Visual Plane
every picture states the point it is correct from
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The figure library — page 4

Page 4 of 4, continuing through the generators in the same alphabetical order.

three-vanishing-points

the pictureVP₁VP₂VP₃orthocentrefocal length from the triangle — 707.4 pxspread 0e+0% across three routes

three-views-two-solids

front view · 32 filledtop view · 36 filledside view · 36 filledthe largest solid with these views — 192 cellsand a solid with the same views — 64 cells6 × 6 × 6 cellsthe three views are identical; the solids differ by 128 cells

through-the-window

no single viewpoint — the rays miss by 4.5 px, depth-dependentf recovered from it: 396.88 px

translating-against-rotating

a rotating eye — the panorama2e-15 ma projectiona translating eye — the scroll7.97 mnot oneboth of these draw a straight world line as a curverms miss of the least-squares centreone of them is a projection

two-grounds

a camera looking downthe carpet is true, the people are nota camera looking levelthe people are true, the carpet is notthe two views a miniature is assembled from90° apart, exactly

two-lamps

correct from 19 cm, at 160 mm widetwo lamps · one homothety, ratio 1.2509

two-rays-that-miss

midpoint — 2.77 mm gapfrom the left eyefrom the right eyegap 2.77 mm at 7.22 mexact marks: 2.2e-16 m

un-cast-the-shadow

the outline, its shadow, and the outline recovered from itcorrect from 20 cm, at 160 mm widerecovered to 4e-16 m

upgrade-chain

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

vanishing-point-off-the-canvas

0510-6-4-20how far the camera looks down, over eight metres (metres, log scale)where the vertical vanishing point falls (log₁₀ pixels)the vanishing pointthe error in the recovered heightthe error curve is offset by 17 decades to be visiblea flat line at machine precision

vault-anamorph

barrel vaulteye · 1.62 mon the floor1e-12 mmon the vault529.4 mmworst miss of the best homography, log scalevault radius 4.0 m7.7% of the extent, against 4e-14%

walking-the-gauge

shift x2.6e-11 pxshift y2.6e-11 pxshift z3.8e-11 pxturn x5.2e-12 pxturn y2.7e-11 pxturn z3.2e-11 pxscale ×2.72.7e-11 pxturn camera 0 by 0.01 rad1.015 pxmove camera 0 by 50 mm2.309 pxmove point 0 by 50 mm0.627 pxchange in reprojection error, log scalebelow: not gauge directionsflat to 3.8e-11 px · stiff from 0.63 px2e+10× apart

what-another-view-buys

-2.80-2.6034567number of viewsworst camera-centre error (fraction of the track's mean radius, log scale)7 flat7 flat7 flat7 flat7 flat60° sweep, filled in12° per view, wideningfilled in: 1.1e-3 → 2.0e-3widened: 3.2e-3 → 1.8e-3

what-each-aspect-keeps

head0.668profile — the outline that names a faceeye0.669frontal — an eye in profile is a wedgeshoulders0.669frontal — the width that says two armslegs0.668profile — a stride is a side viewpond0.326plan — a rectangle of water is a rectangle1.000 — what its own aspect keepsshare of each part that reaches the picture, from the best single direction|d · n| for each part3.000 of 5, swept and in closed form

what-each-room-shows

parallel, 52° above the ground56% · 56% · 56%one eye, 14.5 m away49% · 56% · 49%a square metre of floor varies 1.000× against 1.535×spread across rooms: 0 against 6.2 points

what-each-system-keeps

elevation0.0000two equal, orthographiccabinet0.5000two equal, obliquecavalier1.0000all three equal, obliquedimetric0.4714all three different, orthographicisometric0.8165all three equal, orthographic ←trimetric0.5479all three different, orthographicsmallest of the three axis scalesmeasured from each projection

what-each-system-preserves

a centretrue measurediminutionbounded depthstraight linesperspectivehandscrollisometricdimetrictrimetriccavaliercabinetelevationmilitaryfilled means the system keeps itmeasured from each system's own projectionno row is filled in both of the first two

what-perspective-gave-up

the ratio along a receding line15.6%0% parallelthe depth range in the last tenth69.0%10% lineara square metre, near against far53.5% larger0% parallelthe floor of the far room6.2 points0 parallelwhat it costs, and what the other systems have insteadmeasured on this site's own machinerythe price of a station point

where-parallels-meet

horizon — the image of the line at infinityvanishing point at x = 1464 — off the framecorrect from 26 cm, at 160 mm wide34° across

where-the-reader-sits

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°

where-the-splay-sends-the-point

they meet at y = 924, off the pagefar edge ÷ near edge = 1.32a one-point construction, swept through its splaythe point is below the near edge

where-to-stand

the picture, 160 mm wide22 cm40°the eyefocal length 948 px22 cm at 160 mm wide

window-runs-away-at-the-rim

00.2500.5000.7501020406080zenith angle of the direction above the water (degrees)area scale, and anisotropy — both 1 for a surface that does nothing1/n² = 0.563anisotropyarea scalen = 1.333at 89° the sky is compressed 135× in area

wrong-eye

ground line — right from anywherefaint: intended · solid: seendeparture (mm) against height (m)01.38the error map is an elation, with the ground line as its axisno characteristic ratio — nothing off the axis is fixed250 mm sidewayszero on the axis, 212.5 mm at the top

zoom-against-step

3 m, 50 mm1.50 m, 25 mmsubject ×1.000000 · background ×0.526 · zoom alone would give ×1 for bothnear-to-far ratio 10.00 → 19.00changing the focal length leaves it at 1.000000000000