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

Angular size — where it appears

How wide something looks from where the eye is, measured as an angle rather than as a length. It is what a picture of an object actually records — the ratio of size to distance and nothing else — so a photograph gives an angular size exactly and a size only once a distance is supplied.

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

Also named here as calibration — the same set of essays touches all of them, so they are one junction rather than several.

the eyecorrect from 9 cm, at 160 mm wideoutlines agree to 6e-12 px

One picture of a ball

The outline of a ball in a photograph fixes the cone of rays that graze it, so the cone's axis is the direction of the ball's centre and its half-angle is the arcsine of radius over distance — both exactly, and neither of them separately. A ball a hundred and thirty-seven times larger, a hundred and thirty-seven times further away, draws the identical conic. And the drawn ellipse's own centre is not the image of the ball's.

metrology · ballrecovery 020406012345the baseline between the two eyes (metres)angle between the cone axes (°)42.6°two cones, one ballcentre to 9e-7°

Two pictures of a ball

Two outlines give two tangent cones, and where their axes cross is the ball's centre — with the radius following from either half-angle. There is no correspondence problem, because a ball's outline in one picture and its outline in another are guaranteed to be the same ball; and there is a degeneracy, which is the two eyes and the ball in a line, and the solver refuses it rather than returning something plausible.

metrology · ballrecovery

Named alongside it

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

CalibrationDemonstrationQuadricReconstructionscale ambiguityTangent coneBaselinecentre of projectionConditioningConicDepth from disparityEpipolar geometry

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