], [2.0, 2.0], [0.0, 0.0]]], [[[9.0, 9.0], [8.0, 9.0], [8.0, 8.0], [9.0, 9.0]]]]), ('boundary #17', 'POLYGON ((0 0 1, 4 0 1, 4 4 1, 0 0 2))', [[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]])]]
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	`[[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 4.0], [0.0, 0.0]]]]`	`[[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 4.0], [0.0, 0.0]]]]`	Passed
control #1	`[[[[0.0, 0.0], [10.0, 0.0], [10.0, 10.0], [0.0, 10.0], [0.0, 0.0]], [[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [2.0, 2.0]]]]`	`[[[[0.0, 0.0], [10.0, 0.0], [10.0, 10.0], [0.0, 10.0], [0.0, 0.0]], [[2.0, 2.0], [2.0, 4.0], [4.0, 4.0], [2.0, 2.0]]]]`	Passed
regression #2	`[[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]`	`[[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]`	Passed
regression #3	`[[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]`	`[[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]`	Passed
regression #4	`[[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]`	`[[[[0.0, 0.0], [4.0, 0.0], [4.0, 4.0], [0.0, 0.0]]]]`	Passed
boundary #5	`[]`	`[]`	Passed
regression #7	`[[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]`	`[[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]], [[[5.0, 5.0], [6.0, 5.0], [6.0, 6.0], [5.0, 5.0]], [[5.2, 5.1], [5.8, 5.8], [5.8, 5.1], [5.2, 5.1]]]]`	Passed
regression #8	`[[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]]`	`[[[[0.0, 0.0], [1.0, 0.0], [1.0, 1.0], [0.0, 0.0]]]]`	Passed

SHA-256 / 80b408525c4a719ae9de62eab88f3e80a1376ec134fc311db6169ecc026f6bf1

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 2026-09-29T14:48:23.159671+00:00.

Case digest / f8057ff14ac7becdf8b20e353d1b6740771627755ae0fc2af7d1fe6ab8c27cce