Concept

Convex hull — where it appears

The smallest convex region containing a set of points. A shadow outline determines it and nothing finer, so no number of lamps recovers a concavity: every outline is the boundary of the convex body that would cast the same silhouette.

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

hull 3.1098 · object 2.9193 · floor 3.07498 outlinesthe notch survives all of them

The dish no outline reaches

An outline is a pair of numbers per direction and nothing more, so a shape built from outlines has two errors that behave differently. The part outside the convex hull falls as one over the square of the view count. The part inside a concavity is the same area at four views and at a hundred and twenty-eight, because no pair of supporting lines ever reaches into a bite.

metrology · Visualhull
the true planefirst number of the plane, from the true valuesecond44 points in front: 31.9 % of the slicethe third number held at its true value

Seeing the scene fences in the plane at infinity

A reconstruction made without the calibration does not know which of its planes is infinitely far away. Requiring every point to lie in front of both cameras rules out every candidate that would tear the courtyard, and what is left is a convex region — 32 per cent of a generous slice — that always holds the true plane and never shrinks to it.

twoviews · Cheirality
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

Named alongside it

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

Contour generatorreconstruction ambiguitySilhouetteVisual hullAttached-shadowCamera matrixCheiralityConvergence orderDegeneracyDemonstrationinstrument limitnecessary, not sufficient

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