Glossary

Glossary

Terms used across 4H-Unfolder and this wiki. Papercraft and geometry vocabulary in one place.

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Unfold / unfolding

Flattening a 3D mesh into connected 2D pieces that can be printed, cut, and folded back into the shape. Also called unwrapping or pepakura. See The Unfold Algorithm.

Mesh

The 3D model, made of faces (triangles), edges, and vertices. Loaded from .obj or .pdo. See Quick Start → import.

Face

One triangle of the mesh. Each face becomes a flat polygon in the 2D pattern.

Edge

A boundary between/around faces. In the pattern every edge is a fold, a cut, or a border — see Editing Edges & Flaps.

Dihedral angle

The angle between two faces that share an edge — how sharply the model bends there. It's the weight the unfolder uses to decide which seams to keep vs. cut.

Dual graph

A graph where each face is a node and each shared edge is a link (weighted by dihedral angle). The unfolder builds this to reason about connectivity.

MST (Minimum Spanning Tree) / Kruskal

The set of fold edges chosen to keep the model connected while cutting the fewest / flattest seams. Built with Kruskal's algorithm, adding lowest-angle edges first. See the algorithm.

BFS (Breadth-First Search)

The traversal that walks the fold tree and lays each face flat in 2D, preserving true edge lengths. See placing faces.

Piece

A group of faces that stay connected by fold edges — one shape you cut out as a unit. Computed via Union-Find over the fold edges.

Flap / glue tab

The extra paper along a cut or border edge that you fold under and glue to a neighbouring face. Shapes: trapezoid / rectangle / triangle. See flaps.

FlapMode

A per-edge override deciding whether a tab appears, on which side, or on both. 10 variants (inner-edge and border-edge sets). See per-edge flap modes.

Fold line vs cut line

On the printout, fold lines are dashed (crease, don't cut) and cut lines are solid (cut with a knife/scissors).

Mountain / valley fold

Fold direction. A mountain fold points the crease toward you (ridge); a valley fold away (trough). Border flap modes can annotate which.

Overlap

When a flattened piece folds onto itself in 2D — it can't be cut flat. Detected with a spatial grid + SAT and shown red. See fixing overlaps.

SAT (Separating Axis Theorem)

The geometry test that confirms whether two triangles truly overlap during overlap detection.

.4hu

The project bundle — a ZIP with the mesh, textures, and all your edits. Cross-platform. See Project Files.

UV / UV mapping

Coordinates that map a 2D texture image onto the 3D faces, rendered in both the 3D viewport and the 2D pattern.