Sundial API

Sundial gnomonics maths as an API, computed locally and deterministically — the hour-line, gnomon and longitude-correction numbers a dial maker, horologist or astronomy hobbyist lays a sundial out with. The hour-line-angle endpoint gives the angle of each hour line on the dial plate, measured from the noon line: for a horizontal dial tan(angle) = sin(latitude) × tan(hour angle), and for a vertical south-facing dial cos(latitude) is used instead, where the hour angle is 15° per hour from solar noon. At 50° latitude the 1-o'clock line sits about 11.6° from noon rather than 15° — the lines bunch near noon and spread toward the ends, which is exactly why a sundial's hours are unevenly spaced. The gnomon endpoint gives the style angle: the gnomon's shadow-casting edge must point at the celestial pole, so it rises at the latitude angle on a horizontal dial (50° at 50° N) and at 90° − latitude on a vertical dial — get this wrong and the dial keeps correct time at only one season. The longitude-correction endpoint converts the dial's local apparent time to clock time: 4 minutes of time per degree of longitude, correction = 4 × (reference meridian − local longitude), so a dial at 7.5° E on Central European Time reads 30 minutes slow versus the clock. Everything is computed locally and deterministically, so it is instant and private. Ideal for sundial-design and gnomonics tools, astronomy-education and maker apps, and horology calculators. Pure local computation — no key, no third-party service, instant. Add the equation of time for full clock accuracy. 3 compute endpoints. For the sun's position use a solar-position API; for sunrise and sunset a sunrise API.