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FA-50996 / Raster clipping / Open access

Homogeneous segment clip: boundary classification · case 01

Segments lying exactly on a clip plane are rejected as outside.

Verified by executionVariant 1 · 12 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Segments lying exactly on a clip plane are rejected as outside.

VERIFIED REPAIR

Apply the documented state transition at boundary classification. Clip ordered segments in homogeneous (x,w,u) coordinates against requested left x+w>=0, right w-x>=0 and eye w>=1 halfspaces. Interpolate every component at intersections before perspective division; retain endpoint order. Output exact rational strings, or null for rejected segments. The integer surface size scales horizontal halfspaces.

Unsuccessful approach: Fixing only the first endpoint boundary classification still alters segments whose second endpoint lies on a plane.

Case contract

Clip ordered segments in homogeneous (x,w,u) coordinates against requested left x+w>=0, right w-x>=0 and eye w>=1 halfspaces. Interpolate every component at intersections before perspective division; retain endpoint order. Output exact rational strings, or null for rejected segments. The integer surface size scales horizontal halfspaces.

Why this case matters

Raster clip state can leak coverage across draws even when every individual region is valid.

1 / The failure

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(commands, size):
    from fractions import Fraction
    out=[]
    for first,last,planes in commands:
        a=list(map(Fraction,first)); b=list(map(Fraction,last))
        original_a=list(a); original_b=list(b)
        rejected=False
        for plane in planes:
            def distance(p):
                if plane=='left': return p[0]+size*p[1]
                if plane=='right': return size*p[1]-p[0]
                return p[1]-1
            da=distance(a); db=distance(b)
            ia=da>0; ib=db>0
            if not ia and not ib: rejected=True; break
            if ia and ib: continue
            t=da/(da-db)
            point=[a[i]+t*(b[i]-a[i]) for i in range(3)]
            if not ia: a=point
            else: b=point
        out.append(None if rejected else [[str(v) for v in a],[str(v) for v in b]])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
    check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 4), [[['-4', '1', '8'], ['0', '1', '12']]])
    check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 4), [[['0', '1', '0'], ['4', '1', '4']]])
    check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 4), [None])
    check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 4), [[['-4', '1', '0'], ['-8', '2', '8']]])
    check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 4), [[['0', '1', '5'], ['0', '2', '10']]])
    check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 4), [[['-4', '1', '8'], ['4', '1', '16']]])
    check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 4), [[['0', '1', '0'], ['4', '1', '4']]])
    check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 4), [[['0', '1', '0'], ['1', '1', '1']]])
    check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 4), [[['0', '1', '12'], ['6', '3/2', '18']]])
    check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 4), [None])
    check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 4), [[['0', '1', '1'], ['0', '1', '1']]])
    check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 4), [[['0', '1', '12'], ['40/9', '10/9', '40/3']]])
if N == 2:
    check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 5), [[['-5', '1', '7'], ['0', '1', '12']]])
    check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 5), [[['0', '1', '0'], ['5', '1', '5']]])
    check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 5), [None])
    check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 5), [[['-4', '1', '0'], ['-8', '2', '8']]])
    check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 5), [[['0', '1', '5'], ['0', '2', '10']]])
    check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 5), [[['-5', '1', '7'], ['5', '1', '17']]])
    check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 5), [[['0', '1', '0'], ['5', '1', '5']]])
    check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 5), [[['0', '1', '0'], ['1', '1', '1']]])
    check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 5), [[['0', '1', '12'], ['60/7', '12/7', '144/7']]])
    check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 5), [None])
    check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 5), [[['0', '1', '1'], ['0', '1', '1']]])
    check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 5), [[['0', '1', '12'], ['40/7', '8/7', '96/7']]])
