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

Series — page 6

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 water surfacethe pinholethe rays miss by 9.9 mmno single viewpoint — the rays miss by 9.9 mmdry control: 0e+0 m

Nocentre

  1. 2 A picture through water has no viewpoint
  2. 3 A ball of water has no eye either
2 essays · refraction elevation1.0000a circleisometric0.57741 : 1.732cabinet1.0000a circlecavalier1.0000a circlethe xy plane's drawn ellipseratio of the ellipse's axes, sampled

Oblique

  1. 2 Oblique is a shear, and the shear is the whole system
  2. 3 What one oblique drawing shows
2 essays · parallel no picture at 300°the plane is unbounded at 180°plane — bend 0.0%cylinder — bend 6.0%stereographic — bend 3.5%equidistant — bend 4.5%equal-area — bend 5.1%equirect. — bend 5.7%300° across in every panelsame scene, same angle, six surfaces

Panorama

  1. 1 What a 360-degree photograph actually is
  2. 2 A scroll is not a panorama
2 essays · curved focus, R/2 = 0.800 m184 mm of causticvertex radius 1.60 m, aperture 1.24 m5e-9 mm against 184 mm

Paraboloid

  1. 5 The one shape that focuses
  2. 6 A fitted radius is wrong before it is uncertain
2 essays · mirrors orthographicaspect 1.0000cavalieraspect 1.4142a camera, 37° off axisaspect 1.2593correct from 7 cm, at 160 mm widecentres 4e-14 / 3e-13 / 2.17 px

Parallelquadric

  1. 4 The ball a drawing does not draw round
  2. 5 Two outlines are two curves
2 essays · parallel a flat plate · best view0a bent plate · best view0.1224a dished plate · best view0.2298a bent plate · along its generators0patches wrapping 29°dished / bent = 1.878

Platepatch

  1. 3 No view draws a curved plate true
  2. 4 The drawing and the development
2 essays · parallel the pointone point, one conicconstructed and computed agree to 2e-13

Poleandpolar

  1. 4 The polar with a straightedge
  2. 5 The triangle a camera cannot move
2 essays · foundations 00.50011.50205101520the dome's centre, off the entrance pupil (mm)worst departure from the pinhole it would be in air (degrees)centred: exactly zero6 mm → 0.635°a 100 mm dome in acrylic, n = 1.4910.106° per mm of centring error

Port

  1. 3 The port that is not there
  2. 4 The dome knows its offset in units of itself
2 essays · refraction 1correct from 19 cm, at 160 mm wide46° across

Projectivescale

  1. 4 Seven is not a power of two
  2. 5 What a straightedge reaches on a receding line
2 essays · construction recovered principal pointused to drawrecoveredgapfocal length853.90853.904e-15principal x345.0345.02e-12angle44.0°44.0°—correct from 20 cm, at 160 mm wide44° across

Recovery

  1. 2 Recovering the camera from the picture it drew
  2. 3 A floor with a referent
2 essays · foundations horizoncorrect from 21 cm, at 160 mm wide8 bays · worst departure 8e-13 px

Repeatbay

  1. 3 The bay repeated by a straightedge
  2. 4 The bays that are not equal
2 essays · construction isometric0.57741 : 1.732dimetric0.88191 : 1.134cavalier1.0000a circlemilitary0.57741 : 1.732the xy plane's drawn ellipseratio of the ellipse's axes, sampled

Ruler

  1. 4 A ruler on an isometric drawing
  2. 5 The drawing that gives the solid back
2 essays · parallel 051050100150field of view the picture was rendered at — degreeshow many times the depicted depth is stretchedthe screen subtends 49.3°100° → depth ×2.6027-inch monitor at 650 mmsubtends 49.3°

Screenfov

  1. 1 A wide field on a small screen
  2. 2 The evenness a curve buys
2 essays · screen horizonshadows meet at x = -58, off the frameon the horizon, as it must be

Shadow

  1. 2 A shadow is a second projection
  2. 3 Counting shadows is not counting lamps
2 essays · light 1 holetilt 0°closes at 71.3°

Shadowtopology

  1. 4 A hole is not preserved
  2. 5 Where a shadow splits in two
2 essays · light horizonshadows meet at x = -58, off the frameon the horizon, as it must be

Shadowvp

  1. 3 Where shadows vanish
  2. 4 The forty-five degree shadow
2 essays · light 88.9° between the two circlescorrect from 23 cm, at 160 mm widelamp 2.6 m · shadow circle at 80.0°

Silhouette

  1. 3 The edge of a shadow is drawn on the object
  2. 4 How many shadows determine the object
2 essays · light the lamp is above the top of the ball — an ellipsecorrect from 22 cm, at 160 mm wideaxis ratio 0.4993 · discriminant -9.68e-1

Sphereshadow

  1. 3 The shadow of a ball is a conic
  2. 4 The ball stands at a focus
2 essays · light projectiveaffinemetricmidpointtwo equal sidesa right anglecross-ratioprojective———1.333333333affine0.500000——1.333333333metric0.5000001.00000090.000°1.333333333— means the stage does not determine it at allcross-ratio 1.333333 throughout

Stratification

  1. 4 What one picture of a plane determines
  2. 5 The ladder of assumptions is a ladder of conditioning
2 essays · foundations flat picture plane — straight lines stay straightcylindrical picture surface — even stretch, bowed linesone scene, two picture surfacesneither is the distorted one

Surface

  1. 3 When the picture surface is not flat
  2. 4 No picture surface keeps everything
2 essays · viewing

All essays