Skip to content
1 2 3 4 correct from 15 cm, at 160 mm wide four moments · 8.5e-14 px
Narrative
1
The same person, twice on one panel
1 essay · conventions
to the vertex, 450 px further correct from 22 cm, at 160 mm wide 5 courses · 1e-13 px
Offboard
1
Dividing to a point off the board
1 essay · construction
d = 0 d = 0.5 d = 1 d = 2 d = 4 d = 0 straight 48.06° angle ×17.80 area d = 0.5 4.81% bend 23.08° angle ×4.66 area d = 1 7.21% bend 16.84° angle ×2.65 area d = 2 9.61% bend 23.13° angle ×1.57 area d = 4 11.54% bend 32.71° angle ×1.73 area a general straight line · worst angle · area range, over the field 130° across angular minimum at d = 1.00
Panini
3
One parameter between two surfaces
1 essay · curved
elevation 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
Parallel
2
Parallel projection is not primitive perspective
1 essay · parallel
2 4 6 8 -1 -0.500 0 0.500 1 position along the family the two pictures leave free how far the solid is from the scene's own shape (stretch ratio) the scene every member redraws both pictures to 7e-16 m the ambiguity is a family of solids, not a tolerance
Parallelrecovery
5
What two parallel views leave free
1 essay · parallel
paper construction and projected shadow agree to 1e-16 isometric one angle: 41.76°
Parallelshadow
3
The shadow rules that hold here
1 essay · parallel
S₁ S₂ a b c lean 24° · centre at 0.45 along the join probe closes to 1.2e-13 px
Perspectivity
1
Every projectivity is two perspectivities
1 essay · foundations
pixels 2.00 : 1 recovered focal length 219.9 px the camera's actual one 436.4 px what the recovery returns spread across three estimates 0.0e+0 worst bundle residual 9.1e-13 px both are what a wrong picture would trip pixel aspect 2.00 unmodelled focal length 49.6% short, every diagnostic clean
Pixelaspect
1
The pixel that is not square
1 essay · sensor
correct from 20 cm, at 160 mm wide verticals converge 3.59° · horizon 213 px off centre
Planechoice
3
The plane is a choice
1 essay · construction
what 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
Pohlke
5
Any three lines you draw are a cube
1 essay · parallel
0 0.500 1 10 20 30 40 50 distance from the camera to the wall (m) relative to the value at 1 m the patch, growing as d² the light per unit area, falling as 1/d² their product — what the picture records 2500× the footprint at the far end product flat to 2e-16
Radiance
2
A wall does not get darker as it goes away
1 essay · light
band 1 band 2 band 3 every figure the same height, by construction no horizon
Register
1
A picture in bands
1 essay · conventions
plane — ×24.99 edge to centre cylinder — ×2.40 edge to centre stereographic — ×2.22 edge to centre equidistant — ×1.30 edge to centre equal-area — ×1.00 edge to centre equirect. — ×1.34 edge to centre 36 cells of 377 square degrees, out to 70° equal-area ×1.00 · plane ×25.0
Resolution
1
Where a surface spends its pixels
1 essay · curved
0 5 10 15 20 0 20 40 60 how far off the fovea the line passes (degrees) departure from a straight chord, in degrees of visual angle schematic eye concentric retina a line spanning ±65° of azimuth 17.30° at 40° eccentricity
Retina
1
The eye is a picture surface too
1 essay · curved
what was drawn the solid it depicts — reading 1 of 2 x y z looked at 0.00° off the normal cube edge 1.0000 of the drawn unit residual 1e-16
Reversal
3
The drawing does not say which corner is nearer
1 essay · parallel
the true profile exact marks rms 4.9e-15 m
Scan
1
A shadow edge read as a profile
1 essay · light
horizon the point its shadow correct from 22 cm, at 160 mm wide rays cross at 28.5° · recovered to 9e-16 m
Shadowdepth
4
The lamp is the second eye
1 essay · light
5 7 10 14 20 28 40 0.3 1 3 10 distance along the floor from below the eye (m, log scale) pixels one shadow-map texel spans on screen (log scale) 1 px lamp beside the eye lamp 30 m overhead lamp 40 m ahead, facing back measured against the closed form: 4e-9 1024-texel map · eye 1.7 m · 50° field
Shadowmap
1
A shadow map's texels land by two distances and two cosines
1 essay · pipeline
35.08° correct from 16 cm, at 160 mm wide two maps, meeting at 35.08°
Shadowseam
3
A shadow across an edge
1 essay · light
a dished floor · truly 0.060 0.0600 a flat floor · truly 0 0 a floor with a 60 mm step · truly 0 0.4820 one lamp, one ring occluder the step reports 0.482
Shapefit
5
The curvature a shadow reports
1 essay · metrology
All essays