Origami & Folding
what one sheet can do
Generator

The travel is a step, and the step is at the surface

A generator in the rigid folding library, called 7 times across 1 essay. Below: what it draws with nothing specified and with the settings the essays give it, what it checked while drawing, and everywhere it is used.

hinge-travel is one function. Everything below was drawn by it when the site was last published, at settings taken from the essays rather than invented for this page — so a figure here is the same figure a reader meets in an essay, and when the generator changes, this page changes with it.

With nothing specified

The travel is a step, and the step is at the surfaceHow far a fold in a panel of real depth closes, in each direction, against where its hinge axis sits between the panel's two faces. The two curves are mirror images and they do not overlap anywhere: whichever face the hinge is on, the fold has a direction.how far the fold closes, against where the hinge sitslower faceupper facemid-surface180°0°closing upwardclosing downwardtapering the panels buys most of it back: 166° of the 180°, less twice the taper

view: "sweep", t: 0.12

The travel is a step, and the step is at the surfaceHow far a fold in a panel of real depth closes, in each direction, against where its hinge axis sits between the panel's two faces. The two curves are mirror images and they do not overlap anywhere: whichever face the hinge is on, the fold has a direction.how far the fold closes, against where the hinge sitslower faceupper facemid-surface180°0°closing upwardclosing downwardtapering the panels buys most of it back: 166° of the 180°, less twice the taper

view: "sweep", t: 0.08

The travel is a step, and the step is at the surfaceHow far a fold in a panel of real depth closes, in each direction, against where its hinge axis sits between the panel's two faces. The two curves are mirror images and they do not overlap anywhere: whichever face the hinge is on, the fold has a direction.how far the fold closes, against where the hinge sitslower faceupper facemid-surface180°0°closing upwardclosing downwardtapering the panels buys most of it back: 171° of the 180°, less twice the taper

view: "section", t: 0.12, depths: [-0.5, 0, 0.5]

Where the hinge sits, and which way the fold will goTwo panels of real depth, seen end on. The pale panel is fixed; the coloured one has been turned about the hinge as far as it will go before the two share material. With the hinge on the mid-surface — where a crease pattern puts it — that is nowhere at all.two panels of real depth, hinged at three different placesthickness 12 per cent of the panel's reachhinge on the lower face180° one way, 0° the otherhinge on the mid-surface0° one way, 0° the otherhinge on the upper face0° one way, 180° the othera crease pattern draws the hinge on the mid-surface, which is the one place it cannot be

What it checked while it drew

Collected while it drew, not written by hand. The count is how many separate times that claim was put to the test.

Where it is called

Every figure listed here is drawn by the same rule, so a mistake in the rule would be in all of them at once, and so would a correction.

Thickness has a sign

Swap every mountain for a valley and back again. Kawasaki does not notice, Maekawa gets the same condition the other way round, the lemma still asks the two creases to differ, and the layers come out mirrored. Every theorem on this site is blind to which side of the paper it is looking at — and a hinge in a panel with depth is not. The fold closes one way and jams at nothing at all the other.

All the figures · The rigid folding field · The patterns a reader can fold