FA-51781 / Raster clipping / Open access

Guard band triangle clip: bbox left unclamped · case 01

Guard-band triangles report bounding boxes starting left of the viewport.

Verified by executionVariant 1 · 13 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Guard-band triangles report bounding boxes starting left of the viewport.

THE FAILURE

Guard-band triangles report bounding boxes starting left of the viewport.

Unsuccessful approach: Clamping only trivially accepted triangles leaves the guard-band path unclamped.

Case contract

Each command is a triangle of three exact vertices in continuous raster coordinates. The viewport is [0,size]x[0,size] and the guard band extends one viewport size beyond each side. A triangle is rejected when all vertices lie strictly beyond the same viewport edge; accepted when all vertices are inside the closed viewport; guard-banded when all vertices are inside the closed guard band; otherwise it requires geometric clipping. Accepted and guard-banded triangles report the pixel bounding box [floor(min x),floor(min y),ceil(max x),ceil(max y)) clamped to the viewport, or None if empty.

Why this case matters

Raster clipping decides which pixels a primitive may touch; a single wrong clip decision writes outside the target or scissor, or silently drops visible coverage.

1 / The failure

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(commands, size):
    out=[]
    g=size
    for tri in commands:
        xs=[Fraction(v[0]) for v in tri]
        ys=[Fraction(v[1]) for v in tri]
        if max(xs)<0 or min(xs)>size or max(ys)<0 or min(ys)>size:
            out.append(['reject',None])
            continue
        if min(xs)>=0 and max(xs)<=size and min(ys)>=0 and max(ys)<=size: kind='accept'
        elif min(xs)>=-g and max(xs)<=size+g and min(ys)>=-g and max(ys)<=size+g: kind='guard'
        else:
            out.append(['clip',None])
            continue
        x0=math.floor(min(xs))
        x1=min(math.ceil(max(xs)),size)
        y0=max(math.floor(min(ys)),0)
        y1=min(math.ceil(max(ys)),size)
        out.append([kind,[x0,y0,x1,y1] if x0<x1 and y0<y1 else None])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
    check('explicit case 0', solve([[[1, 1], [5, 1], [2, 5]]], 6), [['accept', [1, 1, 5, 5]]])
    check('explicit case 1', solve([[[-1, -1], [-3, 2], [-2, 6]]], 6), [['reject', None]])
    check('explicit case 2', solve([[[-12, -12], [24, -12], [3, 24]]], 6), [['clip', None]])
    check('explicit case 3', solve([[[6, 0], [8, 1], [7, 3]]], 6), [['guard', None]])
    check('explicit case 4', solve([[['13/2', 0], [9, 1], [7, 3]]], 6), [['reject', None]])
    check('explicit case 5', solve([[[1, -18], [2, 3], [3, 3]]], 6), [['clip', None]])
    check('explicit case 6', solve([[[1, 1], ['5/2', 1], [2, 3]]], 6), [['accept', [1, 1, 3, 3]]])
    check('explicit case 7', solve([[[-5, 1], [2, 2], [1, 3]]], 6), [['guard', [0, 1, 2, 3]]])
    check('explicit case 8', solve([[[1, 1], [8, 1], [2, 3]]], 6), [['guard', [1, 1, 6, 3]]])
