Textile Structure
how cloth is put together
Concept

Developable — where it appears

A surface a flat sheet can take without stretching anywhere, which is to say one with no Gaussian curvature — a cylinder, a cone, or a plane. A cloth takes one at no cost in shear at all, which this site asserts rather than assumes, and takes a curved one only by shearing.

Named by 2 essays across 2 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

Named alongside it

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

DartFishnetGaussian curvatureDrapeInextensibleLocking angleMarker efficiencyShear

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