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

Depth reversal — where it appears

The second reading of a picture, in which each point moves to the other point of its own ray, giving a mirrored solid that draws the identical picture. In a parallel drawing the two readings are exactly equally supported, and in a perspective one they are not, by an amount that grows as the eye comes in.

Named by 5 essays across 2 fields — each of them below, with the objects they name alongside it.

what was drawnthe solid it depicts — reading 1 of 2xyzlooked at 45.00° off the normalcube edge 1.0000 of the drawn unitresidual 5e-16

Any three lines you draw are a cube

Four earlier essays said that cavalier projection is not the projection of anything — because its axis scales sum to three where every orthographic projection sums to two. That is true of orthographic projection and false of projection. Three lines from a point, drawn by hand, are a picture of an actual cube seen from an actual direction, and the cube and the direction come out of the drawing in closed form.

parallel · Pohlke what was drawnthe solid it depicts — reading 1 of 2xyzlooked at 0.00° off the normalcube edge 1.0000 of the drawn unitresidual 1e-16

The drawing does not say which corner is nearer

The Necker cube is filed under optical illusion, as though the flipping were something the eye does. It is not: a parallel drawing of a cube is a drawing of exactly two cubes, mirror images of each other, and they project to the identical picture to the last bit. Perspective rules the second one out at a rate exactly inverse in the eye's distance, and never entirely.

parallel · Reversal each point joined to its place in the inside-out answer — nearer the camera is uptoward the cameratrue 2.4e-13 px · inside out 0.946 px3° field, 60° of arc

A narrow view keeps a second answer, inside out

Six pictures of a courtyard through a 3° field, every mark exact. Started from the scene turned inside out, the adjustment settles there — near points far, far points near — and misfits the marks by under a pixel. The misfit grows in proportion to the field and to the sweep of the cameras, and vanishes only where perspective does.

manyviews · Bundle 34384246505458626660° arc, 3° field60° arc, 25° field20° arc, 3° field20° arc, 10° fieldhalfway: the flattened scenelight: back to the scene · dark: into the twin · column: per cent of the way to the twinexact marks · one adjustment per cell68 starts

A start needs the sign of its depths, not their size

Started part of the way from a courtyard toward its inside-out twin, a bundle adjustment returns to the truth from every start less than 42 per cent of the way — a start with a sixth of the true relief, the right way round — and falls into the twin from every start past 56. Between, neighbouring starts settle in different answers. The band sits in the same place at a 3° field, where the twin misfits by under a pixel, and at 25°, where it misfits by seven and a half.

manyviews · Bundle 020406080100points: per cent of the way to the twin'scameras 0%cameras 10%cameras 20%cameras 30%cameras 40%cameras 50%cameras 60%cameras 70%cameras 80%cameras 90%cameras 100%solid: back to the scene · empty: into the twin · diagonal: the blend that moves both together60° arc, 3° field, exact marks121 adjustments

The cameras decide where a narrow view settles

Scatter a narrow-field bundle adjustment's starting depths and the answer it reaches stops following them: of eighty scattered starts whose depths had the right sign, twenty-six fell into the inside-out twin, and of a hundred with the wrong sign, forty-three came home. Split the start in two and the reason is plain. With the cameras where they are, the courtyard comes home from its own inside-out points; with the cameras on the twin's side, it falls in from the true ones.

manyviews · Bundle

Named alongside it

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

Orthographicbundle adjustmentfield of viewReprojection errorConvergenceDemonstrationDrawing systemLevenberg–MarquardtParallel projectionPohlkestructure from motionAxonometric

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