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FA-51821 / Raster clipping / Open access

Circle span scissor: row sample offset · case 01

Row distance is measured from the row top rather than the pixel center, skewing the disc vertically.

Verified by executionVariant 1 · 10 checks per implementationDownload source bundle ↓JSON ↗

ROOT CAUSE

Row distance is measured from the row top rather than the pixel center, skewing the disc vertically.

VERIFIED REPAIR

Restore the specified clipping decision at row sample offset. Each command is [cx,cy,r,scissor] for a filled disc centred on the integer pixel-corner point (cx,cy). Pixel (x,y) is covered when its center (x+1/2,y+1/2) lies within the closed disc. Rows of the half-open scissor [left,top,right,bottom) intersected with [0,size) are scanned in order, computing exact integer span bounds with half-pixel doubled coordinates and an integer square root, then clipping to scissor columns. Non-empty spans are [row,start,end).

Unsuccessful approach: Measuring from the row bottom mirrors the vertical skew.

Case contract

Each command is [cx,cy,r,scissor] for a filled disc centred on the integer pixel-corner point (cx,cy). Pixel (x,y) is covered when its center (x+1/2,y+1/2) lies within the closed disc. Rows of the half-open scissor [left,top,right,bottom) intersected with [0,size) are scanned in order, computing exact integer span bounds with half-pixel doubled coordinates and an integer square root, then clipping to scissor columns. Non-empty spans are [row,start,end).

