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

Focal recovery — where it appears

Reading a camera's focal length out of the picture it made, from vanishing points of directions known to be orthogonal.

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

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

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.

wrong · cubebyeye 15° of yaw, 6° of pitch, 1.50 throw ratio81.3% of the panel reaches the corrected rectangleouter: the thrown quadrilateral · inner: what correction can keep18.7% of the panel discarded

A projector is a camera run backwards

Turn a projector fifteen degrees from square and it throws a trapezium; keystone correction cannot add light outside it, so it shrinks the picture until it fits and discards a sixth of the panel. And the instrument itself comes back out of the picture it threw — 2880 panel pixels recovered against 2880, by the function the wrong field wrote for hand-drawn cubes.

screen · keystone

Named alongside it

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

Depicted rectangleVanishing pointBack projectionCamera calibrationcentre of projectionDemonstrationFocal lengthFree parameterGround plane rectificationHomographyHorizonMeasuring point

All concepts