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

Series — page 2

A field says what an essay is about. A series follows one idea essay by essay — from the question that introduces it to the one that assumes all the others.
the seatcentre of curvatureR = 1000 mm · seat at 650 mm51.4 px off a homography

Curvedscreen

  1. 2 The screen is a picture surface too
  2. 3 The screen that names the seat
  3. 4 The seats a screen will accept
  4. 5 One picture and three people
4 essays · screen 0.30.50.7125×10⁻⁴0.0010.0020.0050.010.02how finely each point is read (px, log scale)worst camera-centre error, as a fraction of the track's mean radius (log)chained pairsadjusted togetheradjustment is 4.0–9.2× better6 views · identical observations

Drift

  1. 2 A chain and an adjustment
  2. 3 A scale chain leans rather than wanders
  3. 4 Closing a loop mends its ends
  4. 5 A loop's far side is a length
4 essays · manyviews horizon25withheldfive marks fitted, one withheldcorrect from 26 cm, at 160 mm widethe withheld mark is 2e-13 px off the fitted conic

Fiveconic

  1. 3 Five marks and the sixth
  2. 4 Two circles, one picture
  3. 5 Five tangents name the same conic
  4. 6 Pascal's line, and the theorem underneath Pappus
4 essays · foundations × 4.6e+6seven flatand the rest stiffsingular value ÷ the largest, log scale, smallest firstσ₈/σ₇ = 4.6e+6168 parameters · 528 residuals

Gauge

  1. 2 Seven numbers no picture can name
  2. 3 An uncertainty is quoted from something
  3. 4 The eighth held number bends the scene
  4. 5 A survey is trusted at its own accuracy, unless its error has a shape
4 essays · manyviews horizon — the eye's own heightbase — 0 mhorizon crossing — 1.62 mtop — 3.40 m recoveredthe vertical vanishing point is 8586 px above this framerecovered 3.400 m · true 3.400 m1.8 cm per pixel of click error

Height

  1. 1 A height, out of one photograph
  2. 2 How wrong a measurement from one picture can be
  3. 3 Carrying a height across the room
  4. 4 Figures on a street that slopes
4 essays · metrology the centre of curvature, 4.0 mthe sitting distance, 2.6 mno single viewpoint — the rays miss by nothing — this is a plan of a room319′ out where people sit

Matched

  1. 1 Drawn for the cylinder, shown on the cylinder
  2. 2 Three conditions, and three prices
  3. 3 The surface a screen wants
  4. 4 Matching buys one seat
4 essays · curved grey: the reflectiontwo routes, agreeing to 0e+0 px after one flip

Mirror

  1. 3 A mirror is a second camera
  2. 4 Measured down from the waterline
  3. 5 One surface, two images
  4. 5 A mirror that is not parallel to the wall
4 essays · light left pictureright pictureevery one of them fits every mark1.6e-6 px

Planar

  1. 1 A flat scene fixes no second eye
  2. 2 How flat is flat enough
  3. 3 Two marks off a known plane find the other eye
  4. 4 A parallax length is a height over a depth
4 essays · twoviews the far field — where the stitch was fitted2.2 m — 3.2 px out24 m — 0.3 px outthe sky registers to 1e-13 pxthe foreground does not — up to 3.2 px

Pupil

  1. 3 The eye is a place, not a point
  2. 4 The hole a scene actually sees
  3. 5 The entrance pupil walks with the angle
  4. 6 Focusing moves the pivot past its best place
4 essays · lens a room 2.8 m across, eye 1.6 m up1 mthe same plan, 137× bigger137 midenticalpicturesthe picture — both scenes, drawn twice, one on top of the otherlargest disagreement 1e-13 px over 8 verticesone length has to come from outside the picture

Scale

  1. 1 The one thing a single view cannot give
  2. 2 Two views give shape and no size
  3. 3 Five facts that close the same gap
  4. 4 Where each closure enters the stratification
4 essays · metrology no single viewpoint — the rays miss by 4.5 px, depth-dependentf recovered from it: 396.88 px

Slab

  1. 2 What survives a pane of glass
  2. 3 A pane gives a product before it gives two numbers
  3. 4 A wedge of glass turns the camera behind it
  4. 5 The wedge recovered with the camera
4 essays · refraction correct from 19 cm, at 160 mm wideratio 1.2509 · carries one onto the other to 1e-15 m

Twolamps

  1. 3 Two lamps and one map
  2. 4 A floor is read along curves
  3. 5 How many lamps a drawing has
  4. 6 The distance at which two lamps part
4 essays · light axis — the ground line, fixed pointwisecentreaxisthe ground linefixed pointwisecentre(0.150, 4.020)height + distanceratio-1.481481−distance / heightheight × aspect = 2.592, and neither aloneeye recovered to 4.8e-12 mmeye 1.62 m up, 2.40 m backthree numbers back to the eye: 2.2e-16 m

Anamorphrecovery

  1. 5 The marks name the place, not the height
  2. 6 The height a flat floor cannot give
  3. 7 A fold names the height
3 essays · viewing head0.668profile — the outline that names a faceeye0.669frontal — an eye in profile is a wedgeshoulders0.669frontal — the width that says two armslegs0.668profile — a stride is a side viewpond0.326plan — a rectangle of water is a rectangle1.000 — what its own aspect keepsshare of each part that reaches the picture, from the best single direction|d · n| for each part3.000 of 5, swept and in closed form

Aspective

  1. 1 Assembled from several views
  2. 2 The pond with its trees laid flat
  3. 3 No solid casts an aspective figure
3 essays · conventions horizondepicted height ÷ side0.3278corner 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

Cubebyeye

  1. 4 The cube that is a box
  2. 5 A square plan is not a cube
  3. 6 A turned cube punishes the eye, not the construction
3 essays · wrong three side intersections, collinear to 3e-13 pxcentrethree sides paired, three pointscollinear to 3e-13 px

Desargues

  1. 3 Two triangles and the line nobody drew
  2. 4 Desargues read the other way
  3. 5 The theorem that is obvious one dimension up
3 essays · foundations 0100200204060distance of the object, metresits drawn height, pxa pinholean oblique systemdrawn height of a fixed object against its distance20.0× against 1.000

Diminution

  1. 1 A picture with no size–distance signal
  2. 2 Size that means rank
  3. 3 Higher on the page, and where that stops being true
3 essays · conventions points, joinedlines, metevery incidence survives, worst 9.1e-1630 of 30

Duality

  1. 1 A point and a line are one object
  2. 3 Four lines have a cross-ratio
  3. 4 The horizon has a pole
3 essays · foundations 1234512345a point is chosen hereand must be on this linematch to its own epipolar line: 1.4e-13 px5 of 44 correspondences drawn

Epipolar

  1. 1 A point is a line over there
  2. 2 The two pencils keep one number
  3. 3 Rectification is a family, not an operation
3 essays · twoviews 3 m · 47 px6 m · 24 px12 m · 12 pxnear ÷ far = 4.000 against a depth ratio of 4.000exposure 33.3 ms · 6 m/s across the frameeach streak is straight; the set of them is not one kernel

Exposure

  1. 1 A frame is an interval
  2. 2 Turning and travelling blur different worlds
  3. 3 A camera on a bend is sharp on a circle
3 essays · sensor

All essays