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FA-51751 / Raster clipping / Open access

Clipped bresenham prestep: point unclipped · case 01

Zero-length lines bypass scissor testing.

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

ROOT CAUSE

Zero-length lines bypass scissor testing.

THE FAILURE

Zero-length lines bypass scissor testing.

Unsuccessful approach: Testing the raster bounds instead of the scissor still emits points outside an interior scissor.

Case contract

Each command is [x0,y0,x1,y1,scissor] for an x-major integer line with x0<=x1 and |y1-y0|<=x1-x0 (a zero-length line is a single point). The reference pixel in column x is y0+floor((2*(y1-y0)*(x-x0)+dx)/(2*dx)), ties rounding up. Clipping to the half-open scissor [left,top,right,bottom) intersected with [0,size) must emit exactly the reference pixels inside it, in x order. The walk starts at the first visible column with an exact pre-stepped error term and may stop once y has left the scissor in the direction of travel.

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

N = 1
observations = []
def solve(commands, size):
    out=[]
    for x0,y0,x1,y1,clip in commands:
        l,t,r,b=max(clip[0],0),max(clip[1],0),min(clip[2],size),min(clip[3],size)
        dx,dy=x1-x0,y1-y0
        pixels=[]
        if dx==0:
            pixels=[[x0,y0]]
        else:
            xs=max(x0,l)
            xe=min(x1,r-1)
            if xs<=xe:
                num=2*dy*(xs-x0)+dx
                y=y0+num//(2*dx)
                err=num%(2*dx)
                for x in range(xs,xe+1):
                    if y>=b and dy>=0 or y<t and dy<=0: break
                    if t<=y<b: pixels.append([x,y])
                    err+=2*dy
                    while err>=2*dx:
                        err-=2*dx
                        y+=1
                    while err<0:
                        err+=2*dx
                        y-=1
        out.append(pixels)
    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([[0, 0, 5, 2, [0, 0, 6, 6]]], 6), [[[0, 0], [1, 0], [2, 1], [3, 1], [4, 2], [5, 2]]])
    check('explicit case 1', solve([[-3, 0, 5, 3, [0, 0, 6, 6]]], 6), [[[0, 1], [1, 2], [2, 2], [3, 2], [4, 3], [5, 3]]])
    check('explicit case 2', solve([[0, 1, 4, 3, [2, 0, 6, 6]]], 6), [[[2, 2], [3, 3], [4, 3]]])
    check('explicit case 3', solve([[0, 4, 5, 1, [2, 0, 6, 6]]], 6), [[[2, 3], [3, 2], [4, 2], [5, 1]]])
    check('explicit case 4', solve([[1, 1, 9, 1, [0, 0, 6, 6]]], 6), [[[1, 1], [2, 1], [3, 1], [4, 1], [5, 1]]])
