How solid reconstruction and geometry analysis work

The impossible shapes detector checks editable solids, fitted image constructions and line drawings through separate analysis paths. The drawing canvas and 3D viewer share physical primitive geometry: cube, rectangular box, cylinder, sphere, cone and pyramid.

Solids created in the canvas

Each piece stores physical dimensions, an orthonormal orientation and a position. Adjacent faces share corner or ring vertices; spheres share their poles. The canvas projects these vertices through a fixed isometric camera. Reconstruct 3D uses those same vertices and faces, so an ordinary cube retains its equal edges and six faces rather than becoming independent samples.

Rotation applies rigid X, Y and Z transformations about the model centre. It preserves distances, right angles and handedness independently of the camera. Source view restores the original projection. Empty gaps in the open arch and between separate primitives are absent from the mesh.

Connections and contradictions

Named ports connect pieces in the drawing. The 3D solver turns each intended joint into an equation for displacement along the viewing ray. Compatible equations bind shared vertices. A closed route that requires two different depths at one joint fails closure, as in the three-beam triangle and cube-frame construction.

An ascending staircase supplies positive height relationships between successive treads. A directed cycle would require a positive total rise while returning to its original height. The impossible staircase has that contradiction; an open flight of stairs does not.

An impossible construction offers two realizable arrangements. The partial version omits pieces at conflicting joins. The possible version retains individual closed pieces and disconnects incompatible joints. These versions preserve each retained piece's dimensions. The contradiction concerns the supplied intended assembly, not the existence of its individual pieces.

Fitting an uploaded image

Image fitting reads the actual canvas pixels. It separates coloured components, compares their silhouettes with projected solid primitives, and estimates position and size. A complete known construction is accepted only when its silhouette, empty holes and visible piece partition agree. Colours are observations rather than preset identifiers. Moving, resizing or recolouring an image changes the fit.

For a complete recognized construction, intended connection rules are checked after image matching. That recognition differs from discovering a new impossibility in an arbitrary photograph. A single image cannot uniquely determine hidden geometry or the real camera. A nine-cube triangle is tested under its intended repeated-step relationships; unrelated cubes are not assigned those relationships merely because they are cubes.

Separate fitted primitives remain independent objects. An extra enclosed hole rejects a solid candidate that would fill it. Unsupported images fall back to visible surface reconstruction or an ambiguous result. No upload filename or URL forces the verdict.

Line drawings and unresolved surfaces

Line and pen tools create connected editable paths. Each click places a shared joint; dragging a segment's midpoint bends it into a quadratic curve. For ordinary strokes, the legacy analyzer checks endpoints, intersections, repeated directions and coarse contradiction signals. Its heuristic confidence is not a probability or a 3D proof. Read about edge extraction, confidence scoring and false positives when interpreting those results.

Unrecognized ambiguous or impossible pictures offer partial and possible surface interpretations. They trace visible boundaries and holes, infer a three-axis frame from repeated directions and bind compatible surface corners. Depth scale, hidden backs and camera axes remain assumptions. Clear contours and distinct piece colours work better than photographs, textures, shadows or overlapping parts with identical materials; the upload guide explains how to prepare a cleaner input.

Privacy, exports and verification

Drawing, image segmentation, fitting and joint solving run in your browser. Images are not posted to a server. Save assembly retains editable dimensions and connections; OBJ exports geometry; PNG and PDF save result cards without editor handles. Known example URLs are short public links; custom assemblies use compressed data in a private URL fragment.

Tests compare all six basic toolbar solids with their canvas pixels, check closed topology and rigid rotations, and rasterize all twenty constructions before image recognition. They also preserve hollow openings and check staircase cycles. These are implementation checks, not external certification. Start with a possible cube, then build a drawing and inspect the reasons as you change its joints.

Maintained by ShapeKeeper, the anonymous ImpossibleShape site administrator. Send corrections to [email protected].