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
from math import isqrt
N = 1
observations = []
def solve(commands, size):
    out=[]
    for cx,cy,r,clip in commands:
        l,t,rr,b=max(clip[0],0),max(clip[1],0),min(clip[2],size),min(clip[3],size)
        spans=[]
        for y in range(t,b):
            m=4*r*r-(2*y-2*cy)**2
            if m<0: continue
            k=isqrt(m)
            xa=-((1+k-2*cx)//2)
            xb=(2*cx-1+k)//2+1
            xa,xb=max(xa,l),min(xb,rr)
            if xa<xb: spans.append([y,xa,xb])
        out.append(spans)
    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([[3, 3, 2, [0, 0, 6, 6]]], 6), [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]])
    check('explicit case 1', solve([[3, 3, 3, [0, 0, 6, 6]]], 6), [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]])
    check('explicit case 2', solve([[2, 2, 1, [0, 0, 6, 6]]], 6), [[[1, 1, 3], [2, 1, 3]]])
    check('explicit case 3', solve([[3, 3, 3, [1, 1, 6, 5]]], 6), [[[1, 1, 6], [2, 1, 6], [3, 1, 6], [4, 1, 6]]])
    check('explicit case 4', solve([[0, 0, 3, [0, 0, 6, 6]]], 6), [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]])
    check('explicit case 5', solve([[6, 3, 2, [0, 0, 6, 6]]], 6), [[[1, 5, 6], [2, 4, 6], [3, 4, 6], [4, 5, 6]]])
    check('explicit case 6', solve([[4, 2, 4, [2, 0, 6, 4]]], 6), [[[0, 2, 6], [1, 2, 6], [2, 2, 6], [3, 2, 6]]])
    check('explicit case 7', solve([[1, 3, 2, [0, 0, 6, 6]]], 6), [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]])
    check('explicit case 8', solve([[2, 4, 3, [0, 0, 6, 6]]], 6), [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5]]])
    check('explicit case 9', solve([[3, 2, 5, [0, 0, 6, 6]]], 6), [[[0, 0, 6], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 0, 6]]])
if N == 2:
    check('explicit case 0', solve([[3, 3, 2, [0, 0, 7, 7]]], 7), [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]])
    check('explicit case 1', solve([[3, 3, 3, [0, 0, 7, 7]]], 7), [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]])
    check('explicit case 2', solve([[2, 2, 1, [0, 0, 7, 7]]], 7), [[[1, 1, 3], [2, 1, 3]]])
    check('explicit case 3', solve([[3, 3, 3, [1, 1, 7, 6]]], 7), [[[1, 1, 6], [2, 1, 6], [3, 1, 6], [4, 1, 6], [5, 1, 5]]])
    check('explicit case 4', solve([[0, 0, 3, [0, 0, 7, 7]]], 7), [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]])
    check('explicit case 5', solve([[7, 3, 2, [0, 0, 7, 7]]], 7), [[[1, 6, 7], [2, 5, 7], [3, 5, 7], [4, 6, 7]]])
    check('explicit case 6', solve([[4, 2, 4, [2, 0, 7, 4]]], 7), [[[0, 2, 7], [1, 2, 7], [2, 2, 7], [3, 2, 7]]])
    check('explicit case 7', solve([[1, 3, 2, [0, 0, 7, 7]]], 7), [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]])
    check('explicit case 8', solve([[2, 4, 3, [0, 0, 7, 7]]], 7), [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5], [6, 0, 4]]])
    check('explicit case 9', solve([[3, 2, 5, [0, 0, 7, 7]]], 7), [[[0, 0, 7], [1, 0, 7], [2, 0, 7], [3, 0, 7], [4, 0, 7], [5, 0, 7], [6, 1, 5]]])
if N == 3:
    check('explicit case 0', solve([[3, 3, 2, [0, 0, 8, 8]]], 8), [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]])
    check('explicit case 1', solve([[3, 3, 3, [0, 0, 8, 8]]], 8), [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]])
    check('explicit case 2', solve([[2, 2, 1, [0, 0, 8, 8]]], 8), [[[1, 1, 3], [2, 1, 3]]])
    check('explicit case 3', solve([[4, 4, 4, [1, 1, 8, 7]]], 8), [[[1, 1, 7], [2, 1, 8], [3, 1, 8], [4, 1, 8], [5, 1, 8], [6, 1, 7]]])
    check('explicit case 4', solve([[0, 0, 3, [0, 0, 8, 8]]], 8), [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]])
    check('explicit case 5', solve([[8, 3, 2, [0, 0, 8, 8]]], 8), [[[1, 7, 8], [2, 6, 8], [3, 6, 8], [4, 7, 8]]])
    check('explicit case 6', solve([[4, 2, 4, [2, 0, 8, 4]]], 8), [[[0, 2, 8], [1, 2, 8], [2, 2, 8], [3, 2, 8]]])
    check('explicit case 7', solve([[1, 3, 2, [0, 0, 8, 8]]], 8), [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]])
