Concept

Connectedness — where it appears

Whether a region is in one piece or several, counted as connected components. It is not preserved by projection or by union: two overlapping shadows are one region, and one lamp behind two objects makes two, so a count of dark patches is not a count of anything about the light.

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

1 holetilt 0°closes at 71.3°

A hole is not preserved

The shadow of a connected object is connected — always, at every lamp position, and for a reason with no geometry in it. A hole survives in neither direction: a ring's shadow closes up at a computable tilt, and an object with no hole in it casts a shadow that has one.

light · Shadowtopology
lamp 1lamp 2two lamps, close together, in plan1 dark region

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.

light · Shadow
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

Named alongside it

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

Point lightShadow projectionContour generatorDegeneracyOcclusionSampling gridTopologyUmbraArea lightAttached-shadowForeshorteningIdentifiability

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