    check('explicit case 5', solve([[0, 0, 3, 3, [0, 0, 2, 6]]], 6), [[[0, 0], [1, 1]]])
    check('explicit case 6', solve([[2, 2, 5, 3, [0, 0, 6, 6]]], 6), [[[2, 2], [3, 2], [4, 3], [5, 3]]])
    check('explicit case 7', solve([[2, 1, 6, 3, [1, 0, 6, 6]]], 6), [[[2, 1], [3, 2], [4, 2], [5, 3]]])
    check('explicit case 8', solve([[3, 3, 3, 3, [0, 0, 2, 6]]], 6), [[]])
    check('explicit case 9', solve([[3, 3, 3, 3, [0, 0, 6, 6]]], 6), [[[3, 3]]])
    check('explicit case 10', solve([[0, 0, 4, 4, [0, 2, 6, 6]]], 6), [[[2, 2], [3, 3], [4, 4]]])
    check('explicit case 11', solve([[0, 5, 5, 0, [0, 0, 6, 3]]], 6), [[[3, 2], [4, 1], [5, 0]]])
    check('explicit case 12', solve([[0, 0, 6, 2, [0, 1, 6, 2]]], 6), [[[2, 1], [3, 1], [4, 1]]])
if N == 2:
    check('explicit case 0', solve([[0, 0, 6, 2, [0, 0, 7, 7]]], 7), [[[0, 0], [1, 0], [2, 1], [3, 1], [4, 1], [5, 2], [6, 2]]])
    check('explicit case 1', solve([[-3, 0, 6, 3, [0, 0, 7, 7]]], 7), [[[0, 1], [1, 1], [2, 2], [3, 2], [4, 2], [5, 3], [6, 3]]])
    check('explicit case 2', solve([[0, 1, 4, 3, [2, 0, 7, 7]]], 7), [[[2, 2], [3, 3], [4, 3]]])
    check('explicit case 3', solve([[0, 4, 5, 1, [2, 0, 7, 7]]], 7), [[[2, 3], [3, 2], [4, 2], [5, 1]]])
    check('explicit case 4', solve([[1, 1, 10, 1, [0, 0, 7, 7]]], 7), [[[1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1]]])
    check('explicit case 5', solve([[0, 0, 3, 3, [0, 0, 2, 7]]], 7), [[[0, 0], [1, 1]]])
    check('explicit case 6', solve([[2, 2, 5, 3, [0, 0, 7, 7]]], 7), [[[2, 2], [3, 2], [4, 3], [5, 3]]])
    check('explicit case 7', solve([[2, 1, 6, 3, [1, 0, 7, 7]]], 7), [[[2, 1], [3, 2], [4, 2], [5, 3], [6, 3]]])
    check('explicit case 8', solve([[3, 3, 3, 3, [0, 0, 2, 7]]], 7), [[]])
    check('explicit case 9', solve([[3, 3, 3, 3, [0, 0, 7, 7]]], 7), [[[3, 3]]])
    check('explicit case 10', solve([[0, 0, 4, 4, [0, 2, 7, 7]]], 7), [[[2, 2], [3, 3], [4, 4]]])
    check('explicit case 11', solve([[0, 5, 5, 0, [0, 0, 7, 3]]], 7), [[[3, 2], [4, 1], [5, 0]]])
    check('explicit case 12', solve([[0, 0, 6, 2, [0, 1, 7, 2]]], 7), [[[2, 1], [3, 1], [4, 1]]])
if N == 3:
    check('explicit case 0', solve([[0, 0, 7, 2, [0, 0, 8, 8]]], 8), [[[0, 0], [1, 0], [2, 1], [3, 1], [4, 1], [5, 1], [6, 2], [7, 2]]])
    check('explicit case 1', solve([[-3, 0, 7, 3, [0, 0, 8, 8]]], 8), [[[0, 1], [1, 1], [2, 2], [3, 2], [4, 2], [5, 2], [6, 3], [7, 3]]])
    check('explicit case 2', solve([[0, 1, 4, 3, [2, 0, 8, 8]]], 8), [[[2, 2], [3, 3], [4, 3]]])
