Convex hull — where it appears
Named by 5 essays across 3 fields — each of them below, with the objects they name alongside it.
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.
An outline reaches a waist and not a dish
In a cross-section nothing a silhouette does can enter a concavity. On a solid that stops being true, because a solid has lines a section does not contain. A spool's waist comes back in full from a ring of outlines, and a dish in the same object's lid never does. What decides it is whether a straight line can leave, and the answer is water.
A groove is reached only along its own plane
A groove round a drum is the kind of hollow outlines can clear, and a level ring clears it completely. Raise the camera three degrees and more than half of it stays filled at any number of views. On this object the height of the camera decides the result, and the count of views buys almost nothing.
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.
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.
Named alongside it
The objects these essays reach for when they reach for this one.
SilhouetteVisual hullConvergence orderinstrument limitOrthographicReconstructionContour generatorDemonstrationreconstruction ambiguityAttached-shadowCamera matrixCheirality