Skip to content
level — the top is cut off 0.00° of spread tilted 13° 4.55° of spread shifted 95 px 0.00° of spread a shift moves every point by exactly the shift 95.0 px, and no direction at all
Shift
2
The principal point is not the centre
1 essay · lens
one direction — the pole — drawn as the whole of this edge 8° cap at the pole: ×9.2 the same cap, 20° off axis: ×0.646 both caps hold 201 square degrees of sky ×14 between them
Singularity
1
A pole is a line
1 essay · curved
15° 30° 45° 60° 85° the rim: 48.61° from straight up beyond it: the bottom, reflected 45° of sky 0.4694 60° of sky 0.3702 75° of sky 0.2114 85° of sky 0.0738 area scale n = 1.333, so the rim is at asin(1/n) = 48.61° area scale 0.563 at the centre, 0.0738 at 85°
Snellwindow
2
The sky inside a cone
1 essay · refraction
-50 0 50 0.500 1 distance to the thing being stitched (log₁₀ metres) what the stitch leaves behind (px) 2.86 m 80 mm baseline zero at one depth each
Stitchdepth
3
A rig is right on one surface
1 essay · curved
plane every line — cylinder one parameter · parallel no meeting point stereographic one parameter · concurrent they meet to 1e-12 equirect. one parameter · parallel no meeting point 3 of 4 keep a curve the signature has three values, not eight
Straightfamily
5
The lines a surface leaves alone
1 essay · curved
horizon isometric — the same drawing, moved perspective — a different drawing correct from 23 cm, at 160 mm wide parallel: 4e-14 px · perspective: 87.2%
Translation
2
Nothing moves when the object does
1 essay · parallel
the picture plane, in plan to the observer, 208 px further down correct from 12 cm, at 160 mm wide station 520 px
Tworules
1
Two rules for one pavement
1 essay · construction
horizon — 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
Vanishing
1
Where parallel lines meet
1 essay · foundations
barrel vault eye · 1.62 m on the floor 1e-12 mm on the vault 529.4 mm worst miss of the best homography, log scale vault radius 4.0 m 7.7% of the extent, against 4e-14%
Vaultanamorph
4
The ceiling that is not a plane
1 essay · viewing
one pixel is an area centres corners principal point moves 0.707 px focal length changes by 4.5e-13 px an edge-versus-centre viewport 1.303 px a half-pixel convention is a principal-point error; an off-by-one viewport is a focal-length error 8 vertices, all shifted by the same 0.7071 px spread across marks 0.0e+0 px
Viewport
1
A pixel is not a point
1 essay · pipeline
hull 3.1098 · object 2.9193 · floor 3.0749 8 outlines the notch survives all of them
Visualhull
4
The dish no outline reaches
1 essay · metrology
the eye the design is for the camera correct from 14 cm, at 160 mm wide recovered to 2.5e-14 m
Wallrecovery
5
The wall under the paint
1 essay · metrology
54 px 69 px 84° across 27% wider at the edge
Widefield
3
Wide angle is not distortion
1 essay · viewing
All essays