Concept

Attached-shadow — where it appears

The part of an object turned away from a light, bounded by the curve where the surface's normal is perpendicular to the ray. It is a different curve from the cast shadow, which is where the object blocks light from something else, and the two meet tangentially at a rim.

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

lamp, 1.36 mcorrect from 20 cm, at 160 mm wide2 pieces · 1.6 m back

Where a shadow splits in two

A gantry's shadow is two pieces at a lamp height of 1.36 m, and the crossing to one piece happens at a tangency running the whole length of the beam rather than at a point — the same plane that meets a ball at an aspect of 1.00 to 1 meets the beam at 1736 to 1, and a grid finds the true crossing height to a fitted exponent of 1.00 as it is refined. A ring tipped 70° keeps its hole for a completely unrelated reason, closing only at 71.34°, which is the warning that a shadow's topology changes at a tangency names two different accidents rather than one.

light · Shadowtopology
lamp 11 lampwedge holds 10.50× the object

How many shadows determine the object

One lamp's shadow says only that a convex section lies inside a wedge 10.5 times its own area; four already cut that down to 1.17 times, and 128 close a convex section's boundary to 0.10 mm everywhere. The identical sweep on a section with a bite taken out of it stalls at 70.3 mm, 675 times worse, because an outline is the boundary of the smallest convex body with that shadow and no direction ever sees inside a concavity.

light · Silhouette
correct from 22 cm, at 160 mm wide181 cast crossings

A dent breaks the terminator

A ball's lit boundary is one closed curve, 313.2 cm around; press a dimple into its top and, at 45° of elevation, the walk that traces it finds 181 crossings where a point still faces the light but is occluded by the body's own rim — a second curve, 23.1 cm long, that a convex surface can never produce. The two curves meet where the dent's own deepest point goes dark, at 50.952°, with the ray's clearance reaching zero at a stationary point rather than merely a small one.

light · Terminator

Named alongside it

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

Contour generatorShadow projectionDegeneracyPoint lightTangencyConnectednessConvex hullDegenerate configurationnecessary, not sufficientPower lawSampling gridSilhouette

All concepts