    check('explicit case 3', solve([[0, 4, 5, 1, [2, 0, 8, 8]]], 8), [[[2, 3], [3, 2], [4, 2], [5, 1]]])
    check('explicit case 4', solve([[1, 1, 11, 1, [0, 0, 8, 8]]], 8), [[[1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1]]])
    check('explicit case 5', solve([[0, 0, 3, 3, [0, 0, 2, 8]]], 8), [[[0, 0], [1, 1]]])
    check('explicit case 6', solve([[2, 2, 5, 3, [0, 0, 8, 8]]], 8), [[[2, 2], [3, 2], [4, 3], [5, 3]]])
    check('explicit case 7', solve([[2, 1, 6, 3, [1, 0, 8, 8]]], 8), [[[2, 1], [3, 2], [4, 2], [5, 3], [6, 3]]])
    check('explicit case 8', solve([[3, 3, 3, 3, [0, 0, 2, 8]]], 8), [[]])
    check('explicit case 9', solve([[3, 3, 3, 3, [0, 0, 8, 8]]], 8), [[[3, 3]]])
    check('explicit case 10', solve([[0, 0, 4, 4, [0, 2, 8, 8]]], 8), [[[2, 2], [3, 3], [4, 4]]])
    check('explicit case 11', solve([[0, 5, 5, 0, [0, 0, 8, 3]]], 8), [[[3, 2], [4, 1], [5, 0]]])
    check('explicit case 12', solve([[0, 0, 6, 2, [0, 1, 8, 2]]], 8), [[[2, 1], [3, 1], [4, 1]]])
if N == 4:
    check('explicit case 0', solve([[0, 0, 8, 2, [0, 0, 9, 9]]], 9), [[[0, 0], [1, 0], [2, 1], [3, 1], [4, 1], [5, 1], [6, 2], [7, 2], [8, 2]]])
    check('explicit case 1', solve([[-3, 0, 8, 3, [0, 0, 9, 9]]], 9), [[[0, 1], [1, 1], [2, 1], [3, 2], [4, 2], [5, 2], [6, 2], [7, 3], [8, 3]]])
    check('explicit case 2', solve([[0, 1, 4, 3, [2, 0, 9, 9]]], 9), [[[2, 2], [3, 3], [4, 3]]])
    check('explicit case 3', solve([[0, 4, 5, 1, [2, 0, 9, 9]]], 9), [[[2, 3], [3, 2], [4, 2], [5, 1]]])
    check('explicit case 4', solve([[1, 1, 12, 1, [0, 0, 9, 9]]], 9), [[[1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1]]])
    check('explicit case 5', solve([[0, 0, 3, 3, [0, 0, 2, 9]]], 9), [[[0, 0], [1, 1]]])
    check('explicit case 6', solve([[2, 2, 5, 3, [0, 0, 9, 9]]], 9), [[[2, 2], [3, 2], [4, 3], [5, 3]]])
    check('explicit case 7', solve([[2, 1, 6, 3, [1, 0, 9, 9]]], 9), [[[2, 1], [3, 2], [4, 2], [5, 3], [6, 3]]])
    check('explicit case 8', solve([[3, 3, 3, 3, [0, 0, 2, 9]]], 9), [[]])
    check('explicit case 9', solve([[3, 3, 3, 3, [0, 0, 9, 9]]], 9), [[[3, 3]]])
    check('explicit case 10', solve([[0, 0, 4, 4, [0, 2, 9, 9]]], 9), [[[2, 2], [3, 3], [4, 4]]])
    check('explicit case 11', solve([[0, 5, 5, 0, [0, 0, 9, 3]]], 9), [[[3, 2], [4, 1], [5, 0]]])
    check('explicit case 12', solve([[0, 0, 6, 2, [0, 1, 9, 2]]], 9), [[[2, 1], [3, 1], [4, 1]]])
if N == 5:
