Visual Plane
every picture states the point it is correct from
Concept

Tangent developable — where it appears

The surface swept by the tangent lines of a space curve, which is where a lamp has to stand for that curve's shadow to have a corner. It is two-dimensional, so it is a wall in the room rather than a rare coincidence, and a planar curve has none worth the name because its tangents all lie in its own plane.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

the cornercorrect from 19 cm, at 160 mm wide46° across

A wire with a corner in its shadow

A bent wire has no corner anywhere on it, and its shadow has one. The lamps that do it are not a coincidence — they are a surface in the room, two-dimensional, made of the wire's own tangent lines, and a lamp being carried across the room passes through it.

light · Curveshadow stops dead — a real cornerturns at speed — the creasefour receivers, one wire, one lampplane 1+0 · dish 1+0 · ridge 1+0 · step 1+5

The corners a floor cannot add

A wire with no corner anywhere on it casts a shadow with one, wherever its tangent runs along the ray. That condition contains the lamp and the wire and no surface at all — so the same helix over a plane, a dish and a ridge draws shadows that differ by metres and each has exactly one corner. A floor with a crease draws five more, and the two kinds are separable by a hundredfold: a real corner is where the shadow stops dead, and a crease is where it turns at full speed.

light · Curveshadow

Named alongside it

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

CuspShadow projectionConicContour generatorDegeneracyDevelopable surfaceForeshorteningnecessary, not sufficientPlan viewPoint lightProjective mapRay tracing

All concepts