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

The thread: The round trip

Draw the picture from a known camera, forget the camera, recover it from the drawn edges alone, and compare. Agreement to fifteen digits is a statement about the geometry; anything less is a statement about the drawing.
horizoncorner angles90.000° — forced by the methoddepicted side ratio0.7195lens this drawing implies60° acrossdrawn exactly as the method prescribesthe free step is where the far edges go Drawn confidently

The cube that is a box

The two-point cube every book teaches has a step it supplies no construction for. Place the two far edges symmetrically and the drawing depicts a cube for free; place them eight points apart — a difference invisible on the page — and it depicts a box 1.4 times shallower than it is wide.

 recovered principal pointused to drawrecoveredgapfocal length853.90853.904e-15principal x345.0345.02e-12angle44.0°44.0°—correct from 20 cm, at 160 mm wide44° across What survives

Recovering the camera from the picture it drew

Draw a box from a known camera, forget the camera, and get it back from the twelve drawn edges alone. Agreement to one part in 10¹⁵ is a statement about the geometry, because the only thing that crossed between the two halves was a list of line segments.

 grey: the reflectiontwo routes, agreeing to 0e+0 px after one flip Light and mirrors

A mirror is a second camera

Reflect the scene and photograph it, or reflect the camera and photograph the scene. The two routes disagree by 906 px and agree to 6 × 10⁻¹⁴ once one axis of the image is reversed — which is the whole of why a mirror is said to swap left and right, written down.

All themes