    check('explicit case 0', solve([[0, 0, 9, 2, [0, 0, 10, 10]]], 10), [[[0, 0], [1, 0], [2, 0], [3, 1], [4, 1], [5, 1], [6, 1], [7, 2], [8, 2], [9, 2]]])
    check('explicit case 1', solve([[-3, 0, 9, 3, [0, 0, 10, 10]]], 10), [[[0, 1], [1, 1], [2, 1], [3, 2], [4, 2], [5, 2], [6, 2], [7, 3], [8, 3], [9, 3]]])
    check('explicit case 2', solve([[0, 1, 4, 3, [2, 0, 10, 10]]], 10), [[[2, 2], [3, 3], [4, 3]]])
    check('explicit case 3', solve([[0, 4, 5, 1, [2, 0, 10, 10]]], 10), [[[2, 3], [3, 2], [4, 2], [5, 1]]])
    check('explicit case 4', solve([[1, 1, 13, 1, [0, 0, 10, 10]]], 10), [[[1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1]]])
    check('explicit case 5', solve([[0, 0, 3, 3, [0, 0, 2, 10]]], 10), [[[0, 0], [1, 1]]])
    check('explicit case 6', solve([[2, 2, 5, 3, [0, 0, 10, 10]]], 10), [[[2, 2], [3, 2], [4, 3], [5, 3]]])
    check('explicit case 7', solve([[2, 1, 6, 3, [1, 0, 10, 10]]], 10), [[[2, 1], [3, 2], [4, 2], [5, 3], [6, 3]]])
    check('explicit case 8', solve([[3, 3, 3, 3, [0, 0, 2, 10]]], 10), [[]])
    check('explicit case 9', solve([[3, 3, 3, 3, [0, 0, 10, 10]]], 10), [[[3, 3]]])
    check('explicit case 10', solve([[0, 0, 4, 4, [0, 2, 10, 10]]], 10), [[[2, 2], [3, 3], [4, 4]]])
    check('explicit case 11', solve([[0, 5, 5, 0, [0, 0, 10, 3]]], 10), [[[3, 2], [4, 1], [5, 0]]])
    check('explicit case 12', solve([[0, 0, 6, 2, [0, 1, 10, 2]]], 10), [[[2, 1], [3, 1], [4, 1]]])
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[[[0, 0], [1, 0], [2, 1], [3, 1], [4, 2], [5, 2]]][[[0, 0], [1, 0], [2, 1], [3, 1], [4, 2], [5, 2]]]Passed
explicit case 1[[[0, 1], [1, 2], [2, 2], [3, 2], [4, 3], [5, 3]]][[[0, 1], [1, 2], [2, 2], [3, 2], [4, 3], [5, 3]]]Passed
explicit case 2[[[2, 2], [3, 3], [4, 3]]][[[2, 2], [3, 3], [4, 3]]]Passed
explicit case 3[[[2, 3], [3, 2], [4, 2], [5, 1]]][[[2, 3], [3, 2], [4, 2], [5, 1]]]Passed
explicit case 4[[[1, 1], [2, 1], [3, 1], [4, 1], [5, 1]]][[[1, 1], [2, 1], [3, 1], [4, 1], [5, 1]]]Passed
explicit case 5[[[0, 0], [1, 1]]][[[0, 0], [1, 1]]]Passed
explicit case 6[[[2, 2], [3, 2], [4, 3], [5, 3]]][[[2, 2], [3, 2], [4, 3], [5, 3]]]Passed
explicit case 7[[[2, 1], [3, 2], [4, 2], [5, 3]]][[[2, 1], [3, 2], [4, 2], [5, 3]]]Passed
explicit case 8[[[3, 3]]][[]]Failed
explicit case 9[[[3, 3]]][[[3, 3]]]Passed
explicit case 10[[[2, 2], [3, 3], [4, 4]]][[[2, 2], [3, 3], [4, 4]]]Passed
explicit case 11[[[3, 2], [4, 1], [5, 0]]][[[3, 2], [4, 1], [5, 0]]]Passed
explicit case 12[[[2, 1], [3, 1], [4, 1]]][[[2, 1], [3, 1], [4, 1]]]Passed

