How one is
actually made.

A poster cannot be calculated from the word "Edinburgh". The first job is to turn what you typed into a latitude and a longitude, which is done through a geocoder as you type, before you have finished the word.

We keep two labels from that lookup and use them for different things. The long one disambiguates in the dropdown, because Edinburgh in Scotland and Edinburgh in Indiana are 5,700 kilometres apart and would produce visibly different skies. The short one is the only part that reaches the print, because a piece on a wall wants the name of a place, not an address.

The geocoder was chosen for a reason that has nothing to do with accuracy: it imposes no attribution requirement. Several good ones oblige you to print a credit line on anything derived from them, which would mean a licence notice on the bottom of your poster forever.

Calendars are hostile to arithmetic. Months are different lengths, leap years are irregular, time zones move by political decision, and daylight saving deletes an hour every spring and repeats one every autumn. None of that can appear anywhere near a rotation calculation.

So the moment is converted immediately into a Julian Date: a continuous count of days that has been running without interruption since 4713 BC. Once your evening is a single real number, every later step is ordinary arithmetic instead of calendar handling.

JD = t / 86 400 000 + 2 440 587.5

This is the step people expect to be simple and is not. A day is not one rotation. In the twenty four hours between one noon and the next, the Earth has also travelled roughly one degree along its orbit, so it has to turn slightly more than a full circle to point the same face at the Sun again. Measured against the fixed stars, which is what a star map cares about, the planet turns about 360.9856 degrees per solar day.

That extra 0.9856 degrees is not a rounding detail. Ignore it and the sky drifts by roughly four minutes a day, which is two hours after a month and a completely different set of constellations after six. Getting it right is the difference between a star map and a decorative circle of dots.

The quantity that comes out is Greenwich Mean Sidereal Time: how far the sky above the Greenwich meridian has rotated, in degrees.

T    = (JD - 2 451 545.0) / 36 525
GMST = 280.46061837
     + 360.98564736629 × (JD - 2 451 545.0)
     + 0.000387933 × T²
     - T³ / 38 710 000

Greenwich sidereal time describes the sky over one meridian in London. Your longitude rotates it to the sky over you, giving local sidereal time. Subtracting the star's right ascension from that gives the hour angle: how far past your meridian that particular star has already swung.

Every star in the catalogue gets its own hour angle, because every star has its own right ascension. This is the point where the calculation stops being about the Earth and starts being about 5,044 individual objects.

LST = GMST + longitude
H   = LST - right ascension

Star catalogues do not describe the sky as you see it. They use equatorial coordinates, right ascension and declination, which are fixed to the celestial sphere and take no view on where you are standing. They are the same for an observer in Reykjavík and one in Sydney, which is precisely what makes them useless for a poster.

What a poster needs is horizontal coordinates: altitude, the angle above your horizon, and azimuth, the compass bearing. Converting between the two is the mathematical centre of the whole product, and it is done separately for every star, for your latitude, at your moment.

The azimuth has to be computed with a two argument arctangent rather than a plain one. An ordinary arctangent cannot tell northeast from southwest, because it only receives the ratio of the two components and has lost their signs. Use the wrong one and half the sky is reflected into the other half, which looks plausible enough to ship and is completely wrong.

The clamp on the last line is not decoration either. Floating point arithmetic can return 1.0000000000000002 for a quantity that mathematically cannot exceed 1, and the arcsine of that is not a number. One star at the exact zenith would quietly vanish from the print.

sin(altitude) = sin(dec)·sin(lat)
              + cos(dec)·cos(lat)·cos(H)

azimuth = atan2(
    -sin(H)·cos(dec),
     cos(lat)·sin(dec) - sin(lat)·cos(dec)·cos(H)
)

altitude = asin(clamp(sin(altitude), -1, 1))

The sky is a hemisphere and paper is not, so something has to give. The choice of how to flatten it is a real decision with a visible consequence.

The obvious approach is to space stars linearly by altitude: something halfway up the sky lands halfway to the rim. It is easy, and it is wrong in a way anyone can see, because it stretches everything near the horizon and the constellations come out distorted. Orion arrives looking like it has been pulled sideways.

We use a stereographic projection about the zenith instead. It is conformal, meaning it preserves angles locally, so shapes survive. The point directly overhead lands in the centre of the disc and your horizon becomes the rim exactly, which is why the circle on the finished piece is not a decorative frame. It is the horizon.

r = R · tan((90° - altitude) / 2)

A star has no size on paper, only a brightness, so brightness has to be turned into something a printer can lay down. The astronomical magnitude scale makes this awkward twice over: it runs backwards, so smaller numbers are brighter, and it is logarithmic, so a difference of five magnitudes is a factor of a hundred in light.

Mapping that linearly onto a radius produces a page of near identical dots that reads as static. The curve below is deliberately steep, so the handful of genuinely bright stars separate from the field and the constellations become findable. Opacity is varied alongside radius, which is what stops the faint end from looking like print noise.

m = clamp(magnitude, -1.5, 6.5)
t = (6.5 - m) / 8
r = (0.0008 + t^2.6 × 0.0165) × R

The disc, the rim, your heading, the date, the place and the coordinates to four decimal places are composed into vector artwork, which is then rasterised to 4500 by 6000 pixels for the large print.

The proportions are not an aesthetic choice. Every frame we sell is 3:4, so the artwork is 3:4. An earlier version rendered at 5:7 and would have been cropped to fit, and the crop would have taken a bite out of the lettering on every single order before anyone noticed.

The last detail is the one worth insisting on: the preview on the site and the file sent to the printer come from the same function. The preview is not a mock-up of the artwork, it is the artwork, rendered narrower and stamped. Nothing is substituted between what you approve and what is printed.