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

Series — page 4

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.
correct from 8 cm, at 160 mm widestretch 1.358 · centres 4.28 px

Quadric

  1. 3 The ball at the edge of the frame
  2. 4 Every quadric has one outline
  3. 5 A curved surface made of straight lines
3 essays · foundations vanishing point 1vanishing point 2where the camera wasassumed centre 50% alongfocal 1129.9 px · 0.283 : 1

Rectangle

  1. 3 The arc every eye stands on
  2. 4 The proportion is the assumption
  3. 5 The quadrilateral no rectangle casts
3 essays · construction the picturethe same plane, rectifieddoor — 0.5068 widths (true 0.5068)sill — 0.3026 widths (true 0.3026)diagonal — 1.1766 widths (true 1.1766)worst error 4e-16 relativethe probes were not used to build the map

Rectify

  1. 1 Flattening a façade out of the photograph
  2. 2 The plan hidden in the photograph
  3. 3 An angle on the ground
3 essays · metrology 0.0 ms8.3 ms16.7 ms25.0 ms33.3 mslean 1.052° drawn against 1.055° predicted · a still world leans 0.000°no single viewpoint — the rays miss by 33.3 ms of travelthe frame is a stack of projections indexed by row

Rolling

  1. 1 Every row is a different camera
  2. 2 A turning frame can be straightened; a travelling one cannot
  3. 3 A frame's shear knows travel only over depth
3 essays · sensor the outline, its shadow, and the outline recovered from itcorrect from 20 cm, at 160 mm widerecovered to 4e-16 m

Shadowinverse

  1. 3 A shadow can be un-cast
  2. 4 The floor is a choice of coordinates
  3. 5 The lamp and the floor cannot both be recovered
3 essays · light 5710142028400.31310distance along the floor from below the eye (m, log scale)pixels one shadow-map texel spans on screen (log scale)1 pxlamp beside the eyelamp 30 m overheadlamp 40 m ahead, facing backmeasured against the closed form: 4e-91024-texel map · eye 1.7 m · 50° field

Shadowmap

  1. 1 A shadow map's texels land by two distances and two cosines
  2. 2 One warped shadow map, and what it cannot reach
  3. 3 One homography makes a shadow map the eye's picture
3 essays · pipeline 0.0020.00334567number of viewsworst camera-centre error (fraction of the track's mean radius, log scale)7 flat7 flat7 flat7 flat7 flat60° sweep, filled in12° per view, wideningfilled in: 1.1e-3 → 2.0e-3widened: 3.2e-3 → 1.8e-3

Spread

  1. 1 Another picture of the same sweep
  2. 2 The spread a point gets
  3. 3 Split the track and the needles turn
3 essays · manyviews midpoint — 2.77 mm gapfrom the left eyefrom the right eyegap 2.77 mm at 7.22 mexact marks: 2.2e-16 m

Triangulation

  1. 1 Two rays that do not meet
  2. 2 The midpoint is a choice of ruler
  3. 3 A third ray is worth what its picture is worth
3 essays · depth two eyesno single viewpoint — the rays miss by 0.54 mtwo centres, 1.30 m apart

Twocentres

  1. 2 A picture with two eyes in it
  2. 3 The second eye is a shear
  3. 4 Counting the eyes needs the room
3 essays · conventions 2.7:13.1:14.5:15.8:17.2:1in plan; ellipses at 8σworst 7.2:1

Uncertainty

  1. 1 The answer is an ellipse
  2. 2 Which reference to measure from
  3. 3 The floor a better camera cannot reach
3 essays · metrology 5e-14°2.65°0.59°correct from 16 cm, at 160 mm wideaxle solid, minor axis dashed · 2.65° at the edge

Wheel

  1. 4 The minor axis is not the axle
  2. 5 A cylinder has two different ends
  3. 6 A tapered part meets at its apex
3 essays · wrong 00.2500.5000.7501-10123distance from the eye — log₁₀ metresfraction of the buffer's codes used uphalf the codes by 0.20 ma linear map, for comparisonnear 0.1 m, far 1000 mharmonic mean 0.20 m against arithmetic 500 m

Zbuffer

  1. 1 The precision a depth buffer has left
  2. 2 One plane is nearly free
  3. 3 One depth per sample is not enough
3 essays · pipeline the panelhorizon — the centric point's heightthe section — the eye, the panel, the ground470 px — the viewing distancethree routes agree to 6e-14 pxsection, distance point, and a pinhole camera

Alberti

  1. 1 Alberti draws a pavement, and chooses where the reader stands
  2. 2 The distance point is the viewing distance, drawn
2 essays · construction the photographthe ground, rectified5.205 m²four marks fix the plane; the shoelace does the rest1.8e-14

Area

  1. 1 An area, out of one photograph
  2. 2 Counting is a measurement
2 essays · metrology true length1.3928 mpoint viewthe edge is one pointtrue shape1.3232 m²one face, three ray directionseach step is a choice of direction, not a construction on the paper

Auxiliary

  1. 3 The view that makes a line a point
  2. 4 The true shape of a cut
2 essays · parallel 2 — every orthographic projectionisometric · axonometric 0.816 · 0.816 · 0.8162.0000dimetric · axonometric 0.943 · 0.943 · 0.4712.0000trimetric · axonometric 0.876 · 0.966 · 0.5482.0000cavalier · oblique 1.000 · 1.000 · 1.0003.0000cabinet · oblique 1.000 · 1.000 · 0.5002.2500elevation · orthographic 1.000 · 1.000 · 0.0002.0000military · planometric 1.000 · 1.000 · 1.0003.0000isometric's three equal scales are forced to √(2/3) = 0.816497not chosen — the identity leaves no other value

Axonometric

  1. 4 Which axis scales are possible
  2. 5 The dimetric the set square draws
2 essays · parallel the eyecorrect from 9 cm, at 160 mm wideoutlines agree to 6e-12 px

Ballrecovery

  1. 4 One picture of a ball
  2. 5 Two pictures of a ball
2 essays · metrology eyefaint: the row it imitates · solid: the row that is builtbuilt row21.0 pxthe deep row28.4 pxdisparity across the row, two eyes 63 mm apartfar column cut to 0.300the eyes read 74.1%, not 22.2%

Builtset

  1. 3 A set cut for one eye
  2. 4 An anamorph has one eye
2 essays · viewing -4-3-2-1000.50011.502how much more effort, log₁₀ of the controlhow much of the error is left, log₁₀ of the first samplepanorama-seam · −0.92panorama-vertical · floorsilhouette-hull · −2.00silhouette-notch · flooranamorph-sagitta · −2.30anamorph-sagitta-intervals · −2.00mirrorball-size · −1.007 laws, 12 samples each2 with a floor · 5 without

Buyable

  1. 1 An error with two terms
  2. 2 What a null result is worth in decades
2 essays · foundations 184 mm of causticvertex radius 1.60 m, aperture 1.24 m184 mm of envelope

Caustic

  1. 5 Where the focus went
  2. 6 The caustic is the mirror's own ruler
2 essays · mirrors

All essays