SHA-256 / ac5a3c7340792f909dcec0d34977e8aef03213497d41f1c0f5fe705ef103d3be

2 / The unsuccessful fix

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

N = 1
observations = []
def solve(commands, size):
    out=[]
    for x0,y0,x1,y1,clip in commands:
        l,t,r,b=max(clip[0],0),max(clip[1],0),min(clip[2],size),min(clip[3],size)
        dx,dy=x1-x0,y1-y0
        pixels=[]
        if dx==0:
            if 0<=x0<size and 0<=y0<size: pixels=[[x0,y0]]
        else:
            xs=max(x0,l)
            xe=min(x1,r-1)
            if xs<=xe:
                num=2*dy*(xs-x0)+dx
                y=y0+num//(2*dx)
                err=num%(2*dx)
                for x in range(xs,xe+1):
                    if y>=b and dy>=0 or y<t and dy<=0: break
                    if t<=y<b: pixels.append([x,y])
                    err+=2*dy
                    while err>=2*dx:
                        err-=2*dx
                        y+=1
                    while err<0:
                        err+=2*dx
                        y-=1
        out.append(pixels)
    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([[0, 0, 5, 2, [0, 0, 6, 6]]], 6), [[[0, 0], [1, 0], [2, 1], [3, 1], [4, 2], [5, 2]]])
    check('explicit case 1', solve([[-3, 0, 5, 3, [0, 0, 6, 6]]], 6), [[[0, 1], [1, 2], [2, 2], [3, 2], [4, 3], [5, 3]]])
    check('explicit case 2', solve([[0, 1, 4, 3, [2, 0, 6, 6]]], 6), [[[2, 2], [3, 3], [4, 3]]])
    check('explicit case 3', solve([[0, 4, 5, 1, [2, 0, 6, 6]]], 6), [[[2, 3], [3, 2], [4, 2], [5, 1]]])
    check('explicit case 4', solve([[1, 1, 9, 1, [0, 0, 6, 6]]], 6), [[[1, 1], [2, 1], [3, 1], [4, 1], [5, 1]]])
    check('explicit case 5', solve([[0, 0, 3, 3, [0, 0, 2, 6]]], 6), [[[0, 0], [1, 1]]])
    check('explicit case 6', solve([[2, 2, 5, 3, [0, 0, 6, 6]]], 6), [[[2, 2], [3, 2], [4, 3], [5, 3]]])
    check('explicit case 7', solve([[2, 1, 6, 3, [1, 0, 6, 6]]], 6), [[[2, 1], [3, 2], [4, 2], [5, 3]]])
    check('explicit case 8', solve([[3, 3, 3, 3, [0, 0, 2, 6]]], 6), [[]])
    check('explicit case 9', solve([[3, 3, 3, 3, [0, 0, 6, 6]]], 6), [[[3, 3]]])
    check('explicit case 10', solve([[0, 0, 4, 4, [0, 2, 6, 6]]], 6), [[[2, 2], [3, 3], [4, 4]]])
    check('explicit case 11', solve([[0, 5, 5, 0, [0, 0, 6, 3]]], 6), [[[3, 2], [4, 1], [5, 0]]])
    check('explicit case 12', solve([[0, 0, 6, 2, [0, 1, 6, 2]]], 6), [[[2, 1], [3, 1], [4, 1]]])
if N == 2:
    check('explicit case 0', solve([[0, 0, 6, 2, [0, 0, 7, 7]]], 7), [[[0, 0], [1, 0], [2, 1], [3, 1], [4, 1], [5, 2], [6, 2]]])
    check('explicit case 1', solve([[-3, 0, 6, 3, [0, 0, 7, 7]]], 7), [[[0, 1], [1, 1], [2, 2], [3, 2], [4, 2], [5, 3], [6, 3]]])
    check('explicit case 2', solve([[0, 1, 4, 3, [2, 0, 7, 7]]], 7), [[[2, 2], [3, 3], [4, 3]]])
    check('explicit case 3', solve([[0, 4, 5, 1, [2, 0, 7, 7]]], 7), [[[2, 3], [3, 2], [4, 2], [5, 1]]])
    check('explicit case 4', solve([[1, 1, 10, 1, [0, 0, 7, 7]]], 7), [[[1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1]]])
    check('explicit case 5', solve([[0, 0, 3, 3, [0, 0, 2, 7]]], 7), [[[0, 0], [1, 1]]])