    check('explicit case 8', solve([[2, 4, 3, [0, 0, 8, 8]]], 8), [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5], [6, 0, 4]]])
    check('explicit case 9', solve([[3, 2, 5, [0, 0, 8, 8]]], 8), [[[0, 0, 8], [1, 0, 8], [2, 0, 8], [3, 0, 8], [4, 0, 7], [5, 0, 7], [6, 1, 5]]])
if N == 4:
    check('explicit case 0', solve([[3, 3, 2, [0, 0, 9, 9]]], 9), [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]])
    check('explicit case 1', solve([[3, 3, 3, [0, 0, 9, 9]]], 9), [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]])
    check('explicit case 2', solve([[2, 2, 1, [0, 0, 9, 9]]], 9), [[[1, 1, 3], [2, 1, 3]]])
    check('explicit case 3', solve([[4, 4, 4, [1, 1, 9, 8]]], 9), [[[1, 1, 7], [2, 1, 8], [3, 1, 8], [4, 1, 8], [5, 1, 8], [6, 1, 7], [7, 2, 6]]])
    check('explicit case 4', solve([[0, 0, 3, [0, 0, 9, 9]]], 9), [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]])
    check('explicit case 5', solve([[9, 3, 2, [0, 0, 9, 9]]], 9), [[[1, 8, 9], [2, 7, 9], [3, 7, 9], [4, 8, 9]]])
    check('explicit case 6', solve([[4, 2, 4, [2, 0, 9, 4]]], 9), [[[0, 2, 8], [1, 2, 8], [2, 2, 8], [3, 2, 8]]])
    check('explicit case 7', solve([[1, 3, 2, [0, 0, 9, 9]]], 9), [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]])
    check('explicit case 8', solve([[2, 4, 3, [0, 0, 9, 9]]], 9), [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5], [6, 0, 4]]])
    check('explicit case 9', solve([[3, 2, 5, [0, 0, 9, 9]]], 9), [[[0, 0, 8], [1, 0, 8], [2, 0, 8], [3, 0, 8], [4, 0, 7], [5, 0, 7], [6, 1, 5]]])
if N == 5:
    check('explicit case 0', solve([[3, 3, 2, [0, 0, 10, 10]]], 10), [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]])
    check('explicit case 1', solve([[3, 3, 3, [0, 0, 10, 10]]], 10), [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]])
    check('explicit case 2', solve([[2, 2, 1, [0, 0, 10, 10]]], 10), [[[1, 1, 3], [2, 1, 3]]])
    check('explicit case 3', solve([[5, 5, 5, [1, 1, 10, 9]]], 10), [[[1, 1, 9], [2, 1, 9], [3, 1, 10], [4, 1, 10], [5, 1, 10], [6, 1, 10], [7, 1, 9], [8, 1, 9]]])
    check('explicit case 4', solve([[0, 0, 3, [0, 0, 10, 10]]], 10), [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]])
    check('explicit case 5', solve([[10, 3, 2, [0, 0, 10, 10]]], 10), [[[1, 9, 10], [2, 8, 10], [3, 8, 10], [4, 9, 10]]])
    check('explicit case 6', solve([[4, 2, 4, [2, 0, 10, 4]]], 10), [[[0, 2, 8], [1, 2, 8], [2, 2, 8], [3, 2, 8]]])
    check('explicit case 7', solve([[1, 3, 2, [0, 0, 10, 10]]], 10), [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]])
    check('explicit case 8', solve([[2, 4, 3, [0, 0, 10, 10]]], 10), [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5], [6, 0, 4]]])
    check('explicit case 9', solve([[3, 2, 5, [0, 0, 10, 10]]], 10), [[[0, 0, 8], [1, 0, 8], [2, 0, 8], [3, 0, 8], [4, 0, 7], [5, 0, 7], [6, 1, 5]]])
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[[[2, 1, 5], [3, 1, 5], [4, 1, 5]]][[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]]Failed
explicit case 1[[[1, 1, 5], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]][[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]]Failed
explicit case 2[[[2, 1, 3]]][[[1, 1, 3], [2, 1, 3]]]Failed
explicit case 3[[[1, 1, 5], [2, 1, 6], [3, 1, 6], [4, 1, 6]]][[[1, 1, 6], [2, 1, 6], [3, 1, 6], [4, 1, 6]]]Failed
explicit case 4[[[0, 0, 3], [1, 0, 3], [2, 0, 2]]][[[0, 0, 3], [1, 0, 3], [2, 0, 2]]]Passed
explicit case 5[[[2, 4, 6], [3, 4, 6], [4, 4, 6]]][[[1, 5, 6], [2, 4, 6], [3, 4, 6], [4, 5, 6]]]Failed
explicit case 6[[[0, 2, 6], [1, 2, 6], [2, 2, 6], [3, 2, 6]]][[[0, 2, 6], [1, 2, 6], [2, 2, 6], [3, 2, 6]]]Passed
explicit case 7[[[2, 0, 3], [3, 0, 3], [4, 0, 3]]][[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]]Failed
explicit case 8[[[2, 0, 4], [3, 0, 5], [4, 0, 5], [5, 0, 5]]][[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5]]]Failed
explicit case 9[[[0, 0, 6], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 0, 6]]][[[0, 0, 6], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 0, 6]]]Passed

