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

Shift lens — where it appears

A lens displaced across the picture plane, cropping the image rectangle without tilting it. Verticals stay parallel because a shift is a translation of the frame rather than a rotation, and it moves the principal point away from the centre of the print.

Named by 3 essays across 3 fields — each of them below, with the objects they name alongside it.

level — the top is cut off0.00° of spreadtilted 13°4.55° of spreadshifted 95 px0.00° of spreada shift moves every point by exactly the shift95.0 px, and no direction at all

The principal point is not the centre

Every textbook that computes a focal length from two vanishing points supplies the middle of the frame as the principal point. On a shifted or cropped picture that is wrong, and it costs one and a half per cent of the answer at a fifth of a frame's shift.

lens · Shift 0.25°0.5°1°2°5°10°20°45°90°0.1110angle of the span from the horizon's direction (log scale)worst texel along a 120 px span (px, log scale)80 px below the horizon160 px below the horizonparallel to the horizon: 0 pxfloor · eye 1.5 m · 60° field

Along a line of constant depth the page is affine

Stepping a texture by a constant amount per pixel is wrong across a receding floor and exactly right along any line of it that stays at one depth — and on every plane those lines run parallel to its own vanishing line. Turn a 120 px span 1° away from that direction and it is 0.79 px out; roll the camera a hundredth of a degree and a floor drawn to 30 m is out by 0.69 px on its worst scanline.

pipeline · Perspcorrect horizonthe middle of what is leftthe principal pointcorrect from 22 cm, at 160 mm widecrop 20% · centres 81 px apart

The centre of the picture is not the centre of the paper

A crop translates the image rectangle, so the picture's optical centre leaves the middle of the sheet and the focal length does not move — 81.3 pixels apart at a fifth of the picture, with the horizon at 62.5 per cent of the print. A reader who takes the paper's middle for the picture's stands 2.36 cm out of position, which is 4.9 degrees of the wrong direction.

construction · Crop

Named alongside it

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

Principal pointFocal lengthHorizonPicture planeVanishing pointCrop factorDepth divisionForeshorteningHomogeneous coordinatesPrincipal rayProjective invariantStation point

All concepts