Output — the FOLD contract

7. Output: the FOLD contract (since v0.0; dual-frame since v0.7-dev)

beloch fold FILE.bel emits a FOLD file [foldformat] with two frames built from the folded state’s faces: the flat crease pattern (frame 0, the top-level dictionary) and the folded form (file_frames[0]). A program with no @ folds still emits both; the folded form then coincides with the flat sheet.

The planar graph is the face set: vertices are deduplicated by paper coordinate (vertices shared across faces along a crease coincide), each face is one polygon, edges are the deduplicated polygon edges. Square-boundary edges are "B"; an internal edge is a crease.

Frame 0 — creasePattern:

• file_spec, file_creator: "beloch 0.3.0-dev", frame_classes: ["creasePattern"]
• vertices_coords — [x, y] per vertex, in paper coordinates. Exact values are rendered to JSON decimal at serialization (non-terminating reals rounded in the output only; internal values stay exact).
• edges_vertices — [v0, v1] index pairs.
• edges_assignment ([foldformat] §“Edge information”) — "B" for paper-boundary edges, derived "M"/"V" for folded creases (§4.6), and "U" for an unfolded precrease (a crease line with no fold yet). One physical fold through several layers can yield different M/V per layer (the accordion), since each crease edge carries its own derived assignment.
• faces_vertices — each face’s vertex indices, counter-clockwise. A program with no creases yields the single square face [[0, 1, 2, 3]].
• beloch:edges — custom property ([foldformat] §“Custom Properties”) carrying, per crease edge, its originating operation ("axiom1", "axiom2", "axiom3", "axiom5"), the source point/crease names, the source span, and the bound "name" (e.g. "d1" for --d1: …, else null). Additive: stock FOLD consumers ignore it; tools/fold2svg.mjs uses it to colour/label creases.

file_frames[0] — foldedForm (frame_parent: 0, frame_inherit: true, so it inherits the topology and overrides only the coordinates):

• vertices_coords — the same vertices in table (folded) coordinates: each face’s paper polygon through its isometry. Flat folds stay in the plane, so these are 2D; stacking is conveyed by faceOrders, not a z-offset.
• edges_foldAngle — +180 for valley, −180 for mountain, 0 otherwise; the sign matches edges_assignment.
• faceOrders — [f, g, s] layer-ordering triples for face pairs whose table footprints overlap; s = +1 if f is above g (toward g’s normal), −1 below ([foldformat] §“Layer information”). Emitted only for overlapping pairs (empty when nothing overlaps, e.g. a flat program).

The renderer/animation client is a separate consumer; tools/fold2svg.mjs draws frame 0 by default and the folded form with --folded.