    check('explicit case 6', solve([[2, 2, 5, 3, [0, 0, 7, 7]]], 7), [[[2, 2], [3, 2], [4, 3], [5, 3]]])
    check('explicit case 7', solve([[2, 1, 6, 3, [1, 0, 7, 7]]], 7), [[[2, 1], [3, 2], [4, 2], [5, 3], [6, 3]]])
    check('explicit case 8', solve([[3, 3, 3, 3, [0, 0, 2, 7]]], 7), [[]])
    check('explicit case 9', solve([[3, 3, 3, 3, [0, 0, 7, 7]]], 7), [[[3, 3]]])
    check('explicit case 10', solve([[0, 0, 4, 4, [0, 2, 7, 7]]], 7), [[[2, 2], [3, 3], [4, 4]]])
    check('explicit case 11', solve([[0, 5, 5, 0, [0, 0, 7, 3]]], 7), [[[3, 2], [4, 1], [5, 0]]])
    check('explicit case 12', solve([[0, 0, 6, 2, [0, 1, 7, 2]]], 7), [[[2, 1], [3, 1], [4, 1]]])
if N == 3:
    check('explicit case 0', solve([[0, 0, 7, 2, [0, 0, 8, 8]]], 8), [[[0, 0], [1, 0], [2, 1], [3, 1], [4, 1], [5, 1], [6, 2], [7, 2]]])
    check('explicit case 1', solve([[-3, 0, 7, 3, [0, 0, 8, 8]]], 8), [[[0, 1], [1, 1], [2, 2], [3, 2], [4, 2], [5, 2], [6, 3], [7, 3]]])
    check('explicit case 2', solve([[0, 1, 4, 3, [2, 0, 8, 8]]], 8), [[[2, 2], [3, 3], [4, 3]]])
    check('explicit case 3', solve([[0, 4, 5, 1, [2, 0, 8, 8]]], 8), [[[2, 3], [3, 2], [4, 2], [5, 1]]])
    check('explicit case 4', solve([[1, 1, 11, 1, [0, 0, 8, 8]]], 8), [[[1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1]]])
    check('explicit case 5', solve([[0, 0, 3, 3, [0, 0, 2, 8]]], 8), [[[0, 0], [1, 1]]])
    check('explicit case 6', solve([[2, 2, 5, 3, [0, 0, 8, 8]]], 8), [[[2, 2], [3, 2], [4, 3], [5, 3]]])
    check('explicit case 7', solve([[2, 1, 6, 3, [1, 0, 8, 8]]], 8), [[[2, 1], [3, 2], [4, 2], [5, 3], [6, 3]]])
    check('explicit case 8', solve([[3, 3, 3, 3, [0, 0, 2, 8]]], 8), [[]])
    check('explicit case 9', solve([[3, 3, 3, 3, [0, 0, 8, 8]]], 8), [[[3, 3]]])
    check('explicit case 10', solve([[0, 0, 4, 4, [0, 2, 8, 8]]], 8), [[[2, 2], [3, 3], [4, 4]]])
    check('explicit case 11', solve([[0, 5, 5, 0, [0, 0, 8, 3]]], 8), [[[3, 2], [4, 1], [5, 0]]])
    check('explicit case 12', solve([[0, 0, 6, 2, [0, 1, 8, 2]]], 8), [[[2, 1], [3, 1], [4, 1]]])
if N == 4:
    check('explicit case 0', solve([[0, 0, 8, 2, [0, 0, 9, 9]]], 9), [[[0, 0], [1, 0], [2, 1], [3, 1], [4, 1], [5, 1], [6, 2], [7, 2], [8, 2]]])
    check('explicit case 1', solve([[-3, 0, 8, 3, [0, 0, 9, 9]]], 9), [[[0, 1], [1, 1], [2, 1], [3, 2], [4, 2], [5, 2], [6, 2], [7, 3], [8, 3]]])
    check('explicit case 2', solve([[0, 1, 4, 3, [2, 0, 9, 9]]], 9), [[[2, 2], [3, 3], [4, 3]]])
    check('explicit case 3', solve([[0, 4, 5, 1, [2, 0, 9, 9]]], 9), [[[2, 3], [3, 2], [4, 2], [5, 1]]])
    check('explicit case 4', solve([[1, 1, 12, 1, [0, 0, 9, 9]]], 9), [[[1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1]]])
    check('explicit case 5', solve([[0, 0, 3, 3, [0, 0, 2, 9]]], 9), [[[0, 0], [1, 1]]])
    check('explicit case 6', solve([[2, 2, 5, 3, [0, 0, 9, 9]]], 9), [[[2, 2], [3, 2], [4, 3], [5, 3]]])
    check('explicit case 7', solve([[2, 1, 6, 3, [1, 0, 9, 9]]], 9), [[[2, 1], [3, 2], [4, 2], [5, 3], [6, 3]]])
    check('explicit case 8', solve([[3, 3, 3, 3, [0, 0, 2, 9]]], 9), [[]])
    check('explicit case 9', solve([[3, 3, 3, 3, [0, 0, 9, 9]]], 9), [[[3, 3]]])
