Axis of a homology — where it appears
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
A shadow across an edge
A straight rod's shadow crossing the crease between floor and wall is two straight pieces, each dead straight to 1e-15 m, meeting at 35.08°. The corner is a fact about the room and not about the rod. Fit the floor's map from four marks and apply it across the whole shadow and the part on the wall comes back up to 78.9 cm from the object — the wrong map, applied confidently.
Two lamps and one map
A flat object lit by two lamps casts two shadows, and one is the other scaled about a point — ratio 1.2509 here, carrying every point of the first outline onto the second to 1e-15 m. No rotation and no shear is available to it, because a projection between two parallel planes has its axis at infinity. And the ratio is exactly 1 when the two lamps are at the same height, which makes a pair of shadows a measurement of the lamps.
Named alongside it
The objects these essays reach for when they reach for this one.
Planar homologyProjective mapShadow projectionCentral collineationCharacteristic ratioCollinearityCompositionDemonstrationHomographyHomothetyPiecewise mappoint at infinity