Collinearity — where it appears
Named by 5 essays across 3 fields — 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.
A straight stick in water is a kink and a curve
The bent stick is described as one kink at the surface. Traced point by point, the image two level eyes see leaves the surface 14.96° off a stick leaning 30° — the same whichever way it leans — and then keeps turning, by 1.11° when it leans away from the eye and 7.62° when it leans toward it. A photograph from the eye shows the kink and almost none of the curve, 1.63 px over 166 px, and when the stick leans straight toward or away from the eye it shows neither: the picture is one straight line.
The line every nosing is on
Nothing in a staircase points up the pitch. Every surface in it is level or vertical, and its picture has a vanishing point off the horizon all the same — belonging to the line the front edges of the treads lie on. That point is not free: it is collinear with the travel point and the vertical point, and the angle it makes says the rise-to-run the builder chose.
A straight stick tests the index only across the sight
Told that each stick is straight, three eyes fitting a water surface's height and its index still slide down the valley between them — when the stick leans away from them. A wrong index carries such a stick into another straight stick, off its line by 0.016 mm and 116 mm short. Turned to lean across the line of sight, the same wrong index bows it by 2.2 mm, and the straight-line fit's slide falls from 0.058 to nothing. A tape on the stick, read only to ±50 mm, stops the slide outright.
Figures on a street that slopes
Equal-height figures have their heads on one line, and the taught rule says the line is the horizon. On a street rising at 8.33 per cent the heads are still collinear to 2.8e-14 pixels and the line is 58.9 pixels above the horizon — the street plane's own vanishing line. The taught rule loses 1.46 m of a 1.62 m figure at the far figure, and runs out of figure altogether at 19.4 m.
Named alongside it
The objects these essays reach for when they reach for this one.
HorizonInclined planePlane of incidenceRefractive indexsingle-view metrologyTriangulationVanishing pointApparent-depthAstigmatismAxis of a homologyBiasCalibration