No figure on this site is a drawing that was made once and saved. Each one is a function:
it takes parameters and returns SVG, so the same generator produces the p4 plate and the
p6m plate without either being redrawn.
That is the reason the collection can keep growing without the illustrations drifting apart.
A generator is written once, checked once, and every essay that calls it inherits the same
line weights, the same colour roles, and the same behaviour in dark mode. There are
143 of them so far, listed
3 pages at a time.
a-ball-at-the-edgecorrect from 8 cm, at 160 mm wide stretch 1.358 · centres 4.28 px
a-centre-with-an-areaa point at 1.5 m the pupil the sensor where it focuses f/2.8, focused at 3 m 5.8 px across
a-conic-from-anywhere-on-ithorizon 1 2 3 4 the fifth point correct from 23 cm, at 160 mm wide cross-ratio 1.627695 at position 5 of 22
a-conic-from-its-tangentsfitted on five lines, tested on seven points 7.4e-10 px
a-curve-in-flat-piecesthe seat 3 chords against the arc curved monitor, 3 flat pieces 6.80 mm of sag · 5.50 px at the seat
a-fold-names-the-height0 2.50 5 7.50 10 0 20 40 60 80 how far the floor is folded from flat (°) what a 10 cm error in the height leaves (mm) two degrees: 0.58 mm a design 1.4 m wide, the eye 1.62 m up, the crease at 1.2 m flat: 1.5e-13 mm · 90°: 9.3 mm
a-lamp-with-a-sizelamp, 36 cm the card's edge correct from 17 cm, at 160 mm wide a flat floor · band 1.44 m
a-line-and-its-mapsthe point at infinity 0 A B C D A -1.40 B -0.30 C 0.80 D 2.40 the same four, on a straight line the chords cross cross-ratio -0.4211
a-measurement-has-a-shapethe photograph the ground, rectified 5.205 m² four marks fix the plane; the shoelace does the rest 1.8e-14
a-mirror-is-a-pairthe lens correct from 14 cm, at 160 mm wide 12 pairs · 1.4e-12 px
a-point-and-a-linepoints, joined lines, met every incidence survives, worst 5.1e-16 30 of 30
a-ratio-not-a-size0 0.200 0.400 0.600 0.800 20 40 60 how far off the axis the ray leaves the pinhole (°) how far the dome bends it (°) 10 cm dome 20 cm dome both at offset/radius = 0.060 identical to 1e-16°
a-screen-for-an-audience0 10 20 30 40 0 1 2 3 how wide the audience is (m) the worst seat, in pixels of departure 14.1 px per metre a flat panel of the same size curved television, the best single pre-warp the flat panel's line is the axis
a-shadow-that-measurescorrect from 19 cm, at 160 mm wide 0° · 20 marks on the object
a-stair-does-not-use-its-facesthe eye the picture is for 1 faces no ray reaches 9 steps, 18 planes, eye 1.65 m up 17 used · 58.5% of the picture on risers
a-turn-of-the-head-10 -5 0 -2 -1 0 baseline (m, log scale) worst deviation in the recovered shape (log scale) exact points read to 1 px at 2 mm: 4.7e-9 exact, 2.9e+1 read to 1 px 6e+9× apart
a-wire-and-its-cornerthe corner correct from 19 cm, at 160 mm wide 46° across
absorbing-the-second-eyeapart by 4.9e-13 px correct from 17 cm, at 160 mm wide one eye again
anamorphic-wordeye, 74° off grey: the word before the projection black: the same word, projected
auxiliary-viewstrue length 1.3928 m point view the edge is one point true shape 1.3232 m² one face, three ray directions each step is a choice of direction, not a construction on the paper
axes-become-a-cubewhat was drawn the solid it depicts — reading 1 of 2 x y z looked at 45.00° off the normal cube edge 1.0000 of the drawn unit residual 5e-16
ball-says-its-ratioa room point at a known place 115 cm at 2.40 m 403 cm at 8.40 m the ball scaled, the room left where it is outline identical · reflection 8.90° apart
ball-shadow-conicthe lamp is above the top of the ball — an ellipse correct from 22 cm, at 160 mm wide axis ratio 0.5418 · discriminant -1.14e+0
bands-and-foldsband 1 band 2 band 3 every figure the same height, by construction no horizon
barrel-and-pincushionprincipal point k₁ = -0.320, k₂ = 0.110 — barrel distortion centre line 0e+0 px of sag, outermost 17.8 px
by-eye-fails-the-invarianterror against the value the projection must produce four divisions three plus the VP the projection exact exact equal steps exact 14% halving 3.6% 25% tapering 0.9% 21% green: agrees with the projection a necessary condition is not a test
carry-a-heighthorizon 175 cm, known constructed correct from 19 cm, at 160 mm wide 46° across
