Origami Crease-Pattern Folding: Accordion Kinematics (2D)

Crease Pattern

Panels (creases + 1) 8

Max crease angle 165°

Fold progress 0%

Fold Pattern

Live Readout

Paper length

0.0 u

Footprint

0.0 × 0.0

Compaction

1.00×

Peak layers

How it works

A flat paper strip is modeled as N rigid panels of equal length hinged end to end. Each hinge (crease) applies a 2D rotation to everything downstream of it, exactly like real paper folding — the panels never stretch, only rotate. Panel i's two endpoints come from composing rotations:

θ_i = θ_(i-1) + sign_i · angle · progress
p_(i+1) = p_i + L·(cos θ_i, sin θ_i)

The crease-pattern buttons choose the sign sequence: Accordion alternates +/– (a real zig-zag map fold, self-nesting into a compact stack), Spiral keeps every sign the same (a fan/coil that curls outward instead of stacking), and Mixed draws a fixed pseudo-random sign per crease (an irregular crease pattern, reseed to get a new one).

Paper length — N·L, the sum of panel lengths. It never changes as you fold: this is the inextensibility constraint every real paper-folding operation obeys.
Footprint — the bounding box of the whole folded chain. It shrinks as folding progresses (accordion) or grows (spiral).
Compaction — paper length divided by the footprint's longer side; how many times smaller the folded package is than the flat strip.
Peak layers — panels are bucketed onto an L-sized grid by their midpoint; the busiest cell's count estimates how many paper thicknesses stack at the densest point, the way a real accordion fold builds up layers.

Panel 1 (fixed end) Last panel (free end) Crease lines