Drafting Sheets · a film
Lighting the sheet…
Astrolabe Set, Sky Turning
An astrolabe drawn from its own TikZ, then turned to sunset
A planispheric astrolabe that draws itself and then turns the sky. An orange spark reads a TikZ listing and drafts the instrument for Oxford, at the latitude Chaucer gave it: the rim, the degrees in four quadrants and the twenty-four hours under the throne; then the plate, every line a circle of the sky projected from the south pole — the tropics and the equator, the horizon and the twilight line, a circle of equal altitude every two degrees, an azimuth every ten, the twelve unequal hours of the night. Last the rete is laid out in construction lines, the ecliptic and forty-three bright stars where they stand in 2026. Then the working goes, the rete is cut from it, and the sky turns: time runs on from the night of 4 October, the rete wheeling round once a sidereal day while the Sun creeps along the ecliptic and the rule sweeps the hours after it, until it settles at sunset over Oxford on 10 October, the Sun on the horizon line, and light runs out through the rete. Every frame is rendered live in your browser.
- Tempo
- 90 BPM · 30.75 bars
- Picture
- The drafting engine, WebGL
- Program
- One TikZ listing, 60 lines
- Sky
- 43 stars at 2026.0 · Oxford, 51°50′
- Sound
- YuE2 music, effects synthesised from the plan
Chapters5
The listing36 statements
The film is this TikZ, the same listing as Astrolabe's Oxford plate, drawn by the same engine as the other Drafting Sheets; the figures and names are engraved beside it from the same numbers, and the rete is cut and turned over it. Copied with one \tikzsetline for the sheet’s own keys, it compiles in any LaTeX document that loads TikZ.
% title: astrolabe, plate for Oxford% stereographic projection from the south pole; noon (south) at the top, east on the left\begin{tikzpicture} % the mater: its rim and the limb\draw[thick] (0,0) circle (5.22);\draw (0,0) circle (5.12);\draw (0,0) circle (4.62);\draw (0,0) circle (4.32); % the degree scale: every degree, every fifth longer, every tenth across\foreach \a in {0,1,...,359} \draw[very thin] (\a:4) -- (\a:4.1);\foreach \a in {0,5,...,355} \draw (\a:4) -- (\a:4.2);\foreach \a in {0,10,...,350} \draw (\a:4) -- (\a:4.32); % the hour ring: twenty-four hours, noon at the top, quarters between\foreach \a in {7.5,22.5,...,352.5} \draw (\a:4.62) -- (\a:5.12);\foreach \a in {0,3.75,...,356.25} \draw[very thin] (\a:4.62) -- (\a:4.74); % the throne and its shackle, over the noon line\draw (-1.05,5.08) .. controls (-0.95,5.75) and (-0.35,5.82) .. (0,6.12) .. controls (0.35,5.82) and (0.95,5.75) .. (1.05,5.08);\draw (-0.62,5.28) .. controls (-0.5,5.62) and (-0.2,5.64) .. (0,5.82) .. controls (0.2,5.64) and (0.5,5.62) .. (0.62,5.28);\draw (0,5.72) circle (0.14);\draw (0,6.26) circle (0.14);\draw[thick] (0,6.62) circle (0.22); % the plate for Oxford, latitude 51°50′: tropics, equator, meridian\draw[thick] (0,0) circle (4);\draw (0,0) circle (2.626);\draw (0,0) circle (1.724);\draw (0,-4) -- (0,4) (-4,0) -- (4,0); % the horizon and the twilight line (18° below it)\draw[semithick] (-3.34,2.064) arc (-180:2.442:3.34) (-3.337,2.206) arc (177.558:180:3.34);\draw[dashed] (-4,0.026) arc (-139.85:-40.15:5.233); % almucantars: circles of equal altitude, every 2°\draw[very thin] (-3.196,1.976) arc (-180:8.57:3.196) (-3.16,2.452) arc (171.43:180:3.196) (-3.06,1.896) arc (-180:15.206:3.06) (-2.953,2.698) arc (164.794:180:3.06) (-2.932,1.822) arc (-180:22.501:2.932) (-2.708,2.944) arc (157.499:180:2.932) (-2.81,1.753) arc (-180:30.701:2.81) (-2.416,3.188) arc (149.299:180:2.81) (-2.694,1.69) arc (-180:40.254:2.694) (-2.056,3.431) arc (139.746:180:2.694); % 2–10°\draw[very thin] (-2.584,1.632) arc (-180:52.177:2.584) (-1.584,3.673) arc (127.823:180:2.584) (-2.478,1.578) arc (-180:70.418:2.478) (-0.831,3.913) arc (109.582:180:2.478) (-2.377,1.528) arc (-180:180:2.377) (-2.28,1.481) arc (-180:180:2.28) (-2.187,1.438) arc (-180:180:2.187); % 12–20°\draw[very thin] (-2.097,1.398) arc (-180:180:2.097) (-2.011,1.36) arc (-180:180:2.011) (-1.927,1.325) arc (-180:180:1.927) (-1.846,1.292) arc (-180:180:1.846) (-1.768,1.262) arc (-180:180:1.768); % 22–30°\draw[very thin] (-1.692,1.233) arc (-180:180:1.692) (-1.618,1.206) arc (-180:180:1.618) (-1.546,1.181) arc (-180:180:1.546) (-1.476,1.157) arc (-180:180:1.476) (-1.408,1.135) arc (-180:180:1.408); % 32–40°\draw[very thin] (-1.341,1.115) arc (-180:180:1.341) (-1.275,1.096) arc (-180:180:1.275) (-1.211,1.078) arc (-180:180:1.211) (-1.149,1.061) arc (-180:180:1.149) (-1.087,1.045) arc (-180:180:1.087); % 42–50°\draw[very thin] (-1.027,1.031) arc (-180:180:1.027) (-0.967,1.017) arc (-180:180:0.967) (-0.909,1.005) arc (-180:180:0.909) (-0.851,0.993) arc (-180:180:0.851) (-0.795,0.982) arc (-180:180:0.795); % 52–60°\draw[very thin] (-0.739,0.972) arc (-180:180:0.739) (-0.683,0.963) arc (-180:180:0.683) (-0.628,0.955) arc (-180:180:0.628) (-0.574,0.947) arc (-180:180:0.574) (-0.52,0.94) arc (-180:180:0.52); % 62–70°\draw[very thin] (-0.467,0.934) arc (-180:180:0.467) (-0.414,0.929) arc (-180:180:0.414) (-0.362,0.924) arc (-180:180:0.362) (-0.309,0.92) arc (-180:180:0.309) (-0.257,0.916) arc (-180:180:0.257); % 72–80°\draw[very thin] (-0.206,0.913) arc (-180:180:0.206) (-0.154,0.911) arc (-180:180:0.154) (-0.103,0.91) arc (-180:180:0.103) (-0.051,0.909) arc (-180:180:0.051); % 82–88° % azimuths: great circles through the zenith, every 10°\draw[very thin] (0.734,3.932) arc (162.709:170:24.469) (0,0.908) arc (10:17.291:24.469) (1.456,3.726) arc (145.335:160:12.423) (0,0.908) arc (20:34.665:12.423) (2.15,3.373) arc (127.811:150:8.498) (0,0.908) arc (30:52.189:8.498) (2.79,2.866) arc (110.119:140:6.61) (0,0.908) arc (40:69.881:6.61) (3.337,2.201) arc (92.361:130:5.547) (0,0.908) arc (50:87.639:5.547) (3.291,1.494) arc (80.172:120:4.906) (0,0.908) arc (60:99.828:4.906) (3.129,0.895) arc (69.52:110:4.522) (0,0.908) arc (70:110.48:4.522) (2.897,0.402) arc (60.151:100:4.315) (0,0.908) arc (80:119.849:4.315) (2.626,0) arc (51.833:90:4.249) (0,0.908) arc (90:128.167:4.249) (2.335,-0.324) arc (44.366:80:4.315) (0,0.908) arc (100:135.634:4.315) (2.037,-0.583) arc (37.582:70:4.522) (0,0.908) arc (110:142.418:4.522) (1.737,-0.789) arc (31.343:60:4.906) (0,0.908) arc (120:148.657:4.906) (1.44,-0.95) arc (25.535:50:5.547) (0,0.908) arc (130:154.465:5.547) (1.146,-1.073) arc (20.06:40:6.61) (0,0.908) arc (140:159.94:6.61) (0.855,-1.165) arc (14.837:30:8.498) (0,0.908) arc (150:165.163:8.498) (0.568,-1.227) arc (9.795:20:12.423) (0,0.908) arc (160:170.205:12.423) (0.283,-1.264) arc (4.869:10:24.469) (0,0.908) arc (170:175.131:24.469); % unequal hours: twelve night hours below the horizon\draw[very thin] (1.263,-1.173) arc (280.186:335.972:3.58) (1.054,-1.364) arc (263.586:308.214:3.985) (0.816,-1.518) arc (245.355:278.826:4.745) (0.557,-1.631) arc (225.219:247.533:6.442) (0.282,-1.7) arc (203.219:214.376:11.999) (0,-4) -- (0,-1.724) (-1.406,-3.745) arc (325.624:336.781:11.999) (-2.633,-3.012) arc (292.467:314.781:6.442) (-3.523,-1.894) arc (261.174:294.645:4.745) (-3.964,-0.535) arc (231.786:276.414:3.985) (-3.899,0.893) arc (204.028:259.814:3.58); % the rete, laid out for 2026.0 at sidereal time 0: the ecliptic and the stars\draw[help lines] (1.138,0) circle (2.862);\draw[help lines] (1.138,0) circle (2.622);\foreach \x/\y in {-0.065/1.538,-0.411/1.28,-0.143/0.773,-0.881/0.808,-0.749/0.595,-0.915/1.455,-1.833/0.691,-2.974/0.581,-1.043/0.19,-2.324/0.342,-2.306/0.034,-3.461/-0.709,-1.334/-0.596,-1.41/-0.71,-2.172/-1.02,-1.876/-2.42,-0.987/-1.89,-0.157/-0.645,-0.085/-2.034,0.269/-3.583,1.181/-2.976,0.446/-0.869,1.052/-1.547,1.31/-0.954,1.957/-1.301,2.519/-1.232,3.554/-1.454,2.094/-0.219,0.917/-0.011,1.241/0.207,1.982/1.054,1.679/1.341,0.818/0.701,0.412/0.487,1.892/2.927,1.22/1.835,0.955/3.33,0.467/1.947,0.373/1.526,-0.701/3.535,-1.483/2.768,-1.753/1.698,-2.603/2.786} \draw[help lines] (\x,\y) circle (.05); \end{tikzpicture}