Verification step 4

Depth ordering: when front-behind logic loops

Last reviewed 2026-06-23 Contradiction signal Operator: ImpossibleShape.com Cycle detection

Over-under curves forming a circular depth-order contradiction — Depth cues become suspicious when they form a circular demand such as A over B, B over C, and C over A.

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.

Topological sorting test consistent depth order = directed graph with no cycle

This is a structural test, not an artistic judgment. It asks whether the local front-behind clues can all be true at the same time.

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.

Strong clue

A clean T-junction where one edge visibly terminates behind another edge.

Weak clue

Two freehand lines that simply cross without any drawing convention saying which is in front.

Contradiction

A directed loop where every local over-under clue makes sense, but the full ordering cannot exist.

Ambiguity

A crossing group with insufficient occlusion evidence, usually best reported as ambiguous.

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.

Assign labels

Name three crossing beams A, B, and C. Write down each local over-under clue as an arrow.

Sort the arrows

Try to arrange the beams from front to back. If the order works, the depth clues are consistent.

Find the loop

If the arrows say A over B, B over C, and C over A, you found the paradox mechanism.