    check('explicit case 10', solve([[0, 0, 4, 4, [0, 2, 9, 9]]], 9), [[[2, 2], [3, 3], [4, 4]]])
    check('explicit case 11', solve([[0, 5, 5, 0, [0, 0, 9, 3]]], 9), [[[3, 2], [4, 1], [5, 0]]])
    check('explicit case 12', solve([[0, 0, 6, 2, [0, 1, 9, 2]]], 9), [[[2, 1], [3, 1], [4, 1]]])
if N == 5:
    check('explicit case 0', solve([[0, 0, 9, 2, [0, 0, 10, 10]]], 10), [[[0, 0], [1, 0], [2, 0], [3, 1], [4, 1], [5, 1], [6, 1], [7, 2], [8, 2], [9, 2]]])
    check('explicit case 1', solve([[-3, 0, 9, 3, [0, 0, 10, 10]]], 10), [[[0, 1], [1, 1], [2, 1], [3, 2], [4, 2], [5, 2], [6, 2], [7, 3], [8, 3], [9, 3]]])
    check('explicit case 2', solve([[0, 1, 4, 3, [2, 0, 10, 10]]], 10), [[[2, 2], [3, 3], [4, 3]]])
    check('explicit case 3', solve([[0, 4, 5, 1, [2, 0, 10, 10]]], 10), [[[2, 3], [3, 2], [4, 2], [5, 1]]])
    check('explicit case 4', solve([[1, 1, 13, 1, [0, 0, 10, 10]]], 10), [[[1, 1], [2, 1], [3, 1], [4, 1], [5, 1], [6, 1], [7, 1], [8, 1], [9, 1]]])
    check('explicit case 5', solve([[0, 0, 3, 3, [0, 0, 2, 10]]], 10), [[[0, 0], [1, 1]]])
    check('explicit case 6', solve([[2, 2, 5, 3, [0, 0, 10, 10]]], 10), [[[2, 2], [3, 2], [4, 3], [5, 3]]])
    check('explicit case 7', solve([[2, 1, 6, 3, [1, 0, 10, 10]]], 10), [[[2, 1], [3, 2], [4, 2], [5, 3], [6, 3]]])
    check('explicit case 8', solve([[3, 3, 3, 3, [0, 0, 2, 10]]], 10), [[]])
    check('explicit case 9', solve([[3, 3, 3, 3, [0, 0, 10, 10]]], 10), [[[3, 3]]])
    check('explicit case 10', solve([[0, 0, 4, 4, [0, 2, 10, 10]]], 10), [[[2, 2], [3, 3], [4, 4]]])
    check('explicit case 11', solve([[0, 5, 5, 0, [0, 0, 10, 3]]], 10), [[[3, 2], [4, 1], [5, 0]]])
    check('explicit case 12', solve([[0, 0, 6, 2, [0, 1, 10, 2]]], 10), [[[2, 1], [3, 1], [4, 1]]])
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[[[0, 0], [1, 0], [2, 1], [3, 1], [4, 2], [5, 2]]][[[0, 0], [1, 0], [2, 1], [3, 1], [4, 2], [5, 2]]]Passed
explicit case 1[[[0, 1], [1, 2], [2, 2], [3, 2], [4, 3], [5, 3]]][[[0, 1], [1, 2], [2, 2], [3, 2], [4, 3], [5, 3]]]Passed
explicit case 2[[[2, 2], [3, 3], [4, 3]]][[[2, 2], [3, 3], [4, 3]]]Passed
explicit case 3[[[2, 3], [3, 2], [4, 2], [5, 1]]][[[2, 3], [3, 2], [4, 2], [5, 1]]]Passed
explicit case 4[[[1, 1], [2, 1], [3, 1], [4, 1], [5, 1]]][[[1, 1], [2, 1], [3, 1], [4, 1], [5, 1]]]Passed
explicit case 5[[[0, 0], [1, 1]]][[[0, 0], [1, 1]]]Passed
explicit case 6[[[2, 2], [3, 2], [4, 3], [5, 3]]][[[2, 2], [3, 2], [4, 3], [5, 3]]]Passed
explicit case 7[[[2, 1], [3, 2], [4, 2], [5, 3]]][[[2, 1], [3, 2], [4, 2], [5, 3]]]Passed
explicit case 8[[[3, 3]]][[]]Failed
explicit case 9[[[3, 3]]][[[3, 3]]]Passed
explicit case 10[[[2, 2], [3, 3], [4, 4]]][[[2, 2], [3, 3], [4, 4]]]Passed
explicit case 11[[[3, 2], [4, 1], [5, 0]]][[[3, 2], [4, 1], [5, 0]]]Passed
explicit case 12[[[2, 1], [3, 1], [4, 1]]][[[2, 1], [3, 1], [4, 1]]]Passed

SHA-256 / e089654e82759ba3c59579616c43820e76e4525f825bc9f2feddc87b7cf3e00e

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 2026-09-29T14:45:22.071730+00:00.

Case digest / 4f416d527909dc26073418052204ac25d6d4161e7edf5478c9b44b04ba425205