    check('explicit case 9', solve([[[-1, 1], [1, 7], [5, 2]]], 6), [['guard', [0, 1, 5, 6]]])
    check('explicit case 10', solve([[[1, 1], [3, 1], [2, 13]]], 6), [['clip', None]])
    check('explicit case 11', solve([[[1, 1], [2, 1], [2, 30]]], 6), [['clip', None]])
    check('explicit case 12', solve([[[1, -3], [3, -2], [2, -5]]], 6), [['reject', None]])
if N == 2:
    check('explicit case 0', solve([[[1, 1], [6, 1], [2, 6]]], 7), [['accept', [1, 1, 6, 6]]])
    check('explicit case 1', solve([[[-1, -1], [-3, 2], [-2, 7]]], 7), [['reject', None]])
    check('explicit case 2', solve([[[-14, -14], [28, -14], [3, 28]]], 7), [['clip', None]])
    check('explicit case 3', solve([[[7, 0], [9, 1], [8, 3]]], 7), [['guard', None]])
    check('explicit case 4', solve([[['15/2', 0], [10, 1], [8, 3]]], 7), [['reject', None]])
    check('explicit case 5', solve([[[1, -21], [2, 3], [3, 3]]], 7), [['clip', None]])
    check('explicit case 6', solve([[[1, 1], ['5/2', 1], [2, 3]]], 7), [['accept', [1, 1, 3, 3]]])
    check('explicit case 7', solve([[[-6, 1], [2, 2], [1, 3]]], 7), [['guard', [0, 1, 2, 3]]])
    check('explicit case 8', solve([[[1, 1], [9, 1], [2, 3]]], 7), [['guard', [1, 1, 7, 3]]])
    check('explicit case 9', solve([[[-1, 1], [1, 8], [6, 2]]], 7), [['guard', [0, 1, 6, 7]]])
    check('explicit case 10', solve([[[1, 1], [3, 1], [2, 15]]], 7), [['clip', None]])
    check('explicit case 11', solve([[[1, 1], [2, 1], [2, 35]]], 7), [['clip', None]])
    check('explicit case 12', solve([[[1, -3], [3, -2], [2, -5]]], 7), [['reject', None]])
if N == 3:
    check('explicit case 0', solve([[[1, 1], [7, 1], [2, 7]]], 8), [['accept', [1, 1, 7, 7]]])
    check('explicit case 1', solve([[[-1, -1], [-3, 2], [-2, 8]]], 8), [['reject', None]])
    check('explicit case 2', solve([[[-16, -16], [32, -16], [4, 32]]], 8), [['clip', None]])
    check('explicit case 3', solve([[[8, 0], [10, 1], [9, 3]]], 8), [['guard', None]])
    check('explicit case 4', solve([[['17/2', 0], [11, 1], [9, 3]]], 8), [['reject', None]])
    check('explicit case 5', solve([[[1, -24], [2, 3], [3, 3]]], 8), [['clip', None]])
    check('explicit case 6', solve([[[1, 1], ['5/2', 1], [2, 3]]], 8), [['accept', [1, 1, 3, 3]]])
    check('explicit case 7', solve([[[-7, 1], [2, 2], [1, 3]]], 8), [['guard', [0, 1, 2, 3]]])
    check('explicit case 8', solve([[[1, 1], [10, 1], [2, 3]]], 8), [['guard', [1, 1, 8, 3]]])
    check('explicit case 9', solve([[[-1, 1], [1, 9], [7, 2]]], 8), [['guard', [0, 1, 7, 8]]])
    check('explicit case 10', solve([[[1, 1], [3, 1], [2, 17]]], 8), [['clip', None]])
    check('explicit case 11', solve([[[1, 1], [2, 1], [2, 40]]], 8), [['clip', None]])
    check('explicit case 12', solve([[[1, -3], [3, -2], [2, -5]]], 8), [['reject', None]])
if N == 4:
    check('explicit case 0', solve([[[1, 1], [8, 1], [2, 8]]], 9), [['accept', [1, 1, 8, 8]]])
    check('explicit case 1', solve([[[-1, -1], [-3, 2], [-2, 9]]], 9), [['reject', None]])
    check('explicit case 2', solve([[[-18, -18], [36, -18], [4, 36]]], 9), [['clip', None]])