if N == 3:
    check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 6), [[['-6', '1', '6'], ['0', '1', '12']]])
    check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 6), [[['0', '1', '0'], ['6', '1', '6']]])
    check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 6), [None])
    check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 6), [[['-4', '1', '0'], ['-8', '2', '8']]])
    check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 6), [[['0', '1', '5'], ['0', '2', '10']]])
    check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 6), [[['-6', '1', '6'], ['6', '1', '18']]])
    check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 6), [[['0', '1', '0'], ['6', '1', '6']]])
    check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 6), [[['0', '1', '0'], ['1', '1', '1']]])
    check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 6), [[['0', '1', '12'], ['12', '2', '24']]])
    check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 6), [None])
    check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 6), [[['0', '1', '1'], ['0', '1', '1']]])
    check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 6), [[['0', '1', '12'], ['120/17', '20/17', '240/17']]])
if N == 4:
    check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 7), [[['-7', '1', '5'], ['0', '1', '12']]])
    check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 7), [[['0', '1', '0'], ['7', '1', '7']]])
    check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 7), [None])
    check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 7), [[['-4', '1', '0'], ['-8', '2', '8']]])
    check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 7), [[['0', '1', '5'], ['0', '2', '10']]])
    check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 7), [[['-7', '1', '5'], ['7', '1', '19']]])
    check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 7), [[['0', '1', '0'], ['7', '1', '7']]])
    check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 7), [[['0', '1', '0'], ['1', '1', '1']]])
    check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 7), [[['0', '1', '12'], ['12', '2', '24']]])
    check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 7), [None])
    check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 7), [[['0', '1', '1'], ['0', '1', '1']]])
    check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 7), [[['0', '1', '12'], ['280/33', '40/33', '160/11']]])
if N == 5:
    check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 8), [[['-8', '1', '4'], ['0', '1', '12']]])
    check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 8), [[['0', '1', '0'], ['8', '1', '8']]])
    check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 8), [None])
    check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 8), [[['-4', '1', '0'], ['-8', '2', '8']]])
    check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 8), [[['0', '1', '5'], ['0', '2', '10']]])
    check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 8), [[['-8', '1', '4'], ['8', '1', '20']]])
    check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 8), [[['0', '1', '0'], ['8', '1', '8']]])
    check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 8), [[['0', '1', '0'], ['1', '1', '1']]])
    check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 8), [[['0', '1', '12'], ['12', '2', '24']]])
    check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 8), [None])
    check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 8), [[['0', '1', '1'], ['0', '1', '1']]])
    check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 8), [[['0', '1', '12'], ['10', '5/4', '15']]])
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 fixtureActualExpectedOutcome
explicit sequence 0[[['-4', '1', '8'], ['0', '1', '12']]][[['-4', '1', '8'], ['0', '1', '12']]]Passed
explicit sequence 1[[['0', '1', '0'], ['4', '1', '4']]][[['0', '1', '0'], ['4', '1', '4']]]Passed
explicit sequence 2[None][None]Passed
explicit sequence 3[None][[['-4', '1', '0'], ['-8', '2', '8']]]Failed
explicit sequence 4[[['0', '1', '5'], ['0', '2', '10']]][[['0', '1', '5'], ['0', '2', '10']]]Passed
explicit sequence 5[[['-4', '1', '8'], ['4', '1', '16']]][[['-4', '1', '8'], ['4', '1', '16']]]Passed
explicit sequence 6[[['0', '1', '0'], ['4', '1', '4']]][[['0', '1', '0'], ['4', '1', '4']]]Passed
explicit sequence 7[None][[['0', '1', '0'], ['1', '1', '1']]]Failed
explicit sequence 8[[['0', '1', '12'], ['6', '3/2', '18']]][[['0', '1', '12'], ['6', '3/2', '18']]]Passed
explicit sequence 9[None][None]Passed
explicit sequence 10[None][[['0', '1', '1'], ['0', '1', '1']]]Failed
explicit sequence 11[[['0', '1', '12'], ['40/9', '10/9', '40/3']]][[['0', '1', '12'], ['40/9', '10/9', '40/3']]]Passed

