Circularpoints — the series
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The two points a picture hides
The stratification rung says a photograph of a plane is projective, becomes affine when the vanishing line is known, and becomes metric with one more fact. The one more fact has a size and a shape: it is two points, complex conjugates on the vanishing line, and a rectification built from those two and nothing else returns every world angle to a tenth of a picodegree and every ratio of lengths to five parts in a quadrillion — and refuses to name a length.
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Two lines at infinity
A picture of a plane has two of them and they are not the same line. One is the horizon, where the plane's own infinity went; the other is where the picture's coordinates run out. The words ellipse and hyperbola are about the second, and every scrap of metric information is on the first — so a circle whose photograph is a hyperbola calibrates exactly as well as one whose photograph is an oval, to 7e-14 of a degree.