Origami & Folding
what one sheet can do
Generator

From a packing to a crease pattern — the ridges and hinges generator

A generator in the designing a base library, called 5 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.

ridges-and-hinges 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

From a packing to a crease patternThe discs say where the flaps are; the creases say where to fold. A hinge crease is the common tangent where two discs touch, perpendicular to the line joining their centres and passing through the point of contact. A ridge crease bisects the corner of the region left between them. Both are computed from the packing here, and the contact geometry is asserted rather than drawn by eye.what the packing gives5 discs, 4 contactsno two overlapping, checkedhinge creasesone per contact, perpendicularto the line of centresridge creasesalong the axial lines, dividingthe paper between the flapsthe packing is the hard part;this part is a constructioncorner discs of radius 0.28, the middle one 0.427 — every contact measured

r: 0.28, show: "both"

From a packing to a crease patternThe discs say where the flaps are; the creases say where to fold. A hinge crease is the common tangent where two discs touch, perpendicular to the line joining their centres and passing through the point of contact. A ridge crease bisects the corner of the region left between them. Both are computed from the packing here, and the contact geometry is asserted rather than drawn by eye.what the packing gives5 discs, 4 contactsno two overlapping, checkedhinge creasesone per contact, perpendicularto the line of centresridge creasesalong the axial lines, dividingthe paper between the flapsthe packing is the hard part;this part is a constructioncorner discs of radius 0.28, the middle one 0.427 — every contact measured

r: 0.24, show: "both"

From a packing to a crease patternThe discs say where the flaps are; the creases say where to fold. A hinge crease is the common tangent where two discs touch, perpendicular to the line joining their centres and passing through the point of contact. A ridge crease bisects the corner of the region left between them. Both are computed from the packing here, and the contact geometry is asserted rather than drawn by eye.what the packing gives5 discs, 4 contactsno two overlapping, checkedhinge creasesone per contact, perpendicularto the line of centresridge creasesalong the axial lines, dividingthe paper between the flapsthe packing is the hard part;this part is a constructioncorner discs of radius 0.24, the middle one 0.467 — every contact measured

r: 0.28, show: "ridges"

From a packing to a crease patternThe discs say where the flaps are; the creases say where to fold. A hinge crease is the common tangent where two discs touch, perpendicular to the line joining their centres and passing through the point of contact. A ridge crease bisects the corner of the region left between them. Both are computed from the packing here, and the contact geometry is asserted rather than drawn by eye.what the packing gives5 discs, 4 contactsno two overlapping, checkedhinge creasesone per contact, perpendicularto the line of centresridge creasesalong the axial lines, dividingthe paper between the flapsthe packing is the hard part;this part is a constructioncorner discs of radius 0.28, the middle one 0.427 — every contact measured

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.

From a packing to a crease pattern

The circles say where the flaps are. They do not say where to fold, and the step in between is a construction rather than a search — two families of crease, both determined by the packing, neither of them visible in the picture of the discs.

All the figures · The designing a base field · The patterns a reader can fold