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FA-51761 / Raster clipping / Open access

Guard band triangle clip: reject any edge · case 01

Triangles are rejected when every vertex is outside some edge, discarding large triangles that cover the viewport.

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

ROOT CAUSE

Triangles are rejected when every vertex is outside some edge, discarding large triangles that cover the viewport.

THE FAILURE

Triangles are rejected when every vertex is outside some edge, discarding large triangles that cover the viewport.

Unsuccessful approach: Restoring the same-edge test only for the x axis stops rejecting triangles wholly above or below the viewport.

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 all(x<0 or x>size or y<0 or y>size for x,y in zip(xs,ys)):
            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)
        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 fixtureActualExpectedOutcome
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[['reject', None]][['clip', None]]Failed
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', [0, 1, 2, 3]]][['guard', [0, 1, 2, 3]]]Passed
explicit case 8[['guard', [1, 1, 6, 3]]][['guard', [1, 1, 6, 3]]]Passed
explicit case 9[['guard', [0, 1, 5, 6]]][['guard', [0, 1, 5, 6]]]Passed
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 / 5aeaf97db683bc7ca1a45ab5fab5d9cca9122ea7e7345da9796b74e323ecefd7

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:
            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)
        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 fixtureActualExpectedOutcome
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', [0, 1, 2, 3]]][['guard', [0, 1, 2, 3]]]Passed
explicit case 8[['guard', [1, 1, 6, 3]]][['guard', [1, 1, 6, 3]]]Passed
explicit case 9[['guard', [0, 1, 5, 6]]][['guard', [0, 1, 5, 6]]]Passed
explicit case 10[['clip', None]][['clip', None]]Passed
explicit case 11[['clip', None]][['clip', None]]Passed
explicit case 12[['guard', None]][['reject', None]]Failed

SHA-256 / 85022f013828bfc230d5e3444f45a8d3fb72a102039a796770b679c113e56764

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.

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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 / b49e67878975a14bcff3270366a17746a62f3d6dd6522b784fcb763b7b6383a5