SHA-256 / 03915a5f419359260309d06d3a6b2ac3730e2c8e7703ca37fd9595f9d98591b1

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(commands, size):
    from fractions import Fraction
    out=[]
    for first,last,planes in commands:
        a=list(map(Fraction,first)); b=list(map(Fraction,last))
        original_a=list(a); original_b=list(b)
        rejected=False
        for plane in planes:
            def distance(p):
                if plane=='left': return p[0]+size*p[1]
                if plane=='right': return size*p[1]-p[0]
                return p[1]-1
            da=distance(a); db=distance(b)
            ia=da>=0; ib=(db>=0 if da>=0 else db>0)
            if not ia and not ib: rejected=True; break
            if ia and ib: continue
            t=da/(da-db)
            point=[a[i]+t*(b[i]-a[i]) for i in range(3)]
            if not ia: a=point
            else: b=point
        out.append(None if rejected else [[str(v) for v in a],[str(v) for v in b]])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
    check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 4), [[['-4', '1', '8'], ['0', '1', '12']]])
    check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 4), [[['0', '1', '0'], ['4', '1', '4']]])
    check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 4), [None])
    check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 4), [[['-4', '1', '0'], ['-8', '2', '8']]])
    check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 4), [[['0', '1', '5'], ['0', '2', '10']]])
    check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 4), [[['-4', '1', '8'], ['4', '1', '16']]])
    check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 4), [[['0', '1', '0'], ['4', '1', '4']]])
    check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 4), [[['0', '1', '0'], ['1', '1', '1']]])
    check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 4), [[['0', '1', '12'], ['6', '3/2', '18']]])
    check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 4), [None])
    check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 4), [[['0', '1', '1'], ['0', '1', '1']]])
    check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 4), [[['0', '1', '12'], ['40/9', '10/9', '40/3']]])
if N == 2:
    check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 5), [[['-5', '1', '7'], ['0', '1', '12']]])
    check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 5), [[['0', '1', '0'], ['5', '1', '5']]])
    check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 5), [None])
    check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 5), [[['-4', '1', '0'], ['-8', '2', '8']]])
    check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 5), [[['0', '1', '5'], ['0', '2', '10']]])
    check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 5), [[['-5', '1', '7'], ['5', '1', '17']]])
    check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 5), [[['0', '1', '0'], ['5', '1', '5']]])
    check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 5), [[['0', '1', '0'], ['1', '1', '1']]])
    check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 5), [[['0', '1', '12'], ['60/7', '12/7', '144/7']]])
    check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 5), [None])
    check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 5), [[['0', '1', '1'], ['0', '1', '1']]])
    check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 5), [[['0', '1', '12'], ['40/7', '8/7', '96/7']]])
if N == 3:
    check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 6), [[['-6', '1', '6'], ['0', '1', '12']]])
    check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 6), [[['0', '1', '0'], ['6', '1', '6']]])
    check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 6), [None])
    check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 6), [[['-4', '1', '0'], ['-8', '2', '8']]])
    check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 6), [[['0', '1', '5'], ['0', '2', '10']]])
    check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 6), [[['-6', '1', '6'], ['6', '1', '18']]])
    check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 6), [[['0', '1', '0'], ['6', '1', '6']]])
