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

Series — page 5

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.
points in front of both camerasR₁, t0 of 44180° from the truthR₁, t reversed0 of 44180° from the truthR₂, t44 of 44chosenR₂, t reversed0 of 44180° from the truththe chosen pose is the true one to 0.0e+0°cheirality, not algebra, picks it

Cheirality

  1. 2 Four cameras fit, and one of them can see
  2. 3 Seeing the scene fences in the plane at infinity
2 essays · twoviews horizonthe horizon does not cut the circle — the pair is complexrectified from the two points aloneangles: 2.2e-13°ratios: 5.6e-15length: —circle of radius 1.05 ma dash is a quantity two points cannot buy

Circularpoints

  1. 5 The two points a picture hides
  2. 6 Two lines at infinity
2 essays · foundations clipped at the near planedivided without clippingdirection cosine -1.0000 — the far end is drawn 2142 px away20 grid segments, 2.4 m of them behind the eyea reversed line is not a large error, it is a different picture

Clipping

  1. 1 What happens behind the eye
  2. 2 The near plane can be any plane
2 essays · pipeline both explain both photographs exactly11.4 m apart, median

Critical

  1. 1 The surface two pictures cannot separate
  2. 2 An ambiguity is not an uncertainty
2 essays · twoviews horizonABCDon the groundin the picturelength AB1.00011.3930ratio AB:CD0.56670.6837cross-ratio1.31681.3168correct from 26 cm, at 160 mm wide34° across

Crossratio

  1. 1 What a projection destroys
  2. 2 The bias out of reach
2 essays · foundations leftfrontrightbackupdownacross the left/front seam: 1.80°, with each side straight to 7e-16corner area ×5.196anisotropy √3 = 1.7321 there

Cubemap

  1. 3 Six flat pictures of everything
  2. 4 The kink at a seam
2 essays · curved eyethe best fit — no ray goes through itno single viewpoint — the rays miss by 2.46 mmover 20 cm of a 2.00 m ball

Curvedmirror

  1. 4 A curved mirror has no eye
  2. 5 Closer than they appear, by a factor with a number in it
2 essays · mirrors 111 mm outcorrect from 21 cm, at 160 mm wide1e-12 mm with the floor · 111 mm without

Curvedrectify

  1. 4 Undoing a picture made on a curve
  2. 5 How well the floor has to be known
2 essays · curved the cornercorrect from 19 cm, at 160 mm wide46° across

Curveshadow

  1. 3 A wire with a corner in its shadow
  2. 4 The corners a floor cannot add
2 essays · light fitted conic: a circle to 1e-9stereographicdashed: the fit, not the samples

Curvilinear

  1. 4 The arcs a curvilinear drawing uses
  2. 5 The arcs the five-point construction actually draws
2 essays · curved the floor, in placeunrolled — 2.611 m of surfacea ridged floor, k = 0.062.6 m of plan is 2.611 m of floor

Developable

  1. 3 The floors that unroll
  2. 4 A picture that can be printed
2 essays · curved 0.5120.1110100how finely each point is read off the picture (px, log scale)worst epipolar error against the exact geometry (px, log scale)raw pixelscentred and scaled1.1× apart at 0.25 px, 29.9× at 4 pxspread 102 against 2.5e+5

Eightpoint

  1. 2 Eight points and the basis they are read in
  2. 3 Seven marks, three answers
2 essays · twoviews 012020406080angle off the axis (degrees)area printed per solid angle, against its value on axis (log₁₀)equal-areaequidistantcylinderstereographicplaneswept at 45° to the axes, out to 80°equal-area 1.000 · flat plane 191×

Equalarea

  1. 3 The third column is area
  2. 4 Counting cloud by counting pixels
2 essays · curved the distance pointone mark on the horizonleaves another exact drawingAlberti's sectionone mark per braccio, each from the panelleaves errors each its ownthe measuring pointdividers walked along the measuring lineleaves errors that accumulatea photographnoneleaves a smooth curvethe constant ratioone ratio, applied throughoutleaves a smooth curveone hand step eachand four kinds of trace

Handerror

  1. 1 One hand step each
  2. 2 Stepped, or measured from the zero
2 essays · construction the diagonals against a ruler, at 3.2 mthe diagonals — exactthe ruler — 22.7 px outcorrect from 23 cm, at 160 mm wideharmonic set -1.000000 · 8e-14 px

Harmonic

  1. 2 The diagonals find the middle
  2. 3 The quadrilateral that finds the middle
2 essays · foundations horizonthe eye stands 8.78 m from the centrecorrect from 26 cm, at 160 mm wideellipse · nearest point +3.96 m

Imagedcircle

  1. 3 The conic a circle becomes
  2. 4 Three conics are one conic and a choice of horizon
2 essays · foundations true ellipse — axis ratio 0.5774four arcs — 5.72% short along the major axisthe four tangent points are exactworst departure 5.72% of the semi-major axis

Isocircle

  1. 4 The ellipse the drawing office draws
  2. 5 A circle off the coordinate planes
2 essays · parallel halfway along the drawn linethe actual midpointcorrect from 26 cm, at 160 mm wide7 px apart

Limit

  1. 3 The eye taken to infinity
  2. 4 Two distances to infinity
2 essays · parallel 00.2500.5000.7501050100150angle of the direction from the camera's own axis (degrees)where it lands in the picture, as a fraction of the picture's radiusequisolidequidistantorthographica ball 24 cm across, camera 24 radii offequal-area within 0.82% · equidistant 21.5%

Mirrorball

  1. 5 A mirror ball is an equal-area fisheye
  2. 6 A mirror ball does not know its size
2 essays · mirrors apart by 6.4e-11 pxcorrect from 17 cm, at 160 mm wideone eye again

Mixedcentre

  1. 3 A parallel floor under a perspective room
  2. 4 Two stations in one picture
2 essays · conventions

All essays