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
28 of them so far.
anamorphic-wordeye, 74° off grey: the word before the projection black: the same word, projected
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
centre-offset-curve0 2 4 6 3 4 5 6 distance from the eye to the circle (m) offset between the two centres (% of the ellipse's width) r = 0.50 m r = 0.80 m measured from fitted ellipses 6.5% at 2.5 m
circle-centre-movescentre of the ellipse image of the centre correct from 22 cm, at 160 mm wide offset 21.1 px
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-that-is-a-boxhorizon 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-by-eyehorizon equal steps halve the taper by worst error, in metres of depth equal steps to the horizon 11.72 m halve the remaining gap 225.13 m taper by eye 347.80 m correct from 26 cm, at 160 mm wide 34° across
distance-against-angle0 20 40 60 20 40 60 80 horizontal field of view (degrees) correct viewing distance for a 160 mm wide picture (cm) long lens — 38 cm a normal photograph — 22 cm wide — 13 cm very wide — 8 cm same picture width throughout the only variable is the angle
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 five preserve midpoints
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
horizon-is-eye-levelhorizon = eye level, 1.62 m 91.01% correct from 26 cm, at 160 mm wide spread 0
how-wrong-is-the-cube0.500 1 1.50 2 -10 0 10 difference between the two by-eye placements (points) side ratio of the box the drawing depicts (1 = a cube) a cube even-handed the one free choice in the taught method and it decides the whole solid
lamp-is-a-second-eyecorrect from 26 cm, at 160 mm wide 34° across
measuring-point2 4 VP correct from 26 cm, at 160 mm wide 34° across
midpoint-is-the-differencehalfway along the drawn line the actual midpoint correct from 26 cm, at 160 mm wide 22 px apart
one-two-three-pointhorizon 3 vanishing points at a finite distance 2564 px · 8129 px · 531 px
parallel-has-no-station-pointisometric — the limit 2.5 m 6 m 20 m 200 m same box, same drawn size the eye recedes
plan-and-pictureplan, looking down picture plane one camera, two views of it 34° across
recover-the-camerarecovered principal point used to draw recovered gap focal length 853.90 853.90 4e-15 principal x 345.0 345.0 2e-12 angle 44.0° 44.0° — correct from 20 cm, at 160 mm wide 44° across
reflection-is-a-second-cameragrey: the reflection two routes, agreeing to 0e+0 px after one flip
shadow-length-curve0 2 4 6 20 40 60 80 elevation of the sun (degrees) length of the shadow of a 1 m post (m) 45° — shadow equals height cot of the elevation unbounded as the sun sets
spheres-across-the-frame54 px 69 px 84° across 27% wider at the edge
stretch-and-its-cure0 20 40 60 20 40 60 80 100 horizontal field of view (degrees) how much wider a shape images at the frame edge (%) 3% 15% 41% 1/cos θ at the frame edge a property of the projection, not the glass
sun-shadows-convergehorizon shadows meet at x = -58, off the frame on the horizon, as it must be
three-vanishing-pointsthe picture VP₁ VP₂ VP₃ orthocentre focal length from the triangle — 707.4 px spread 0e+0% across three routes
what-each-system-keepselevation 0.0000 two equal cabinet 0.5000 two equal cavalier 1.0000 all three equal dimetric 0.4714 all three different isometric 0.8165 all three equal trimetric 0.5479 all three different smallest of the three axis scales measured from each projection
where-parallels-meethorizon — the image of the line at infinity vanishing point at x = 1464 — off the frame correct from 26 cm, at 160 mm wide 34° across
where-to-standthe picture, 160 mm wide 22 cm 40° the eye focal length 948 px 22 cm at 160 mm wide