SHA-256 / e673a7bbad193bce917755510ddd8835b43655687daef1cd312962358665c3d8

2 / The unsuccessful fix

Exit 1
"""Failure Map reference implementation. Python standard library only."""
import json
from math import isqrt
N = 1
observations = []
def solve(commands, size):
    out=[]
    for cx,cy,r,clip in commands:
        l,t,rr,b=max(clip[0],0),max(clip[1],0),min(clip[2],size),min(clip[3],size)
        spans=[]
        for y in range(t,b):
            m=4*r*r-(2*y+2-2*cy)**2
            if m<0: continue
            k=isqrt(m)
            xa=-((1+k-2*cx)//2)
            xb=(2*cx-1+k)//2+1
            xa,xb=max(xa,l),min(xb,rr)
            if xa<xb: spans.append([y,xa,xb])
        out.append(spans)
    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([[3, 3, 2, [0, 0, 6, 6]]], 6), [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]])
    check('explicit case 1', solve([[3, 3, 3, [0, 0, 6, 6]]], 6), [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]])
    check('explicit case 2', solve([[2, 2, 1, [0, 0, 6, 6]]], 6), [[[1, 1, 3], [2, 1, 3]]])
    check('explicit case 3', solve([[3, 3, 3, [1, 1, 6, 5]]], 6), [[[1, 1, 6], [2, 1, 6], [3, 1, 6], [4, 1, 6]]])
    check('explicit case 4', solve([[0, 0, 3, [0, 0, 6, 6]]], 6), [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]])
    check('explicit case 5', solve([[6, 3, 2, [0, 0, 6, 6]]], 6), [[[1, 5, 6], [2, 4, 6], [3, 4, 6], [4, 5, 6]]])
    check('explicit case 6', solve([[4, 2, 4, [2, 0, 6, 4]]], 6), [[[0, 2, 6], [1, 2, 6], [2, 2, 6], [3, 2, 6]]])
    check('explicit case 7', solve([[1, 3, 2, [0, 0, 6, 6]]], 6), [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]])
    check('explicit case 8', solve([[2, 4, 3, [0, 0, 6, 6]]], 6), [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5]]])
    check('explicit case 9', solve([[3, 2, 5, [0, 0, 6, 6]]], 6), [[[0, 0, 6], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 0, 6]]])
if N == 2:
    check('explicit case 0', solve([[3, 3, 2, [0, 0, 7, 7]]], 7), [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]])
    check('explicit case 1', solve([[3, 3, 3, [0, 0, 7, 7]]], 7), [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]])
    check('explicit case 2', solve([[2, 2, 1, [0, 0, 7, 7]]], 7), [[[1, 1, 3], [2, 1, 3]]])
    check('explicit case 3', solve([[3, 3, 3, [1, 1, 7, 6]]], 7), [[[1, 1, 6], [2, 1, 6], [3, 1, 6], [4, 1, 6], [5, 1, 5]]])
    check('explicit case 4', solve([[0, 0, 3, [0, 0, 7, 7]]], 7), [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]])
    check('explicit case 5', solve([[7, 3, 2, [0, 0, 7, 7]]], 7), [[[1, 6, 7], [2, 5, 7], [3, 5, 7], [4, 6, 7]]])
    check('explicit case 6', solve([[4, 2, 4, [2, 0, 7, 4]]], 7), [[[0, 2, 7], [1, 2, 7], [2, 2, 7], [3, 2, 7]]])
    check('explicit case 7', solve([[1, 3, 2, [0, 0, 7, 7]]], 7), [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]])
    check('explicit case 8', solve([[2, 4, 3, [0, 0, 7, 7]]], 7), [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5], [6, 0, 4]]])
    check('explicit case 9', solve([[3, 2, 5, [0, 0, 7, 7]]], 7), [[[0, 0, 7], [1, 0, 7], [2, 0, 7], [3, 0, 7], [4, 0, 7], [5, 0, 7], [6, 1, 5]]])
if N == 3:
    check('explicit case 0', solve([[3, 3, 2, [0, 0, 8, 8]]], 8), [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]])
    check('explicit case 1', solve([[3, 3, 3, [0, 0, 8, 8]]], 8), [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]])
    check('explicit case 2', solve([[2, 2, 1, [0, 0, 8, 8]]], 8), [[[1, 1, 3], [2, 1, 3]]])
    check('explicit case 3', solve([[4, 4, 4, [1, 1, 8, 7]]], 8), [[[1, 1, 7], [2, 1, 8], [3, 1, 8], [4, 1, 8], [5, 1, 8], [6, 1, 7]]])
    check('explicit case 4', solve([[0, 0, 3, [0, 0, 8, 8]]], 8), [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]])
    check('explicit case 5', solve([[8, 3, 2, [0, 0, 8, 8]]], 8), [[[1, 7, 8], [2, 6, 8], [3, 6, 8], [4, 7, 8]]])
    check('explicit case 6', solve([[4, 2, 4, [2, 0, 8, 4]]], 8), [[[0, 2, 8], [1, 2, 8], [2, 2, 8], [3, 2, 8]]])
    check('explicit case 7', solve([[1, 3, 2, [0, 0, 8, 8]]], 8), [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]])