circle-centre-movescentre of the ellipse image of the centre correct from 22 cm, at 160 mm wide offset 21.1 px
copied-and-distant0.600 0.700 0.800 0 10 20 30 40 generations of copying the drawing's depth-spacing ratio copying the method copying the marks one hand error, two kinds of copyist 9 lineages
cross-ratio-surviveshorizon A B C D on the ground in the picture length AB 1.0001 1.3930 ratio AB:CD 0.5667 0.6837 cross-ratio 1.3168 1.3168 correct from 26 cm, at 160 mm wide 34° across
cube-netleft front right back up down across the left/front seam: 1.80°, with each side straight to 7e-16 corner area ×5.196 anisotropy √3 = 1.7321 there
cube-that-is-a-boxhorizon depicted height ÷ side 0.3278 corner angles 90.000° — forced by the method depicted side ratio 0.7195 lens this drawing implies 60° across drawn exactly as the method prescribes the free step is where the far edges go
depth-codesnear 0.1 m · far 1000 m · 24-bit codes within 20 cm 50.0% within 50 cm 80.0% within 1 m 90.0% within 5 m 98.0% within 50 m 99.8% half the codes are gone by 0.20 m — the harmonic mean of the two planes share of the depth buffer used up within each distance arithmetic midpoint would be 500 m
disparity-and-depth0 10 20 30 40 -25 0 25 50 disparity on the screen — millimetres where the point is depicted — metres from the eyes d = 63 mm — the eyes' separation on the glass screen at 2.0 m · eyes 63 mm apart the ceiling is the head, and it does not move when the screen does
error-laws-4 -3 -2 -1 0 0 0.500 1 1.50 2 how much more effort, log₁₀ of the control how much of the error is left, log₁₀ of the first sample panorama-seam · −0.92 panorama-vertical · floor silhouette-hull · −2.00 silhouette-notch · floor anamorph-sagitta · −2.30 anamorph-sagitta-intervals · −2.00 mirrorball-size · −1.00 7 laws, 12 samples each 2 with a floor · 5 without
error-per-pixel0 5 10 15 50 100 150 200 distance from the camera (metres) error in the recovered height, per pixel of click error (%) 5 m — 0.46% 25 m — 2.27% 100 m — 9.04% 190 m — 17.16% one pixel, on a 690 px picture linear in distance
facing-is-not-reachingfacing the reader, and never reached a corner 0% of the facing area · 0 of 2 faces a cluster of blocks 8% of the facing area · 4 of 12 faces a seating rake 27% of the facing area · 3 of 10 faces a corridor with a doorway 1% of the facing area · 1 of 7 faces an ascending flight 21% of the facing area · 3 of 18 faces eye at 1.70 m, 2.4 m in front of the picture area, not face count
five-drawing-systemselevation x 1.000 y 1.000 z 0.000 cavalier x 1.000 y 1.000 z 1.000 cabinet x 1.000 y 1.000 z 0.500 isometric x 0.816 y 0.816 z 0.816 dimetric x 0.943 y 0.943 z 0.471 axis scales measured from the drawing all 5 preserve midpoints
fixed-structurecentre faint dots: before · solid: after homology ratio 2.4000
flat-against-curvedflat picture plane — straight lines stay straight cylindrical picture surface — even stretch, bowed lines one scene, two picture surfaces neither is the distorted one
floor-is-a-coordinatethe lamp the occluder, and where the ray puts it back the mark, on the floor where the plan puts it — 4 mm out a dished floor, k = 0.06 by ray: exact · in plan: 4 mm
full frame · 39.6° APS-C · 26.6° Micro Four Thirds · 19.6° 1 inch · 15.0° phone (1/1.7″) · 8.7° one 50 mm lens · the angle is a property of the rectangle behind it Micro Four Thirds: 2.00× diagonal, 2.08× wide, 1.85× tall 50 mm across five formats 39.6° down to 8.7°
great-circle-imagefitted conic: a circle to 1e-9 stereographic dashed: the fit, not the samples
horizon-is-eye-levelhorizon = eye level, 1.62 m 91.01% correct from 26 cm, at 160 mm wide spread 0
how-many-lampshorizon correct from 19 cm, at 160 mm wide 2 centres · 2.12 px
interpolation-error-0.400 -0.200 0 0 0.200 0.400 0.600 0.800 1 position across the drawn surface how far along the real surface, minus how far along the drawn one (√k−1)/(√k+1) = 0.5195 at the page's midpoint, 40.9% depth ratio 10 : 1 peak 0.5195 at s = 0.760
ladder-is-conditioning0 20 40 60 20 40 60 how oblique the view of the plane is (°) what one pixel costs, against its cost at 20° a ratio of lengths — affine an angle — metric 1 px on four corners, one homography a cross-ratio moves by 0e+0
lamp-is-a-second-eyecorrect from 26 cm, at 160 mm wide 34° across