Textile Structure
how cloth is put together
Concept

Fishnet — where it appears

A construction that lays inextensible threads over a curved surface by stepping out from two chosen lines at a fixed pitch, cell by cell. It is the construction every drape figure on this site is built with, and it is checked segment by segment for a thread that has changed length.

Named by 3 essays across 3 fields — each of them below, with the objects they name alongside it.

A cloth laid over a sphere. Every thread segment is exactly one pitch and none has stretched. What has changed is the angle at each crossing, and the amount is decided by the surface — a developable one costs nothing and a curved one costs more the further the cloth goes.

Why clothes need darts

A flat cloth goes round a cylinder for nothing and cannot go round a sphere at all without shearing. The amount of shear is decided by the curvature, and when it exceeds what the threads allow, something has to be cut out.

mechanics · Drape How much of the curvature a cloth can take without being cut. The dart angle a spherical cap still demands after the fabric's own shear has absorbed what it can, against how closely the cloth is set. The total the cap demands is fixed by Gauss–Bonnet and is the same for all of them; what changes is how much of it the trellis can supply before its threads jam. An open cloth drapes a hemisphere with no dart at all; a closely set one has to be cut from the start.

A hemisphere costs one full turn

The total angle a pattern must remove to cover a hemisphere is exactly 360 degrees, and it is the same for a hat and for a stadium dome. What changes with the fabric is how much of that the cloth can supply by shearing instead of by being cut — and that is a property of the sett, computed from the angle at which its threads jam.

applied · Cutting Mock leno, 3 threads to a bundle. Threads that interlace identically have no weft passing between them, so nothing holds them apart and they lie touching. The reed still sets the average spacing, so the space they leave collects at the bundle's edge — a hole 0.60 by 0.60 mm, made without one thread crossing another. Drawn to scale on a fixed 9 mm square of cloth at 20 threads per centimetre and a 0.3 mm yarn.

A hole with nothing crossing

A real leno holds its holes open by crossing one thread over another, which is a topological arrangement and cannot come undone. A mock leno makes the same holes by grouping threads that nothing separates, and everything about it is friction.

weaves · Texture weaves

Named alongside it

The objects these essays reach for when they reach for this one.

DartDevelopableGaussian curvatureCoverCover factorDoupDrapeFloat lengthFrictionGauzeInextensibleLeno

All concepts