Topology — where it appears
Named by 3 essays across one field — each of them below, with the objects they name alongside it.
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.
Counting shadows is not counting lamps
Two lamps close together cast one connected dark patch and the drawn lines say two. One lamp behind two cards casts two patches and the lines say one, exactly. And the arrangement where the patch count is right — two lamps far apart — has no fully dark region at all, so the same floor answers one, two or zero depending on which darkness is being counted.
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.
Named alongside it
The objects these essays reach for when they reach for this one.
Shadow projectionConnectednessPoint lightArea lightAttached-shadowContour generatorCuspDegeneracyDevelopable surfaceIdentifiabilityLight recoveryOcclusion