    check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 6), [[['0', '1', '0'], ['1', '1', '1']]])
    check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 6), [[['0', '1', '12'], ['12', '2', '24']]])
    check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 6), [None])
    check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 6), [[['0', '1', '1'], ['0', '1', '1']]])
    check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 6), [[['0', '1', '12'], ['120/17', '20/17', '240/17']]])
if N == 4:
    check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 7), [[['-7', '1', '5'], ['0', '1', '12']]])
    check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 7), [[['0', '1', '0'], ['7', '1', '7']]])
    check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 7), [None])
    check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 7), [[['-4', '1', '0'], ['-8', '2', '8']]])
    check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 7), [[['0', '1', '5'], ['0', '2', '10']]])
    check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 7), [[['-7', '1', '5'], ['7', '1', '19']]])
    check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 7), [[['0', '1', '0'], ['7', '1', '7']]])
    check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 7), [[['0', '1', '0'], ['1', '1', '1']]])
    check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 7), [[['0', '1', '12'], ['12', '2', '24']]])
    check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 7), [None])
    check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 7), [[['0', '1', '1'], ['0', '1', '1']]])
    check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 7), [[['0', '1', '12'], ['280/33', '40/33', '160/11']]])
if N == 5:
    check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 8), [[['-8', '1', '4'], ['0', '1', '12']]])
    check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 8), [[['0', '1', '0'], ['8', '1', '8']]])
    check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 8), [None])
    check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 8), [[['-4', '1', '0'], ['-8', '2', '8']]])
    check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 8), [[['0', '1', '5'], ['0', '2', '10']]])
    check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 8), [[['-8', '1', '4'], ['8', '1', '20']]])
    check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 8), [[['0', '1', '0'], ['8', '1', '8']]])
    check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 8), [[['0', '1', '0'], ['1', '1', '1']]])
    check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 8), [[['0', '1', '12'], ['12', '2', '24']]])
    check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 8), [None])
    check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 8), [[['0', '1', '1'], ['0', '1', '1']]])
    check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 8), [[['0', '1', '12'], ['10', '5/4', '15']]])
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 fixtureActualExpectedOutcome
explicit sequence 0[[['-4', '1', '8'], ['0', '1', '12']]][[['-4', '1', '8'], ['0', '1', '12']]]Passed
explicit sequence 1[[['0', '1', '0'], ['4', '1', '4']]][[['0', '1', '0'], ['4', '1', '4']]]Passed
explicit sequence 2[None][None]Passed
explicit sequence 3[[['-4', '1', '0'], ['-8', '2', '8']]][[['-4', '1', '0'], ['-8', '2', '8']]]Passed
explicit sequence 4[[['0', '1', '5'], ['0', '2', '10']]][[['0', '1', '5'], ['0', '2', '10']]]Passed
explicit sequence 5[[['-4', '1', '8'], ['4', '1', '16']]][[['-4', '1', '8'], ['4', '1', '16']]]Passed
explicit sequence 6[[['0', '1', '0'], ['4', '1', '4']]][[['0', '1', '0'], ['4', '1', '4']]]Passed
explicit sequence 7[[['0', '1', '0'], ['1', '1', '1']]][[['0', '1', '0'], ['1', '1', '1']]]Passed
explicit sequence 8[[['0', '1', '12'], ['6', '3/2', '18']]][[['0', '1', '12'], ['6', '3/2', '18']]]Passed
explicit sequence 9[None][None]Passed
explicit sequence 10[None][[['0', '1', '1'], ['0', '1', '1']]]Failed
explicit sequence 11[[['0', '1', '12'], ['40/9', '10/9', '40/3']]][[['0', '1', '12'], ['40/9', '10/9', '40/3']]]Passed