    check('explicit case 3', solve([[[9, 0], [11, 1], [10, 3]]], 9), [['guard', None]])
    check('explicit case 4', solve([[['19/2', 0], [12, 1], [10, 3]]], 9), [['reject', None]])
    check('explicit case 5', solve([[[1, -27], [2, 3], [3, 3]]], 9), [['clip', None]])
    check('explicit case 6', solve([[[1, 1], ['5/2', 1], [2, 3]]], 9), [['accept', [1, 1, 3, 3]]])
    check('explicit case 7', solve([[[-8, 1], [2, 2], [1, 3]]], 9), [['guard', [0, 1, 2, 3]]])
    check('explicit case 8', solve([[[1, 1], [11, 1], [2, 3]]], 9), [['guard', [1, 1, 9, 3]]])
    check('explicit case 9', solve([[[-1, 1], [1, 10], [8, 2]]], 9), [['guard', [0, 1, 8, 9]]])
    check('explicit case 10', solve([[[1, 1], [3, 1], [2, 19]]], 9), [['clip', None]])
    check('explicit case 11', solve([[[1, 1], [2, 1], [2, 45]]], 9), [['clip', None]])
    check('explicit case 12', solve([[[1, -3], [3, -2], [2, -5]]], 9), [['reject', None]])
if N == 5:
    check('explicit case 0', solve([[[1, 1], [9, 1], [2, 9]]], 10), [['accept', [1, 1, 9, 9]]])
    check('explicit case 1', solve([[[-1, -1], [-3, 2], [-2, 10]]], 10), [['reject', None]])
    check('explicit case 2', solve([[[-20, -20], [40, -20], [5, 40]]], 10), [['clip', None]])
    check('explicit case 3', solve([[[10, 0], [12, 1], [11, 3]]], 10), [['guard', None]])
    check('explicit case 4', solve([[['21/2', 0], [13, 1], [11, 3]]], 10), [['reject', None]])
    check('explicit case 5', solve([[[1, -30], [2, 3], [3, 3]]], 10), [['clip', None]])
    check('explicit case 6', solve([[[1, 1], ['5/2', 1], [2, 3]]], 10), [['accept', [1, 1, 3, 3]]])
    check('explicit case 7', solve([[[-9, 1], [2, 2], [1, 3]]], 10), [['guard', [0, 1, 2, 3]]])
    check('explicit case 8', solve([[[1, 1], [12, 1], [2, 3]]], 10), [['guard', [1, 1, 10, 3]]])
    check('explicit case 9', solve([[[-1, 1], [1, 11], [9, 2]]], 10), [['guard', [0, 1, 9, 10]]])
    check('explicit case 10', solve([[[1, 1], [3, 1], [2, 21]]], 10), [['clip', None]])
    check('explicit case 11', solve([[[1, 1], [2, 1], [2, 50]]], 10), [['clip', None]])
    check('explicit case 12', solve([[[1, -3], [3, -2], [2, -5]]], 10), [['reject', None]])
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
explicit case 0	`[['accept', [1, 1, 5, 5]]]`	`[['accept', [1, 1, 5, 5]]]`	Passed
explicit case 1	`[['reject', None]]`	`[['reject', None]]`	Passed
explicit case 2	`[['clip', None]]`	`[['clip', None]]`	Passed
explicit case 3	`[['guard', None]]`	`[['guard', None]]`	Passed
explicit case 4	`[['reject', None]]`	`[['reject', None]]`	Passed
explicit case 5	`[['clip', None]]`	`[['clip', None]]`	Passed
explicit case 6	`[['accept', [1, 1, 3, 3]]]`	`[['accept', [1, 1, 3, 3]]]`	Passed
explicit case 7	`[['guard', [-5, 1, 2, 3]]]`	`[['guard', [0, 1, 2, 3]]]`	Failed
explicit case 8	`[['guard', [1, 1, 6, 3]]]`	`[['guard', [1, 1, 6, 3]]]`	Passed
explicit case 9	`[['guard', [-1, 1, 5, 6]]]`	`[['guard', [0, 1, 5, 6]]]`	Failed
explicit case 10	`[['clip', None]]`	`[['clip', None]]`	Passed
explicit case 11	`[['clip', None]]`	`[['clip', None]]`	Passed
explicit case 12	`[['reject', None]]`	`[['reject', None]]`	Passed

