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.

What to check first

What this means

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

Why it matters

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

What to notice

• 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 read it

• 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 change the result

Condition	Threshold	What it means
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

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.

Example

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.

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.

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.

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.

Next Step

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