Verification step 4

Depth ordering: when front-behind logic loops

Depth ordering is the front-behind relationship between parts of a drawing, such as beam A passing over beam B at a crossing.

Start with the drawing

The plain version

Depth ordering is the front-behind relationship between parts of a drawing, such as beam A passing over beam B at a crossing.

Why your eye buys it

A depth cue becomes strong evidence only when the local over-under relationships can be traced around the whole drawing.

Small details that matter

• A consistent physical object can be arranged from front to back without looping back on itself.
• A directed depth cycle means the drawing asks A to be over B, B over C, and C over A.
• Ordinary crossings are weak evidence until the surrounding junctions make the over-under story clear.

How to think about the result

• If the arrows can be sorted from front to back, the depth story is at least globally consistent.
• If the arrows form a cycle, no strict depth order exists.
• When crossings are unclear, ambiguity is safer than pretending the detector has proof.

What can shift the verdict

Cue	A useful sign	How it changes the reading
Local overlap	A visible over-under cue at a crossing	Creates one directed relationship
Depth cycle	Three or more relationships loop back to the start	Supports an impossible-looking verdict
Unclear crossing	No reliable over-under cue	Keeps the result cautious

Try it with your sketch

1. Label the parts that appear in front at each crossing.
2. Draw arrows from front parts to behind parts.
3. Look for a loop before calling the shape impossible.
4. Compare the depth story with the confidence-scoring guide.

A small scene

Compare a braided-looking crossing with a Penrose-like loop before judging the result; one confusing overlap is not the same as a complete circular depth demand.

Impossible objects often depend on contradictory over-under relationships. One part of a drawing implies beam A is in front of beam B. Another implies B is in front of C. A third implies C is in front of A. That loop is the visual trap.

In physical space, a strict front-behind order cannot chase itself in a circle. If the local cues imply a directed cycle, the detector treats that as evidence of impossibility.

This is the part of an impossible drawing that can feel almost musical: over, under, over, under, and then suddenly the rhythm asks one beam to be both earlier and later in the same little story.

The core idea

Depth ordering can be represented as a directed graph. If A is in front of B, draw an arrow from A to B. If the arrows can be arranged from front to back without contradiction, the relationships are at least globally consistent. If the arrows form a cycle, no strict ordering exists.

You do not need formal math to feel the problem. Trace each crossing with your finger and whisper "front" or "behind." If the words eventually loop back and disagree with the place you started, the drawing has given you a real contradiction to study.

Why this is hard in a browser toy

Most line drawings do not explicitly label which edge is in front. The detector has to infer depth from crossings, T-junctions, occlusion-like breaks, and preset hints. That inference is fallible, so depth cycles are treated as evidence that must be weighed against other signals.

A person can use context, taste, and patience. A browser-side tool only gets visible line evidence. That is why a beautiful shaded drawing may need to be redrawn as simple line art before the depth story becomes fair to test.

Mini experiment

Draw three bands that weave over and under each other. If you can assign a consistent front-to-back order, the drawing can still be possible. If every band must be both in front of and behind another band in a loop, you have created the core logic of many impossible objects.

Where to go next

• Previous: angle families
• Next: impossible patterns
• Read the detector methodology