    check('explicit case 8', solve([[2, 4, 3, [0, 0, 8, 8]]], 8), [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5], [6, 0, 4]]])
    check('explicit case 9', solve([[3, 2, 5, [0, 0, 8, 8]]], 8), [[[0, 0, 8], [1, 0, 8], [2, 0, 8], [3, 0, 8], [4, 0, 7], [5, 0, 7], [6, 1, 5]]])
if N == 4:
    check('explicit case 0', solve([[3, 3, 2, [0, 0, 9, 9]]], 9), [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]])
    check('explicit case 1', solve([[3, 3, 3, [0, 0, 9, 9]]], 9), [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]])
    check('explicit case 2', solve([[2, 2, 1, [0, 0, 9, 9]]], 9), [[[1, 1, 3], [2, 1, 3]]])
    check('explicit case 3', solve([[4, 4, 4, [1, 1, 9, 8]]], 9), [[[1, 1, 7], [2, 1, 8], [3, 1, 8], [4, 1, 8], [5, 1, 8], [6, 1, 7], [7, 2, 6]]])
    check('explicit case 4', solve([[0, 0, 3, [0, 0, 9, 9]]], 9), [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]])
    check('explicit case 5', solve([[9, 3, 2, [0, 0, 9, 9]]], 9), [[[1, 8, 9], [2, 7, 9], [3, 7, 9], [4, 8, 9]]])
    check('explicit case 6', solve([[4, 2, 4, [2, 0, 9, 4]]], 9), [[[0, 2, 8], [1, 2, 8], [2, 2, 8], [3, 2, 8]]])
    check('explicit case 7', solve([[1, 3, 2, [0, 0, 9, 9]]], 9), [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]])
    check('explicit case 8', solve([[2, 4, 3, [0, 0, 9, 9]]], 9), [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5], [6, 0, 4]]])
    check('explicit case 9', solve([[3, 2, 5, [0, 0, 9, 9]]], 9), [[[0, 0, 8], [1, 0, 8], [2, 0, 8], [3, 0, 8], [4, 0, 7], [5, 0, 7], [6, 1, 5]]])
if N == 5:
    check('explicit case 0', solve([[3, 3, 2, [0, 0, 10, 10]]], 10), [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]])
    check('explicit case 1', solve([[3, 3, 3, [0, 0, 10, 10]]], 10), [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]])
    check('explicit case 2', solve([[2, 2, 1, [0, 0, 10, 10]]], 10), [[[1, 1, 3], [2, 1, 3]]])
    check('explicit case 3', solve([[5, 5, 5, [1, 1, 10, 9]]], 10), [[[1, 1, 9], [2, 1, 9], [3, 1, 10], [4, 1, 10], [5, 1, 10], [6, 1, 10], [7, 1, 9], [8, 1, 9]]])
    check('explicit case 4', solve([[0, 0, 3, [0, 0, 10, 10]]], 10), [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]])
    check('explicit case 5', solve([[10, 3, 2, [0, 0, 10, 10]]], 10), [[[1, 9, 10], [2, 8, 10], [3, 8, 10], [4, 9, 10]]])
    check('explicit case 6', solve([[4, 2, 4, [2, 0, 10, 4]]], 10), [[[0, 2, 8], [1, 2, 8], [2, 2, 8], [3, 2, 8]]])
    check('explicit case 7', solve([[1, 3, 2, [0, 0, 10, 10]]], 10), [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]])
    check('explicit case 8', solve([[2, 4, 3, [0, 0, 10, 10]]], 10), [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5], [6, 0, 4]]])
    check('explicit case 9', solve([[3, 2, 5, [0, 0, 10, 10]]], 10), [[[0, 0, 8], [1, 0, 8], [2, 0, 8], [3, 0, 8], [4, 0, 7], [5, 0, 7], [6, 1, 5]]])
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[[[1, 1, 5], [2, 1, 5], [3, 1, 5]]][[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]]Failed
explicit case 1[[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 1, 5]]][[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]]Failed
explicit case 2[[[1, 1, 3]]][[[1, 1, 3], [2, 1, 3]]]Failed
explicit case 3[[[1, 1, 6], [2, 1, 6], [3, 1, 6], [4, 1, 5]]][[[1, 1, 6], [2, 1, 6], [3, 1, 6], [4, 1, 6]]]Failed
explicit case 4[[[0, 0, 3], [1, 0, 2]]][[[0, 0, 3], [1, 0, 3], [2, 0, 2]]]Failed
explicit case 5[[[1, 4, 6], [2, 4, 6], [3, 4, 6]]][[[1, 5, 6], [2, 4, 6], [3, 4, 6], [4, 5, 6]]]Failed
explicit case 6[[[0, 2, 6], [1, 2, 6], [2, 2, 6], [3, 2, 6]]][[[0, 2, 6], [1, 2, 6], [2, 2, 6], [3, 2, 6]]]Passed
explicit case 7[[[1, 0, 3], [2, 0, 3], [3, 0, 3]]][[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]]Failed
explicit case 8[[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 4]]][[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5]]]Failed
explicit case 9[[[0, 0, 6], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 0, 6]]][[[0, 0, 6], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 0, 6]]]Passed