SHA-256 / c45dc22a6f21290cdfcfaab837a2869983618902151d8f58c522eb80c26dd8a3

2 / The unsuccessful fix

Exit 1

"""Failure Map reference implementation. Python standard library only."""
import json
import math
from fractions import Fraction
N = 1
observations = []
def solve(commands, size):
    out=[]
    g=size
    for tri in commands:
        xs=[Fraction(v[0]) for v in tri]
        ys=[Fraction(v[1]) for v in tri]
        if max(xs)<0 or min(xs)>size or max(ys)<0 or min(ys)>size:
            out.append(['reject',None])
            continue
        if min(xs)>=0 and max(xs)<=size and min(ys)>=0 and max(ys)<=size: kind='accept'
        elif min(xs)>=-g and max(xs)<=size+g and min(ys)>=-g and max(ys)<=size+g: kind='guard'
        else:
            out.append(['clip',None])
            continue
        x0=max(math.floor(min(xs)),0) if kind=='accept' else math.floor(min(xs))
        x1=min(math.ceil(max(xs)),size)
        y0=max(math.floor(min(ys)),0)
        y1=min(math.ceil(max(ys)),size)
        out.append([kind,[x0,y0,x1,y1] if x0<x1 and y0<y1 else None])
    return out
def check(label, actual, expected):
    observations.append({"check": label, "actual": actual, "expected": expected, "passed": actual == expected})
if N == 1:
    check('explicit case 0', solve([[[1, 1], [5, 1], [2, 5]]], 6), [['accept', [1, 1, 5, 5]]])
    check('explicit case 1', solve([[[-1, -1], [-3, 2], [-2, 6]]], 6), [['reject', None]])
    check('explicit case 2', solve([[[-12, -12], [24, -12], [3, 24]]], 6), [['clip', None]])
    check('explicit case 3', solve([[[6, 0], [8, 1], [7, 3]]], 6), [['guard', None]])
    check('explicit case 4', solve([[['13/2', 0], [9, 1], [7, 3]]], 6), [['reject', None]])
    check('explicit case 5', solve([[[1, -18], [2, 3], [3, 3]]], 6), [['clip', None]])
    check('explicit case 6', solve([[[1, 1], ['5/2', 1], [2, 3]]], 6), [['accept', [1, 1, 3, 3]]])
    check('explicit case 7', solve([[[-5, 1], [2, 2], [1, 3]]], 6), [['guard', [0, 1, 2, 3]]])
    check('explicit case 8', solve([[[1, 1], [8, 1], [2, 3]]], 6), [['guard', [1, 1, 6, 3]]])
    check('explicit case 9', solve([[[-1, 1], [1, 7], [5, 2]]], 6), [['guard', [0, 1, 5, 6]]])
    check('explicit case 10', solve([[[1, 1], [3, 1], [2, 13]]], 6), [['clip', None]])
    check('explicit case 11', solve([[[1, 1], [2, 1], [2, 30]]], 6), [['clip', None]])
    check('explicit case 12', solve([[[1, -3], [3, -2], [2, -5]]], 6), [['reject', None]])
if N == 2:
    check('explicit case 0', solve([[[1, 1], [6, 1], [2, 6]]], 7), [['accept', [1, 1, 6, 6]]])
    check('explicit case 1', solve([[[-1, -1], [-3, 2], [-2, 7]]], 7), [['reject', None]])
    check('explicit case 2', solve([[[-14, -14], [28, -14], [3, 28]]], 7), [['clip', None]])
    check('explicit case 3', solve([[[7, 0], [9, 1], [8, 3]]], 7), [['guard', None]])
    check('explicit case 4', solve([[['15/2', 0], [10, 1], [8, 3]]], 7), [['reject', None]])
    check('explicit case 5', solve([[[1, -21], [2, 3], [3, 3]]], 7), [['clip', None]])