SHA-256 / f47b4ee84d80cf9e74454403c073cafd42f54f027fc6f14bf75dab822d6b389b

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json

N = 1
observations = []
def solve(commands, size):
    from fractions import Fraction
    out=[]
    for first,last,planes in commands:
        a=list(map(Fraction,first)); b=list(map(Fraction,last))
        original_a=list(a); original_b=list(b)
        rejected=False
        for plane in planes:
            def distance(p):
                if plane=='left': return p[0]+size*p[1]
                if plane=='right': return size*p[1]-p[0]
                return p[1]-1
            da=distance(a); db=distance(b)
            ia=da>=0; ib=db>=0
            if not ia and not ib: rejected=True; break
            if ia and ib: continue
            t=da/(da-db)
            point=[a[i]+t*(b[i]-a[i]) for i in range(3)]
            if not ia: a=point
            else: b=point
        out.append(None if rejected else [[str(v) for v in a],[str(v) for v in b]])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
    check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 4), [[['-4', '1', '8'], ['0', '1', '12']]])
    check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 4), [[['0', '1', '0'], ['4', '1', '4']]])
    check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 4), [None])
    check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 4), [[['-4', '1', '0'], ['-8', '2', '8']]])
    check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 4), [[['0', '1', '5'], ['0', '2', '10']]])
    check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 4), [[['-4', '1', '8'], ['4', '1', '16']]])
    check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 4), [[['0', '1', '0'], ['4', '1', '4']]])
    check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 4), [[['0', '1', '0'], ['1', '1', '1']]])
    check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 4), [[['0', '1', '12'], ['6', '3/2', '18']]])
    check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 4), [None])
    check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 4), [[['0', '1', '1'], ['0', '1', '1']]])
    check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 4), [[['0', '1', '12'], ['40/9', '10/9', '40/3']]])
if N == 2:
    check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 5), [[['-5', '1', '7'], ['0', '1', '12']]])
    check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 5), [[['0', '1', '0'], ['5', '1', '5']]])
    check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 5), [None])
    check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 5), [[['-4', '1', '0'], ['-8', '2', '8']]])
    check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 5), [[['0', '1', '5'], ['0', '2', '10']]])
    check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 5), [[['-5', '1', '7'], ['5', '1', '17']]])
    check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 5), [[['0', '1', '0'], ['5', '1', '5']]])
    check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 5), [[['0', '1', '0'], ['1', '1', '1']]])
    check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 5), [[['0', '1', '12'], ['60/7', '12/7', '144/7']]])
    check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 5), [None])
    check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 5), [[['0', '1', '1'], ['0', '1', '1']]])
    check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 5), [[['0', '1', '12'], ['40/7', '8/7', '96/7']]])
if N == 3:
    check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 6), [[['-6', '1', '6'], ['0', '1', '12']]])
    check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 6), [[['0', '1', '0'], ['6', '1', '6']]])
    check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 6), [None])
    check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 6), [[['-4', '1', '0'], ['-8', '2', '8']]])
    check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 6), [[['0', '1', '5'], ['0', '2', '10']]])
    check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 6), [[['-6', '1', '6'], ['6', '1', '18']]])
    check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 6), [[['0', '1', '0'], ['6', '1', '6']]])
    check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 6), [[['0', '1', '0'], ['1', '1', '1']]])
    check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 6), [[['0', '1', '12'], ['12', '2', '24']]])
    check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 6), [None])
