Silhouette — where it appears
Named by 8 essays across 4 fields — each of them below, with the objects they name alongside it.
The shadow of a ball is a conic
A cone cut by a plane is a conic section — which is the definition of the phrase, not an analogy — and the shadow of a ball is exactly that cut. So the shadow closes or runs to the horizon depending on where the lamp is, and the condition is not what anyone guesses: it is that the lamp is above the top of the ball. The ball's distance appears nowhere in it.
A pupil sees around an edge
Two backgrounds identical everywhere a pinhole can see, differing only in the strip an occluder hides from it, produce identical pinhole pictures and pupil pictures 42 per cent apart. So no function of the sharp image — no kernel, no depth-dependent kernel, nothing — produces the picture a real lens makes, and the reach behind the edge is R(Z₂/Z₁ − 1), which is 120 mm here.
A lamp lights less than half a ball
Everyone knows a sphere is half lit. It is half lit by a source at infinity and by nothing else: a lamp two radii away lights a quarter of it, and the boundary it draws is a circle offset toward the light rather than a great circle. The offset is R²/D, which means a photograph of a lit ball carries the distance to whatever lit it.
Three views do not fix the solid
A stepped block on a six-cell grid draws a front, a top and a side view. So does a solid with a third of its material, and so does one with more than the block has — 192 cells against 64, every filled square in all three views identical. The drawing office's triple bounds a part between two solids and does not determine it, and the gap runs to a factor of n.
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.
Two outlines are two curves
The whole method of multiview drawing is the transfer line — a feature at a position in the front view is at the same position along that axis in the top view. On a flat-faced solid the feature is a vertex and the rule is exact. On a ball the two views draw two different great circles, meeting in exactly two points, and the transfer line joins places that are √2 radii apart.
Two distances to infinity
A parallel projection is the limit of a perspective one, and the limit arrives twice. Which faces get painted settles within three object radii, because a face is either round the back or it is not; where each mark lands falls like one over the distance and is still out at thirty-four. Far enough away has two answers an order of magnitude apart.
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.
Demonstrationcentre of projectionContour generatorreconstruction ambiguityVisual hullAsymptoticsConicConvex hullnecessary, not sufficientOcclusionOrthographicParallel projection