    check('explicit case 6', solve([[[1, 1], ['5/2', 1], [2, 3]]], 7), [['accept', [1, 1, 3, 3]]])
    check('explicit case 7', solve([[[-6, 1], [2, 2], [1, 3]]], 7), [['guard', [0, 1, 2, 3]]])
    check('explicit case 8', solve([[[1, 1], [9, 1], [2, 3]]], 7), [['guard', [1, 1, 7, 3]]])
    check('explicit case 9', solve([[[-1, 1], [1, 8], [6, 2]]], 7), [['guard', [0, 1, 6, 7]]])
    check('explicit case 10', solve([[[1, 1], [3, 1], [2, 15]]], 7), [['clip', None]])
    check('explicit case 11', solve([[[1, 1], [2, 1], [2, 35]]], 7), [['clip', None]])
    check('explicit case 12', solve([[[1, -3], [3, -2], [2, -5]]], 7), [['reject', None]])
if N == 3:
    check('explicit case 0', solve([[[1, 1], [7, 1], [2, 7]]], 8), [['accept', [1, 1, 7, 7]]])
    check('explicit case 1', solve([[[-1, -1], [-3, 2], [-2, 8]]], 8), [['reject', None]])
    check('explicit case 2', solve([[[-16, -16], [32, -16], [4, 32]]], 8), [['clip', None]])
    check('explicit case 3', solve([[[8, 0], [10, 1], [9, 3]]], 8), [['guard', None]])
    check('explicit case 4', solve([[['17/2', 0], [11, 1], [9, 3]]], 8), [['reject', None]])
    check('explicit case 5', solve([[[1, -24], [2, 3], [3, 3]]], 8), [['clip', None]])
    check('explicit case 6', solve([[[1, 1], ['5/2', 1], [2, 3]]], 8), [['accept', [1, 1, 3, 3]]])
    check('explicit case 7', solve([[[-7, 1], [2, 2], [1, 3]]], 8), [['guard', [0, 1, 2, 3]]])
    check('explicit case 8', solve([[[1, 1], [10, 1], [2, 3]]], 8), [['guard', [1, 1, 8, 3]]])
    check('explicit case 9', solve([[[-1, 1], [1, 9], [7, 2]]], 8), [['guard', [0, 1, 7, 8]]])
    check('explicit case 10', solve([[[1, 1], [3, 1], [2, 17]]], 8), [['clip', None]])
    check('explicit case 11', solve([[[1, 1], [2, 1], [2, 40]]], 8), [['clip', None]])
    check('explicit case 12', solve([[[1, -3], [3, -2], [2, -5]]], 8), [['reject', None]])
if N == 4:
    check('explicit case 0', solve([[[1, 1], [8, 1], [2, 8]]], 9), [['accept', [1, 1, 8, 8]]])
    check('explicit case 1', solve([[[-1, -1], [-3, 2], [-2, 9]]], 9), [['reject', None]])
    check('explicit case 2', solve([[[-18, -18], [36, -18], [4, 36]]], 9), [['clip', None]])
    check('explicit case 3', solve([[[9, 0], [11, 1], [10, 3]]], 9), [['guard', None]])
    check('explicit case 4', solve([[['19/2', 0], [12, 1], [10, 3]]], 9), [['reject', None]])
    check('explicit case 5', solve([[[1, -27], [2, 3], [3, 3]]], 9), [['clip', None]])
    check('explicit case 6', solve([[[1, 1], ['5/2', 1], [2, 3]]], 9), [['accept', [1, 1, 3, 3]]])
    check('explicit case 7', solve([[[-8, 1], [2, 2], [1, 3]]], 9), [['guard', [0, 1, 2, 3]]])
    check('explicit case 8', solve([[[1, 1], [11, 1], [2, 3]]], 9), [['guard', [1, 1, 9, 3]]])
    check('explicit case 9', solve([[[-1, 1], [1, 10], [8, 2]]], 9), [['guard', [0, 1, 8, 9]]])
    check('explicit case 10', solve([[[1, 1], [3, 1], [2, 19]]], 9), [['clip', None]])
    check('explicit case 11', solve([[[1, 1], [2, 1], [2, 45]]], 9), [['clip', None]])