SHA-256 / e42374eab7016fc5e1dc553ab085f8e31d503896625f1b576c27777d2c9a6d59

3 / The verified repair

Exit 0
"""Failure Map reference implementation. Python standard library only."""
import json
from math import isqrt
N = 1
observations = []
def solve(commands, size):
    out=[]
    for cx,cy,r,clip in commands:
        l,t,rr,b=max(clip[0],0),max(clip[1],0),min(clip[2],size),min(clip[3],size)
        spans=[]
        for y in range(t,b):
            m=4*r*r-(2*y+1-2*cy)**2
            if m<0: continue
            k=isqrt(m)
            xa=-((1+k-2*cx)//2)
            xb=(2*cx-1+k)//2+1
            xa,xb=max(xa,l),min(xb,rr)
            if xa<xb: spans.append([y,xa,xb])
        out.append(spans)
    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([[3, 3, 2, [0, 0, 6, 6]]], 6), [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]])
    check('explicit case 1', solve([[3, 3, 3, [0, 0, 6, 6]]], 6), [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]])
    check('explicit case 2', solve([[2, 2, 1, [0, 0, 6, 6]]], 6), [[[1, 1, 3], [2, 1, 3]]])
    check('explicit case 3', solve([[3, 3, 3, [1, 1, 6, 5]]], 6), [[[1, 1, 6], [2, 1, 6], [3, 1, 6], [4, 1, 6]]])
    check('explicit case 4', solve([[0, 0, 3, [0, 0, 6, 6]]], 6), [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]])
    check('explicit case 5', solve([[6, 3, 2, [0, 0, 6, 6]]], 6), [[[1, 5, 6], [2, 4, 6], [3, 4, 6], [4, 5, 6]]])
    check('explicit case 6', solve([[4, 2, 4, [2, 0, 6, 4]]], 6), [[[0, 2, 6], [1, 2, 6], [2, 2, 6], [3, 2, 6]]])
    check('explicit case 7', solve([[1, 3, 2, [0, 0, 6, 6]]], 6), [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]])
    check('explicit case 8', solve([[2, 4, 3, [0, 0, 6, 6]]], 6), [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5]]])
    check('explicit case 9', solve([[3, 2, 5, [0, 0, 6, 6]]], 6), [[[0, 0, 6], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 0, 6]]])
if N == 2:
    check('explicit case 0', solve([[3, 3, 2, [0, 0, 7, 7]]], 7), [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]])
    check('explicit case 1', solve([[3, 3, 3, [0, 0, 7, 7]]], 7), [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]])
    check('explicit case 2', solve([[2, 2, 1, [0, 0, 7, 7]]], 7), [[[1, 1, 3], [2, 1, 3]]])
    check('explicit case 3', solve([[3, 3, 3, [1, 1, 7, 6]]], 7), [[[1, 1, 6], [2, 1, 6], [3, 1, 6], [4, 1, 6], [5, 1, 5]]])
    check('explicit case 4', solve([[0, 0, 3, [0, 0, 7, 7]]], 7), [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]])
    check('explicit case 5', solve([[7, 3, 2, [0, 0, 7, 7]]], 7), [[[1, 6, 7], [2, 5, 7], [3, 5, 7], [4, 6, 7]]])
    check('explicit case 6', solve([[4, 2, 4, [2, 0, 7, 4]]], 7), [[[0, 2, 7], [1, 2, 7], [2, 2, 7], [3, 2, 7]]])
    check('explicit case 7', solve([[1, 3, 2, [0, 0, 7, 7]]], 7), [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]])
