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

Site plan — where it appears

A drawing of the ground from directly above, which a photograph of that ground can be rectified into exactly. Producing one from a photograph is exact, because it is a homography between two planes, and it needs four points whose true positions are known.

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

the picturethe same plane, rectifiedacross — 0.6000 widths (true 0.6000)along — 0.7667 widths (true 0.7667)diagonal — 1.2023 widths (true 1.2023)worst error 1e-15 relativethe probes were not used to build the map

The plan hidden in the photograph

Rectifying the ground is the same operation as rectifying a wall, and it turns a photograph into a site plan. The horizon is not an input to it and comes out as a consequence — the plan's points at infinity land on it, at first order, which is the check that the plan is a plan and not a plausible warp.

metrology · Rectify a camera looking downthe carpet is true, the people are nota camera looking levelthe people are true, the carpet is notthe two views a miniature is assembled from90° apart, exactly

A carpet and the people on it

A Persian miniature draws the ground as though from above and the figures standing on it as though from in front. The two views want optical axes exactly ninety degrees apart, and the plan view does not shorten a standing figure — it replaces its height with its distance from the point under the eye.

conventions · Twogrounds

Named alongside it

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

Ground plane rectificationCamera tiltControl pointDemonstrationDrawing systemForeshorteningHomographyHorizonline at infinityOcclusionOrthographicPicture plane

All concepts