    check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 6), [[['0', '1', '1'], ['0', '1', '1']]])
    check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 6), [[['0', '1', '12'], ['120/17', '20/17', '240/17']]])
if N == 4:
    check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 7), [[['-7', '1', '5'], ['0', '1', '12']]])
    check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 7), [[['0', '1', '0'], ['7', '1', '7']]])
    check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 7), [None])
    check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 7), [[['-4', '1', '0'], ['-8', '2', '8']]])
    check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 7), [[['0', '1', '5'], ['0', '2', '10']]])
    check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 7), [[['-7', '1', '5'], ['7', '1', '19']]])
    check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 7), [[['0', '1', '0'], ['7', '1', '7']]])
    check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 7), [[['0', '1', '0'], ['1', '1', '1']]])
    check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 7), [[['0', '1', '12'], ['12', '2', '24']]])
    check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 7), [None])
    check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 7), [[['0', '1', '1'], ['0', '1', '1']]])
    check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 7), [[['0', '1', '12'], ['280/33', '40/33', '160/11']]])
if N == 5:
    check('explicit sequence 0', solve([[[-12, 1, 0], [0, 1, 12], ['left']]], 8), [[['-8', '1', '4'], ['0', '1', '12']]])
    check('explicit sequence 1', solve([[[0, 1, 0], [12, 1, 12], ['right']]], 8), [[['0', '1', '0'], ['8', '1', '8']]])
    check('explicit sequence 2', solve([[[-20, 1, 0], [-15, 1, 5], ['left']]], 8), [None])
    check('explicit sequence 3', solve([[[-4, 1, 0], [-8, 2, 8], ['left']]], 8), [[['-4', '1', '0'], ['-8', '2', '8']]])
    check('explicit sequence 4', solve([[[0, 0, 0], [0, 2, 10], ['eye']]], 8), [[['0', '1', '5'], ['0', '2', '10']]])
    check('explicit sequence 5', solve([[[-12, 1, 0], [12, 1, 24], ['left', 'right']]], 8), [[['-8', '1', '4'], ['8', '1', '20']]])
    check('explicit sequence 6', solve([[[0, 1, 0], [12, 1, 12], ['left', 'right']]], 8), [[['0', '1', '0'], ['8', '1', '8']]])
    check('explicit sequence 7', solve([[[0, 1, 0], [1, 1, 1], ['eye', 'left', 'right']]], 8), [[['0', '1', '0'], ['1', '1', '1']]])
    check('explicit sequence 8', solve([[[-12, 0, 0], [12, 2, 24], ['left', 'right', 'eye']]], 8), [[['0', '1', '12'], ['12', '2', '24']]])
    check('explicit sequence 9', solve([[[-15, 1, 0], [-20, 1, 5], ['left']]], 8), [None])
    check('explicit sequence 10', solve([[[0, 0, 0], [0, 1, 1], ['eye']]], 8), [[['0', '1', '1'], ['0', '1', '1']]])
    check('explicit sequence 11', solve([[[-40, 0, 0], [40, 2, 24], ['right', 'eye']]], 8), [[['0', '1', '12'], ['10', '5/4', '15']]])
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 fixtureActualExpectedOutcome
explicit sequence 0[[['-4', '1', '8'], ['0', '1', '12']]][[['-4', '1', '8'], ['0', '1', '12']]]Passed
explicit sequence 1[[['0', '1', '0'], ['4', '1', '4']]][[['0', '1', '0'], ['4', '1', '4']]]Passed
explicit sequence 2[None][None]Passed
explicit sequence 3[[['-4', '1', '0'], ['-8', '2', '8']]][[['-4', '1', '0'], ['-8', '2', '8']]]Passed
explicit sequence 4[[['0', '1', '5'], ['0', '2', '10']]][[['0', '1', '5'], ['0', '2', '10']]]Passed
explicit sequence 5[[['-4', '1', '8'], ['4', '1', '16']]][[['-4', '1', '8'], ['4', '1', '16']]]Passed
explicit sequence 6[[['0', '1', '0'], ['4', '1', '4']]][[['0', '1', '0'], ['4', '1', '4']]]Passed
explicit sequence 7[[['0', '1', '0'], ['1', '1', '1']]][[['0', '1', '0'], ['1', '1', '1']]]Passed
explicit sequence 8[[['0', '1', '12'], ['6', '3/2', '18']]][[['0', '1', '12'], ['6', '3/2', '18']]]Passed
explicit sequence 9[None][None]Passed
explicit sequence 10[[['0', '1', '1'], ['0', '1', '1']]][[['0', '1', '1'], ['0', '1', '1']]]Passed
explicit sequence 11[[['0', '1', '12'], ['40/9', '10/9', '40/3']]][[['0', '1', '12'], ['40/9', '10/9', '40/3']]]Passed

SHA-256 / 551181ac5740f2507d9332ca503db85d2645c36fd736ab690694549542774375

Verification & scope

Finite one-dimensional integer sample sets model coverage state only; no geometric intersection, memory layout, GPU or graphics-standard conformance 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 2026-09-29T14:45:14.542761+00:00.

Case digest / aa07dd5cbd9875ce497333f67d8a8a6c0734e318dfb56c0dbe5909d7957f7838