    check('explicit case 8', solve([[2, 4, 3, [0, 0, 7, 7]]], 7), [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5], [6, 0, 4]]])
    check('explicit case 9', solve([[3, 2, 5, [0, 0, 7, 7]]], 7), [[[0, 0, 7], [1, 0, 7], [2, 0, 7], [3, 0, 7], [4, 0, 7], [5, 0, 7], [6, 1, 5]]])
if N == 3:
    check('explicit case 0', solve([[3, 3, 2, [0, 0, 8, 8]]], 8), [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]])
    check('explicit case 1', solve([[3, 3, 3, [0, 0, 8, 8]]], 8), [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]])
    check('explicit case 2', solve([[2, 2, 1, [0, 0, 8, 8]]], 8), [[[1, 1, 3], [2, 1, 3]]])
    check('explicit case 3', solve([[4, 4, 4, [1, 1, 8, 7]]], 8), [[[1, 1, 7], [2, 1, 8], [3, 1, 8], [4, 1, 8], [5, 1, 8], [6, 1, 7]]])
    check('explicit case 4', solve([[0, 0, 3, [0, 0, 8, 8]]], 8), [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]])
    check('explicit case 5', solve([[8, 3, 2, [0, 0, 8, 8]]], 8), [[[1, 7, 8], [2, 6, 8], [3, 6, 8], [4, 7, 8]]])
    check('explicit case 6', solve([[4, 2, 4, [2, 0, 8, 4]]], 8), [[[0, 2, 8], [1, 2, 8], [2, 2, 8], [3, 2, 8]]])
    check('explicit case 7', solve([[1, 3, 2, [0, 0, 8, 8]]], 8), [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]])
    check('explicit case 8', solve([[2, 4, 3, [0, 0, 8, 8]]], 8), [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5], [6, 0, 4]]])
    check('explicit case 9', solve([[3, 2, 5, [0, 0, 8, 8]]], 8), [[[0, 0, 8], [1, 0, 8], [2, 0, 8], [3, 0, 8], [4, 0, 7], [5, 0, 7], [6, 1, 5]]])
if N == 4:
    check('explicit case 0', solve([[3, 3, 2, [0, 0, 9, 9]]], 9), [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]])
    check('explicit case 1', solve([[3, 3, 3, [0, 0, 9, 9]]], 9), [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]])
    check('explicit case 2', solve([[2, 2, 1, [0, 0, 9, 9]]], 9), [[[1, 1, 3], [2, 1, 3]]])
    check('explicit case 3', solve([[4, 4, 4, [1, 1, 9, 8]]], 9), [[[1, 1, 7], [2, 1, 8], [3, 1, 8], [4, 1, 8], [5, 1, 8], [6, 1, 7], [7, 2, 6]]])
    check('explicit case 4', solve([[0, 0, 3, [0, 0, 9, 9]]], 9), [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]])
    check('explicit case 5', solve([[9, 3, 2, [0, 0, 9, 9]]], 9), [[[1, 8, 9], [2, 7, 9], [3, 7, 9], [4, 8, 9]]])
    check('explicit case 6', solve([[4, 2, 4, [2, 0, 9, 4]]], 9), [[[0, 2, 8], [1, 2, 8], [2, 2, 8], [3, 2, 8]]])
    check('explicit case 7', solve([[1, 3, 2, [0, 0, 9, 9]]], 9), [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]])
    check('explicit case 8', solve([[2, 4, 3, [0, 0, 9, 9]]], 9), [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5], [6, 0, 4]]])
    check('explicit case 9', solve([[3, 2, 5, [0, 0, 9, 9]]], 9), [[[0, 0, 8], [1, 0, 8], [2, 0, 8], [3, 0, 8], [4, 0, 7], [5, 0, 7], [6, 1, 5]]])
