Verification step 2

Graph construction: what touches what?

Last reviewed 2026-06-23 Geometry graph layer Operator: ImpossibleShape.com Topology before verdict
Line drawing converted into a graph of vertices, edges, and cycles
The detector needs graph structure: vertices, edges, crossings, adjacency, and loops that can be inspected.

Once the detector has line segments, it needs a structure it can reason about. Graph construction turns a drawing into vertices, edges, intersections, connected components, and candidate cycles.

This is the moment where the site stops looking at "a picture" and starts asking structural questions: which endpoints meet, which edges cross, how many lines join at a vertex, and whether a loop closes in a way that could support a face, beam, or contradiction.

Graph construction from segments A hand-drawn wireframe becomes snapped vertices, graph edges, and an adjacency list. From strokes to graph Small drawing errors are normalized before topology is scored. raw segments snapped vertices A: B, C B: A, C C: A, B adjacency list

The core idea

A graph is a set of nodes and connections. In this site, nodes are usually endpoints or intersections, and connections are line segments. That representation lets the detector count junctions, spot loops, check crossings, and compare local neighborhoods.

Vertex

A point where a segment ends or where two segments intersect. Vertices carry position and degree.

Edge

A cleaned line segment connecting two vertices. Edges carry length, angle, and crossing information.

Degree

The number of edges touching a vertex. A degree-three junction can be a real corner or a suspicious impossible fork.

Cycle

A closed path in the graph. Cycles can represent faces, tunnels, beams, or a loop that later depth rules inspect.

Worked example

A clean triangle creates three vertices and three edges. A cube wireframe creates more vertices, repeated angle families, and multiple rectangular cycles. An impossible trident creates junctions whose endpoint story and prong story disagree. The graph does not know that something is impossible yet, but it gives later rules the facts they need.

Graph signal What it can suggest Why it is not enough alone
Closed cycle A face, loop, tunnel, or path that can carry depth relationships. Many ordinary possible objects contain cycles.
High-degree vertex A complex junction, overdraw, or possible impossible fork. Sketches and uploads often create accidental extra junctions.
Clean crossing Potential over-under relationship. Crossing lines in a 2D drawing are not automatically contradictory.

Mini experiment

Load the cube preset, then clear one connector or leave a tiny gap at one corner. The shape may still look like a cube to your eye, but the graph may no longer contain the same closed cycles. That is a useful lesson: humans complete missing structure automatically; a detector should be more explicit.

Clean graph

Use the cube preset and count how many corners and connectors are obvious before analysis.

Broken graph

Erase one connector or leave a tiny endpoint gap. The drawing may still look complete to you.

Compare

Rerun the detector and watch whether confidence falls or the verdict becomes more cautious.

Sources And Next Step