    check('explicit case 12', solve([[[1, -3], [3, -2], [2, -5]]], 9), [['reject', None]])
if N == 5:
    check('explicit case 0', solve([[[1, 1], [9, 1], [2, 9]]], 10), [['accept', [1, 1, 9, 9]]])
    check('explicit case 1', solve([[[-1, -1], [-3, 2], [-2, 10]]], 10), [['reject', None]])
    check('explicit case 2', solve([[[-20, -20], [40, -20], [5, 40]]], 10), [['clip', None]])
    check('explicit case 3', solve([[[10, 0], [12, 1], [11, 3]]], 10), [['guard', None]])
    check('explicit case 4', solve([[['21/2', 0], [13, 1], [11, 3]]], 10), [['reject', None]])
    check('explicit case 5', solve([[[1, -30], [2, 3], [3, 3]]], 10), [['clip', None]])
    check('explicit case 6', solve([[[1, 1], ['5/2', 1], [2, 3]]], 10), [['accept', [1, 1, 3, 3]]])
    check('explicit case 7', solve([[[-9, 1], [2, 2], [1, 3]]], 10), [['guard', [0, 1, 2, 3]]])
    check('explicit case 8', solve([[[1, 1], [12, 1], [2, 3]]], 10), [['guard', [1, 1, 10, 3]]])
    check('explicit case 9', solve([[[-1, 1], [1, 11], [9, 2]]], 10), [['guard', [0, 1, 9, 10]]])
    check('explicit case 10', solve([[[1, 1], [3, 1], [2, 21]]], 10), [['clip', None]])
    check('explicit case 11', solve([[[1, 1], [2, 1], [2, 50]]], 10), [['clip', None]])
    check('explicit case 12', solve([[[1, -3], [3, -2], [2, -5]]], 10), [['reject', None]])
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
explicit case 0	`[['accept', [1, 1, 5, 5]]]`	`[['accept', [1, 1, 5, 5]]]`	Passed
explicit case 1	`[['reject', None]]`	`[['reject', None]]`	Passed
explicit case 2	`[['clip', None]]`	`[['clip', None]]`	Passed
explicit case 3	`[['guard', None]]`	`[['guard', None]]`	Passed
explicit case 4	`[['reject', None]]`	`[['reject', None]]`	Passed
explicit case 5	`[['clip', None]]`	`[['clip', None]]`	Passed
explicit case 6	`[['accept', [1, 1, 3, 3]]]`	`[['accept', [1, 1, 3, 3]]]`	Passed
explicit case 7	`[['guard', [-5, 1, 2, 3]]]`	`[['guard', [0, 1, 2, 3]]]`	Failed
explicit case 8	`[['guard', [1, 1, 6, 3]]]`	`[['guard', [1, 1, 6, 3]]]`	Passed
explicit case 9	`[['guard', [-1, 1, 5, 6]]]`	`[['guard', [0, 1, 5, 6]]]`	Failed
explicit case 10	`[['clip', None]]`	`[['clip', None]]`	Passed
explicit case 11	`[['clip', None]]`	`[['clip', None]]`	Passed
explicit case 12	`[['reject', None]]`	`[['reject', None]]`	Passed

SHA-256 / 244e0dbcb2f419b5ec9d4cc55209178bf316b72e92b1be9cf3e53ba16a944b58

HELD IN THE MEMBER ARCHIVE

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

This mechanism has 13 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.

Member access is invitation-based. Sign in with your invited account to inspect the repair.

Verification & scope

Exact integer/rational arithmetic on small stipulated fixtures models the clipping decision only; no memory layout, GPU pipeline, graphics API or standards 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 2026-09-29T14:45:22.351230+00:00.

Case digest / c91ac1bd13676d32bc34da251fd1ccb2512c8849bb0bfc237ead75d79d06551f