if N == 5:
    check('explicit case 0', solve([[3, 3, 2, [0, 0, 10, 10]]], 10), [[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]])
    check('explicit case 1', solve([[3, 3, 3, [0, 0, 10, 10]]], 10), [[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]])
    check('explicit case 2', solve([[2, 2, 1, [0, 0, 10, 10]]], 10), [[[1, 1, 3], [2, 1, 3]]])
    check('explicit case 3', solve([[5, 5, 5, [1, 1, 10, 9]]], 10), [[[1, 1, 9], [2, 1, 9], [3, 1, 10], [4, 1, 10], [5, 1, 10], [6, 1, 10], [7, 1, 9], [8, 1, 9]]])
    check('explicit case 4', solve([[0, 0, 3, [0, 0, 10, 10]]], 10), [[[0, 0, 3], [1, 0, 3], [2, 0, 2]]])
    check('explicit case 5', solve([[10, 3, 2, [0, 0, 10, 10]]], 10), [[[1, 9, 10], [2, 8, 10], [3, 8, 10], [4, 9, 10]]])
    check('explicit case 6', solve([[4, 2, 4, [2, 0, 10, 4]]], 10), [[[0, 2, 8], [1, 2, 8], [2, 2, 8], [3, 2, 8]]])
    check('explicit case 7', solve([[1, 3, 2, [0, 0, 10, 10]]], 10), [[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]])
    check('explicit case 8', solve([[2, 4, 3, [0, 0, 10, 10]]], 10), [[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5], [6, 0, 4]]])
    check('explicit case 9', solve([[3, 2, 5, [0, 0, 10, 10]]], 10), [[[0, 0, 8], [1, 0, 8], [2, 0, 8], [3, 0, 8], [4, 0, 7], [5, 0, 7], [6, 1, 5]]])
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[[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]][[[1, 2, 4], [2, 1, 5], [3, 1, 5], [4, 2, 4]]]Passed
explicit case 1[[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]][[[0, 1, 5], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 1, 5]]]Passed
explicit case 2[[[1, 1, 3], [2, 1, 3]]][[[1, 1, 3], [2, 1, 3]]]Passed
explicit case 3[[[1, 1, 6], [2, 1, 6], [3, 1, 6], [4, 1, 6]]][[[1, 1, 6], [2, 1, 6], [3, 1, 6], [4, 1, 6]]]Passed
explicit case 4[[[0, 0, 3], [1, 0, 3], [2, 0, 2]]][[[0, 0, 3], [1, 0, 3], [2, 0, 2]]]Passed
explicit case 5[[[1, 5, 6], [2, 4, 6], [3, 4, 6], [4, 5, 6]]][[[1, 5, 6], [2, 4, 6], [3, 4, 6], [4, 5, 6]]]Passed
explicit case 6[[[0, 2, 6], [1, 2, 6], [2, 2, 6], [3, 2, 6]]][[[0, 2, 6], [1, 2, 6], [2, 2, 6], [3, 2, 6]]]Passed
explicit case 7[[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]][[[1, 0, 2], [2, 0, 3], [3, 0, 3], [4, 0, 2]]]Passed
explicit case 8[[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5]]][[[1, 0, 4], [2, 0, 5], [3, 0, 5], [4, 0, 5], [5, 0, 5]]]Passed
explicit case 9[[[0, 0, 6], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 0, 6]]][[[0, 0, 6], [1, 0, 6], [2, 0, 6], [3, 0, 6], [4, 0, 6], [5, 0, 6]]]Passed

SHA-256 / c548acc932506688c4fae5fdb9262f2a9392099598ab72612c7ca12b67705445

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 2026-09-29T14:45:22.670494+00:00.

Case digest / a77f183e1af92a128cce1dec06ac63a7faf44b3f6bb5f6d4c25f19487966f611