Visual Plane
every picture states the point it is correct from
Concept

Imaged circle — where it appears

The conic a circle in the world becomes when it is photographed, together with the two-fold pose ambiguity that comes with it. Which of the three kinds of conic it is depends on a single incidence with the plane through the eye, and neither the size nor the distance of the circle enters.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

horizonthe horizon does not cut the circle — the pair is complexrectified from the two points aloneangles: 2.2e-13°ratios: 5.6e-15length: —circle of radius 1.05 ma dash is a quantity two points cannot buy

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.

foundations · circularpoints correct from 8 cm, at 160 mm widestretch 1.358 · centres 4.28 px

The ball at the edge of the frame

A ball photographed near the edge of a wide picture is not drawn as a circle. It is an ellipse, longer along the radius from the centre of the picture than across it, and the centre of that ellipse is not the image of the centre of the ball. Both are properties of the flat sheet the picture is on, and an exact pinhole produces both.

foundations · quadric

Named alongside it

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

ConicDemonstrationAbsolute conicCamera matrixcentre of projectionCircular pointsConic fitContour generatordegrees of freedomDual conicDual quadricEdge stretch

All concepts